Accessing acute care hospitals in the San Francisco Bay Area after a major hayward earthquake

Domain: earth_science
Published: 2025-10-22
Editorial outcome: major_revision

Abstract
Earthquakes can severely disrupt healthcare access, especially in dense cities. Here, we provide a comprehensive assessment of how a magnitude 7.25 earthquake on the Hayward Fault would impact access to acute care hospitals in the San Francisco Bay Area. By integrating seismic hazard with hospital and transportation infrastructure’s vulnerability and connectivity data, we analyze 76 hospitals (426 buildings with 16,639 beds) and 5163 bridges within a vast network of ~1.5 million edges and ~0.5 million nodes. We leverage the rich data to formulate a coupled risk-network model to quantify simultaneous failures and cascading disruptions across the healthcare and transportation systems. Our results revealed that hospital bed capacity could drop to 51%, with Alameda County retaining only 20%. Widespread transportation failures further restrict access, increasing regional travel times by 177% and exceeding 1000% in parts of East Bay, potentially fully isolating a hospital and an entire urban community. These findings underscore the urgent need for resilient healthcare and transportation infrastructure to mitigate life-threatening disruptions following major earthquakes.

Introduction
Earthquakes wield the power to severely disrupt healthcare systems, placing vulnerable populations at significant risk1. In the 2023 M7.8 Türkiye earthquake, more than 50 hospitals were damaged, leaving tens of thousands without access to medical care2. In other major earthquakes—such as 2005 Pakistan, 2010 Haiti, 2008 China, 2011 Japan, and 2023 Türkiye—thousands of injured individuals experienced worsening conditions, sometimes leading to fatal outcomes, due to delays in receiving medical attention3–10. Healthcare disruptions can persist long after the disaster: following the 2003 Bam earthquake in Iran, access to critical services like dialysis remained limited for up to five years11,12.

Transportation failures further compound these healthcare disruptions. The 2008 Wenchuan earthquake in China and the 2010 Haiti earthquake demonstrated how disrupted transportation networks delayed or prevented access to emergency medical care13–15. In the U.S., the 1989 M 6.9 Loma Prieta earthquake damaged 91 state highway bridges and forced 13 closures, severely disrupting hospital access across the Bay Area.

Even moderate earthquakes in the U.S. have led to critical healthcare system failures, prompting major policy reforms. The 1971 M6.6 San Fernando Earthquake caused the structural collapse of two major hospitals in the San Fernando Valley—most notably the Veterans Administration Hospital, where more than 40 people died, and Olive View Medical Center—alongside damage to other medical buildings16. This prompted the Alfred E. Alquist Hospital Seismic Safety Act of 1973, mandating that hospitals remain functional after disasters—but applying only to new construction. In 1994, the M 6.7 Northridge Earthquake forced evacuations at eight acute care hospitals, and rendered twelve pre-Alquist hospital buildings unsafe17–19. Though newer hospitals experienced less structural damage, non-structural failures were still extensive. These events led to Senate Bill 1953, requiring seismic retrofits of acute care hospitals by 203020,21. Yet, many hospitals face financial barriers to meeting these mandates22.

Past research has examined hospital seismic risk primarily at the building scale. Studies have used structural engineering methods, fault-tree analyses, and performance-based assessments to evaluate damage in isolated facilities23–26. Others have used flow models and discrete-event simulations to explore patient care delays and medical bottlenecks in single-hospital scenarios27–30. While valuable, these studies often overlook how failures can propagate across urban systems.

In parallel, a growing body of work has started to model access to hospital services at the regional scale. Studies in Lima, Peru31,32, and Butte County, California33, have shown that even small reductions in overall healthcare capacity can significantly affect local access to care.

More recent efforts have begun to jointly consider disruptions to both healthcare and transportation systems, e.g., in Istanbul, Türkiye34, and in a synthetic medium-sized city in China35. We contribute to this growing literature by modeling these compounding effects at scale across the San Francisco Bay Area using detailed, real-world datasets on hospital and bridge infrastructure.

Recent earthquakes in Chile, New Zealand, and Japan have also underscored the importance of treating hospitals as part of broader interdependent systems24,36–39. Failures at one facility can cascade across a regional network—overwhelming nearby hospitals, increasing patient travel distances, and worsening health outcomes. To support resilience planning across large metropolitan areas, there is a need for region-wide models grounded in real exposure data that capture operational interdependencies between healthcare and transportation infrastructure40–42. Developing such models remains challenging due to limited data, computational demands, and regional variation in infrastructure.

In this work, we evaluate post-earthquake healthcare access across the entire San Francisco Bay Area by simulating joint disruptions in healthcare and transportation systems. We integrate seismic risk models with regional-scale network analysis using publicly available data on 426 hospital buildings and 5163 bridges across a transportation network comprising approximately 1.5 million edges and 0.5 million nodes. Our study contributes to the growing field of integrated disaster risk modeling by providing one of the most extensive simulations to date of interdependent failures affecting healthcare access after an earthquake. Although grounded in the San Francisco Bay Area, our study highlights systemic barriers to accessing healthcare after earthquakes under conditions common to many dense urban regions—such as high seismic risk, aging infrastructure, complex emergency response systems, and population disparities. These findings underscore the need for integrated planning approaches that account for infrastructure interdependencies and can inform resilience policy in similarly exposed metropolitan areas.

Results
The Bay Area is home to more than 7 M people in Northern California, and as a major city, it has a large demand for healthcare. The region’s 76 acute care hospitals provide critical inpatient care and specialized medical services for surgery, acute conditions, and injuries, making them essential for disaster response.

Much of the Bay Area’s healthcare infrastructure faces significant seismic risks due to proximity to major active faults. Most hospitals lie near the San Andreas and the Hayward Fault, where major earthquakes (>7.0) can occur (Fig. 1). The Laguna Honda Hospital and Rehabilitation Center and the University of California, San Francisco (UCSF) Medical Center are the largest facilities, with 780 and 580 beds. Both are located in San Francisco, less than 2 km from each other, highlighting the concentration of critical medical resources in geographically small areas. The three zip codes with the most beds are Palo Alto, San Francisco (where the two largest hospitals are), and San Jose, with 1410, 1360, and 932 beds, respectively.

Acute Care Vulnerability in the San Francisco Bay
We found that a significant part of the acute care portfolio is seismically vulnerable due to structural or non-structural deficiencies (Fig. 1). To quantify these vulnerabilities, we compiled information from 426 buildings belonging to the 76 acute care hospitals in the Bay Area, including structural typologies, year of construction, number of stories, and seismic vulnerability ratings21,43,44. Supplementary Note 1 and Supplementary Fig. 1 describe and summarize the hospitals’ years of construction, structural typologies, and the number of stories. The Methods section establishes how to use this information to model seismic vulnerability, as these building features indicate buildings’ dynamic properties, strength, and ductility. In this paper, we used the Structural Performance Categories (SPC) and Non-structural Performance Categories (NPC), established and reported by California’s Department of Health Care Access and Information (HCAI), to characterize structural and non-structural deficiencies45. Each hospital building receives vulnerability ratings (SPC or NPC) ranging from 1 to 5, from the most to the least vulnerable (see full descriptions in HCAI documentation45).

Structural vulnerabilities are pronounced across the portfolio (Fig. 1). Sixteen (4%) hospital buildings have an SPC of 1. All these buildings, constructed before 1974, face a higher collapse risk due to earthquakes than regular modern buildings (e.g., those designed for life safety in 475-year return period events)46. None of these buildings were supposed to provide acute care services by 2020. An additional 87 (20%) hospital buildings have an SPC of 2; of these, 65 were built before 1974 and 20 between 1974 and 1994. SPC-2 buildings meet pre-1973 standards for regular buildings but not those for hospitals, requiring upgrading by 203047. Only buildings rated SPC-3 or above may operate as acute care facilities after this deadline. Only buildings rated SPC-3 or above may operate as acute care facilities after this deadline. Buildings with an SPC-5 rating—163 buildings (38%), predominantly constructed after 1994—meet essential-facility standards under modern codes46; thus, they can remain operational immediately after 475-year return period events.

Non-structural vulnerabilities are even more widespread. Over half of the buildings (220, 52%) have an NPC rating of 2 or lower, with most constructed before 1994 (Fig. 1). NPC-2 buildings have anchorage and bracing only for limited components, typically for basic building access, and were mandated to be upgraded by 2002 to support acute care services. Buildings rated NPC-4 (131 buildings, predominantly built after 1994) have comprehensive anchorage and bracing for all non-structural components, meeting the standard required for acute care facilities after 2030. Only two buildings currently meet the stringent NPC-5 criteria, requiring additional onsite provisions for continuous 72-hour acute care operations. Even facilities meeting modern structural codes may not attain an NPC-5 rating due to the presence of vulnerable external resources, such as water tanks, necessary for sustained hospital operations during emergencies.

Earthquake Scenario and Projected Building Damage
We studied an earthquake scenario of M 7.25 on the Hayward Fault in East Bay (Fig. 2), a fault that has accumulated energy for over more than a century. Its last major earthquake (M 6.8, 1868) caused extensive damage across the region. Our selected scenario magnitude is based on an established reference case widely used in resilience policy-making for the Bay Area48.

We modeled the rupture geometry (see Methods) and found that 10 acute care hospitals with 2167 beds (13% of the Bay’s total) are within just 5 km of the projected rupture. Our shaking intensity estimates indicate that many hospitals could experience levels of ground motion not observed in recent earthquakes (See Methods). On average, our analysis predicts 51 hospitals will experience peak ground accelerations above 0.2 g (Fig. 2). By comparison, the 1989 M 6.9 Loma Prieta Earthquake—previously the strongest since the devastating 1906 M 7.9 San Francisco Earthquake—subjected only 14 hospitals to similar shaking intensities (Fig. 2). Supplementary Fig. 2 further contextualizes these findings, illustrating how recent events such as the 2014 Napa Earthquake (M 6.0) exposed just three hospitals to significant shaking (>0.2 g). In contrast, the historic 1906 earthquake exposed nearly the entire portfolio (72 out of 76 hospitals).

We then estimated structural and non-structural damage across all 426 acute care hospital buildings, as both types of damage critically disrupt continuous hospital operations. We employed damage thresholds as tipping points to model potential service interruptions at various levels of severity (see Methods). For simplicity, we refer to the probability of exceeding these thresholds as the “probability of damage” or “probability of failure.” Our findings reveal extensive potential damage: 214 buildings (50%) have greater than a 25% probability of structural damage, and 254 buildings (60%) exceed this threshold for non-structural components. Notably, 71% and 94% of these at-risk buildings lie within 20 km of the Hayward Fault or have low SPC/NPC ratings (Supplementary Fig. 3, Supplementary Note 3).

Post-earthquake hospital capacity
Our risk analysis predicts a substantial loss of hospital capacity throughout the Bay Area following the earthquake scenario (see Methods). We estimate a loss of 8165 hospital beds, resulting in only 51% of total acute care beds remaining functional (standard deviation: 21%). This significant reduction in capacity is highly uneven across the region (Fig. 3, Table 1). Our baseline predictions assume hospitals lose functionality when structural or non-structural damage exceeds a threshold of slight damage (see Methods). These damage conditions are often shown to disrupt hospital services24,36–39. See descriptions of multiple damage levels in HAZUS Earthquake Model Technical Manual49. We also analyzed more optimistic scenarios with moderate (“favorable”) and extensive (“idealistic”) damage thresholds, resulting in increased overall functionality of 79% and 93%, respectively (Fig. 3 and Supplementary Table 1). However, empirical evidence supports our baseline assumption, as hospitals often lose operations at early stages of damage24,36–39.

Alameda County faces the most severe impacts due to its proximity to the Hayward Fault and the concentration of vulnerable hospitals (Table 1). Bed functionality there would drop dramatically, from 3221 to only 651 functional beds (20%, standard deviation: 19%). As Alameda houses 1.6 million residents—making it the Bay Area’s second most populous county—this represents a critical healthcare disruption for numerous communities. Marin County, situated northward near the fault rupture, will be the second-most impacted, retaining only 45% of its original capacity. However, with a significantly smaller population (251,000 residents), Marin’s absolute impact is lower, further highlighting Alameda’s critical vulnerability.

Hospitals within 20 km of the fault retain, on average, only 25% functionality, compared to 51% at 20-40 km and 82% beyond 40 km (Supplementary Fig. 4, Supplementary Note 4). Facilities with over half their buildings rated structurally poor (SPC ≤ 2) have 14% lower functionality (40% vs. 54%), and those with predominantly poor non-structural ratings (NPC ≤ 3) have 17% lower functionality (45% vs. 62%). Structural damage dominates near the fault, but non-structural damage remains critical at greater distances (64% structural vs. 70% non-structural damage within 20 km; 30% vs. 38% beyond 40 km).

Post-earthquake Bridge Functionality
Our risk analysis model predicts that 1469 bridges out of 5163 would be damaged due to the earthquake scenario (see Methods). Consequently, 3693 bridges (72%, standard deviation: 17%) are expected to remain undamaged and fully operational (Fig. 3). Some damaged bridges could continue operating, albeit at reduced capacities. Under our “baseline scenario”, where only bridges with at most slight damage remain operational, a total of 3964 bridges (77%, standard deviation: 15%) would function. In a more optimistic “favorable scenario”, where bridges with at most moderate damage also remain partially operational, 4069 bridges (79%, standard deviation: 14%) could provide service. In an idealistic scenario, which assumes that bridges even with extensive damage retain emergency functionality50, 4527 bridges (88%, standard deviation: 11%) would remain operational.

Similar to hospitals, Alameda County faces the most severe transportation impacts (Fig. 3, Table 2). Under the baseline scenario, Alameda retains only 44% functional bridges (from 642 down to 282). Marin County is second most impacted, retaining 64% (from 195 to 125 bridges). Additionally, estimates of reductions in bridge travel speeds50 (see Methods)—calculated from their damage probabilities—highlight Alameda’s higher vulnerability due to proximity to the Hayward Fault rupture (Fig. 3, Table 2).

Acute Care Accessibility
Our results show that the earthquake scenario will radically change healthcare access in the Bay. We coupled the risk model for the hospital and bridge portfolio with a network model to assess the cascading effects of earthquakes on healthcare access across the Bay (see Methods).

We evaluated accessibility based on travel times to functioning hospitals. Across the Bay Area, average travel times to the nearest operational acute care hospital increase from 6.1 minutes pre-earthquake to 16.9 minutes post-earthquake—a 177% increase. However, this impact varies significantly by county. Alameda County, the second most populous (1.6 M residents), experiences the most drastic increase of 407%, from 5.1 to 25.6 minutes (Table 3). Marin and Contra Costa counties follow, with increases of 314% and 147%, respectively, demonstrating widespread disruption to healthcare access.

At a more detailed neighborhood scale, these disruptions are even more pronounced (Fig. 4). We identified six densely populated zip codes (each exceeding 15,000 residents, labeled #1 to #6 in Fig. 4) facing substantial reductions in healthcare access. The most severely impacted is Novato (#1, Marin County), where travel times increase nearly 25-fold, from 7.3 to 185.5 minutes, affecting approximately 18,000 residents. Similarly, a Fremont zip code (#6, Alameda County) with roughly 66,000 residents experiences an eightfold increase (from 8.4 to 42.2 minutes). Other significantly impacted zip codes in Richmond (#4), Oakland (#2 and #5, Alameda County), and San Jose (#3, Santa Clara County) face travel time increases of 10, 11, 9, and 11 times their pre-earthquake levels, respectively. These results underscore the dramatic reshaping of healthcare access throughout East Bay communities along the earthquake rupture.

Finally, we explored the relative contributions of hospital and transportation infrastructure disruptions through scenario analyses (Fig. 4). We compared the baseline (None, no infrastructure disruptions) against scenarios modeling probabilistic damage only to transportation infrastructure (Transp., hospitals fully resilient), only to hospital infrastructure (Hosp., transportation fully resilient), and simultaneous probabilistic disruptions to both (Transp. & Hosp.). When considering disruptions only to transportation infrastructure (Transp.), average Bay Area travel times increase by 41% (from 6.1 to 8.6 minutes), notably less than the combined scenario (Transp. & Hosp., 177% increase). Conversely, modeling only hospital infrastructure disruptions (Hosp.) yields a 79% increase (from 6.1 to 10.9 minutes), highlighting greater relative fragility in hospital networks.

At localized urban scales, the compounding effects of simultaneous transportation and hospital infrastructure failures lead to disproportionately severe impacts (Fig. 4). for example, as mentioned earlier, in the most severely impacted zip code (novato, labeled #1 in Fig. 4), travel times dramatically increase from 7.3 to 185.5 minutes under combined disruptions (transp. & hosp.), compared to only 14.1 minutes when transportation disruptions are excluded (hosp. only). similarly, for other highly affected zip codes (labeled #2 to #6 in Fig. 4), travel-time ratios notably decrease—from 11, 11, 10, 9, and 8 under combined disruptions, to 6, 3, 6, 5, and 3 when transportation disruptions are not considered—highlighting the critical influence of compounding infrastructure failures on healthcare access.

Isolated Hospitals and Communities
To understand the drivers behind the sharp increases in travel times observed earlier, we analyzed travel volumes to the closest acute care hospitals before and after the earthquake. Fig. 5 shows pre-earthquake road usage, with line thickness representing travel volume. Roads in brown highlight those whose usage falls above the 90th percentile based on pre-earthquake conditions, emphasizing the most critical travel routes. As expected, the highest-usage roads prior to the earthquake were located near hospitals, especially in densely populated areas with fewer hospitals. For instance, communities in Fremont (#6 in Figs. 4 and 5) are served by only two hospitals, while Richmond (#4) relies on just one.

Figure 5 also displays post-earthquake road usage, using the same pre-earthquake 90th percentile threshold to highlight heavily traveled roads. After the earthquake, patient travel patterns shift significantly, with many communities forced to travel longer distances along major corridors. For example, residents in Oakland (#2 and #5 in Figs. 4 and 5), who previously relied on nearby hospitals, will now have to travel west to the San Francisco Peninsula or east to Walnut Creek due to simultaneous disruptions in both hospital and transportation infrastructure. These shifts help explain the steep increases in travel times observed in East Bay communities along the rupture zone.

Four major bridges connect the East and West Bay: the Richmond-San Rafael, Oakland-San Francisco Bay, San Mateo-Hayward, and Dumbarton bridges. Before the earthquake, no patients needed to cross these bridges to reach their nearest acute care hospital (Fig. 5). After the earthquake, however, these bridges become critical, with travel volumes increasing to 3.6, 9.3, 6.3, and 13.6 times the pre-earthquake 90th percentile values—reflecting the large-scale redistribution of healthcare demand.

Our analysis also revealed a more complex post-disaster phenomenon: micro-scale isolation of a hospital and a community due to localized bridge failures. The hospital serving the most severely impacted zip code in Novato (#1 in Figs. 4 and 5), which has 64 beds, depends entirely on a single bridge for access. If this bridge fails, the hospital becomes inaccessible, increasing travel times from 7.3 to 185.5 minutes for the surrounding population.

More concerning, we found that an urban neighborhood near Fremont (#6) could become fully isolated (Fig. 5). In one area, failure of three bridges would trap one part of the neighborhood; in another, a different set of three bridge failures would isolate the remaining part. This community would lose access not only to hospitals but also to other essential services such as grocery stores and pharmacies—illustrating how cascading infrastructure failures can sever lifeline access in disaster scenarios.

Methods
Risk Formulation: From single to multiple infrastructure units
We utilize an extension of the performance-based earthquake engineering (PBEE) framework, initially established to assess earthquake consequences in an infrastructure unit, and analyze multiple hospital buildings53–55. Under Markovian (conditional independency) assumptions described in canonical PBEE formulations54,55, we find the probability distribution of an earthquake consequence, e.g., economic losses or fatalities, as

P(DV,DS,IM)(dv,ds,im) = P(DV|DS)P(DS|IM)P(IM), (1)

where P() is a probability distribution (or mass) function, and DV is a random variable representing an earthquake consequence (also called a decision variable). For example, DV can track repair costs in buildings. In this case, DV will be a positive number with an upper bound of dv_u, i.e., the total replacement cost of the building. In other applications, DV has a different variable space, e.g., DV ∈ Z for the number of injured people in a building9,10. DS is an ordinal random variable that evaluates structural damage in an infrastructure unit, and typically DS ∈ {None, Slight, Moderate, Extensive, Complete}. Finally, IM is a random variable representing an intensity measure of shaking at the building site, and generally, IM ∈ R ≥ 0. Note that earthquake shaking on the Earth’s crust has a physical upper bound; however, this bound is not generally modeled, as large shaking cannot produce a DS greater than Complete, thereby having a minimal impact on seismic risk analysis. Frequently, DS and IM are marginalized from P(DV,DS,IM)(dv,ds,im) (e.g., through summation and integration) to find P(DV)(dv)53–55.

Lee and Kiremidjian56 first formalized the extension of the PBEE formulation to multiple infrastructure units57–59,59,60, focusing on transportation infrastructure. After finding marginal distributions of damage in single units, they formulate joint distributions of damage for all units by defining spatial correlations and their decay for distant sites. However, in the last two decades, empirical studies have better characterized spatial correlation on shaking (i.e., IM) rather than building damage61–64. To account for it, Ceferino et al9. first formulated an extension of regional PBEE incorporating earthquake shaking’s spatial correlation, defining fully the set of conditional independencies in state-of-the-art regional risk models and applications65–68. Ceferino et al9. defined the regional model for earthquake casualties in the residential building portfolio, and here we apply it to hospital and transportation infrastructure portfolios in a region.

We first formulate the model for hospital infrastructure. We redefine the traditional PBEE notation to keep the equations concise in the extension to a regional analysis with many buildings. We denote a random variable X’s probability distribution P_X(x) = π(x). Similarly, for a multi-variate vector X, we denote its probability distribution P_X(x) = π(x), where x is a specific realization of X. Using this notation, we define the damage ordinal variable D, instead of DS, and call D_s^k and D_n^k the structural and non-structural damage of building k. Thus, we are interested in the damage vector D = {D_s^1, D_n^1, ..., D_s^m, D_n^m}, where m is the total number of buildings in the region. We also define the shaking variable I, instead of IM, and call I_s^k and I_n^k the shaking measure affecting structural and non-structural damage of building k. We use the more concise notation I rather than IM to improve the readability of expressions in high-dimensional regional models, where large sets of correlated variables are simulated. For example, I_s^k can be the peak ground acceleration or spectral acceleration affecting the structural components of buildings, and I_n^k is the peak floor acceleration affecting acceleration-sensitive non-structural components, e.g., ceilings. Thus, we are interested in the shaking intensity vector I = {I_s^1, I_n^1, ..., I_s^m, I_n^m}, where m is the total number of buildings in the region. We extend the Markovian (or conditional independence) assumptions from single buildings54,55 to multiple buildings9 to estimate the joint probability distribution of damage and intensity vectors as

π(d, i) = π(d|i)π(i) (2a)

π(d|i) = Π_{k=1}^m π(d_s^k|i_s^k)π(d_n^k|i_n^k), (2b)

where d = {d_s^1, d_n^1, ..., d_s^m, d_n^m} and i = {i_s^1, i_n^1, ..., i_s^m, i_n^m} are specific realizations of D and I, respectively. Eq. (2b) assumes damage is independent at different buildings conditioned on their respective shaking intensities; thus π(d|i) can be estimated as the product of probability distributions of damage in each building. However, unconditional damages will be correlated through the joint probability distribution of shaking in the region, π(i). This formulation follows the chain rule of probability, where Eq. (2a) represents the joint distribution of damage and intensity. Eq. (2b) assumes that, conditional on shaking intensity, the damage at each building is independent—an assumption that simplifies regional modeling. This allows the conditional joint distribution π(d|i) to be expressed as the product of per-building fragility functions. While this assumes no direct interaction between buildings once shaking is known, the spatial correlation of ground motion in π(i) introduces dependence across damage outcomes.

Similarly, we assume that structural and non-structural damage (D_s^k and D_n^k) within a building k are conditionally independent given their respective shaking intensities (I_s^k and I_n^k). Yet, these two random variables of damage will be correlated since these shaking intensities in the building are also correlated, e.g., peak ground acceleration and peak floor acceleration. Supplementary Fig. 5 illustrates and summarizes all conditional dependencies through a probabilistic graphical model for the hospital buildings.

Although non-structural damage may not be conditionally independent of structural damage—given that structural damage can alter the dynamic properties of a building and, in turn, affect demands on acceleration-sensitive non-structural components—we consider the independence assumption to be reasonable within the failure space of hospitals. Specifically, our model assumes that hospital functionality is lost once early damage thresholds (e.g., slight damage) are exceeded; at this stage, structural degradation is unlikely to significantly modify the system’s dynamic characteristics. While we are not aware of empirical studies explicitly validating this hypothesis, the assumption allows us to simplify the model without compromising its ability to capture key failure mechanisms relevant to hospital functionality.

We assess the building functionality vector F = {F_1, ..., F_m}, where F_k is a Bernoulli random variable that assesses whether the hospital building k will work (F_k = 1) after the earthquake. We model F_k as a deterministic function of the structural and non-structural damage of the building as an input. Thus, under a change of variables, Eq. 2 becomes

π(f, i) = π(f|i)π(i) (3)

where f = {f_1, ..., f_m} is a specific realization of F. Supplementary Fig. 6 illustrates and summarizes all conditional dependencies through a probabilistic graphical model. Note that a probabilistic formulation that links damage to functionality could also be incorporated, introducing an additional term to Eq. (3), similar to Eq. (1). Thus, our approach admits such extensions.

Hospitals can rapidly lose functionality at early stages of structural and non-structural damage, as observed in the 2023 M 7.8 Kahramanmaras Earthquake in Turkey8, 2011 M 6.1 Christchurch Earthquake in New Zealand24, and 2010 M 8.8 Maule Earthquake in Chile69. We consider that damage thresholds, d_s^k and d_n^k, for the structural and non-structural components trigger the disruption of hospital functionality, i.e., if either fails, the hospital loses functionality. We can estimate the probabilities of not exceeding these thresholds as p_s^k = π(D_s^k ≤ d_s^k | I_s^k = i_s^k) and p_n^k = π(D_n^k ≤ d_n^k | I_n^k = i_n^k), respectively, which can be evaluated with earthquake fragility functions. Thus, we can model functionality as the intersection of both random events, i.e., the structural and non-structural components work after the earthquake. Since D_s^k and D_n^k are conditionally independent, the F_k is a Bernoulli random variable with probability p_s^k p_n^k. Accordingly,

π(f|d) = Π_{k=1}^m (p_s^k p_n^k)^{f_k} (1 - p_s^k p_n^k)^{1 - f_k} (4)

The functionality of the hospital relies on the structural and non-structural components as described in Eq. (4). This formulation reflects our focus on estimating hospital functionality during the initial post-earthquake period, where service disruption is most directly tied to structural and non-structural damage. Rather than modeling the full trajectory of hospital recovery70—which depends on permitting, logistics, and staffing—we assess whether each building is likely to remain operational immediately after the event. To enable this analysis across hundreds of facilities and correlated scenarios, we use Bernoulli random variables derived from fragility-based exceedance probabilities, accounting for spatial dependencies in seismic intensity and building response (Supplementary Fig. 6).

The hospital portfolio has various levels of SPC and NPC that control the final functionality of the hospital.

We are also interested in the probability distribution of the total number of functional beds B_t in the region, which can be estimated as

B_t = Σ_{k=1}^m β_k F_k (5)

where β_k is the number of beds (all functional before the earthquake) at the hospital building k. We are also interested in estimating the distributions of the total number of functional beds B_h in hospital h as each hospital can have multiple buildings with beds. Let k_h be the set containing all indexes of the buildings belonging to the hospital h. Thus,

B_h = Σ_{k ∈ k_h} β_k F_k (6)

In addition, we want to evaluate the contributions of structural and non-structural damage in buildings to the loss of functionality on the hospital campus. We can model the expected number of buildings with structural damage in a hospital campus given that the hospital only has a portion φ ∈ [0, 1] of functional beds as

E[Σ_{k ∈ k_h} 1_{{D_s^k > d_s^k}} | B_h < φ Σ_{k ∈ k_h} β_k] = Σ_{k ∈ k_h} π(D_s^k > d_s^k | B_h < φ Σ_{k ∈ k_h} β_k) (7)

Similarly, we can evaluate the number of buildings with non-structural damage in a hospital campus given that the hospital only has a portion φ ∈ [0, 1] of functional beds as

E[Σ_{k ∈ k_h} 1_{{D_n^k > d_n^k}} | B_h < φ Σ_{k ∈ k_h} β_k] = Σ_{k ∈ k_h} π(D_n^k > d_n^k | B_h < φ Σ_{k ∈ k_h} β_k) (8)

We formulate the model for damage to the bridge infrastructure and its post-earthquake functionality following the state of the art in previous implementations71. As with buildings, we use fragility functions to estimate structural damage to bridges. Post-earthquake functionality is represented in terms of reduced maximum free-flow travel speed. We adopt deterministic relationships between damage levels and speed reductions based on previous research, as fully described later below.

Approaches for numerical solutions
Regional seismic risk analysis is a high-dimensional problem. While the joint distribution π(f, i) in Eq. (3) can be analytically evaluated due to closed-form expressions for π(f|i) and π(i)62–64,72, computing the marginal distribution π(f) is not analytically tractable. This is because it involves integrating over a set of correlated random variables in i, for which no closed-form marginalization exists. Numerical integration methods (e.g., Riemann integration) quickly become computationally infeasible, even for a modest number of buildings9. To address this, several approaches have been proposed to efficiently approximate π(f) in large-scale settings. For example, Ceferino et al9,10. demonstrated—both theoretically and empirically—that under certain conditions, Central Limit Theorem (CLT)-based approximations can accurately and efficiently estimate π(f). More recently, Heresi and Miranda60 showed that similar approximations remain valid even under mild correlation structures in seismic risk models. However, in situations where the CLT does not apply, modern risk models often rely on Monte Carlo methods to estimate π(f). In our case, we seek to estimate the distribution of b_t, the total number of functional beds across hospital buildings, where functionality follows the distribution π(f). Since the number of hospital buildings varies widely—from a few to many—CLT approximations are not generally applicable. Therefore, we use Monte Carlo simulation to evaluate π(b_t). We implemented this using the NHERI SimCenter’s R2D Tool73–75, which enables scalable regional risk assessments. Specifically, we used R2D to generate 5000 realizations of i and d for both hospitals and bridges, which form the basis for evaluating Eq. 2.

Earthquake rupture and shaking modeling
We study an M 7.25 earthquake scenario on the Hayward Fault. Similar scenarios have been extensively studied to inform resilience policy-making in the Bay Area48. The rupture geometry was obtained from the Uniform California Earthquake Rupture Forecast (UCERF) 276. The earthquake ruptures the Hayward South and North sections over a total length of ~110 km.

Estimates of shallow shear wave velocities (averages at the top 30 m of soil) are utilized over the entire Bay Area77. With this information, we built the joint probability distribution of shaking intensities π(i) in R2D. We utilized a ground motion model78 for shallow crustal earthquakes to estimate medians and logarithm standard deviations of i. i’s uncertainty is divided into two components79. The first component captures between-event uncertainty and affects the entire region equally, but it varies per intensity measure type, e.g., peak ground acceleration or spectral acceleration. The second component captures within-event uncertainty and affects the entire region and intensity measure types differently. This component captures spatial correlation and correlation across different intensity measure types. We use a computationally efficient method to account for the second component64,81. As stated earlier, we sampled 5000 realizations of i and show expected values E[i] for the entire region (Fig. 1). Notice that for illustration purposes, we show E[i] for the entire Bay Area (10,000 locations), but the actual analysis is performed at the 426 building locations and 5163 bridge locations.

Hospital vulnerability modeling
This paper utilized building-level lognormal fragility functions to determine damage to structural and non-structural components. For example, to determine the likelihood of reaching or exceeding a structural damage threshold d_s^k in building k as a function of the shaking intensity measure, we use fragility functions like

π(D_s^k ≥ d_s^k | I_s^k = i_s^k) = Φ((log(i_s^k) - log(α)) / β) (9)

where Φ is the standard normal cumulative distribution function82. The parameters α and β define the fragility function and vary according to the damage threshold d_s^k and the building’s structural type and vulnerability (e.g., SPC rating) for building k. α equals the shaking intensity (e.g., PGA) that exposes the building to a 50% probability of damage of at least d_s^k. β is a normalizing factor that defines the width of the transition range between shaking with low and high damage probability, and it is a measure of aleatory uncertainty in the vulnerability analysis. In the limit, when β → 0, Eq. (9) becomes equivalent to a deterministic assessment, where the building would fail after a fixed shaking threshold. An analogous equation is used for non-structural damage.

We assessed structural damage across a variety of structural system types and five levels of structural vulnerability (Fig. 1 and Supplementary Fig. 1). To represent this range, we used and adapted structural fragility functions from HAZUS49, also available through the R2D tool83. Based on the definitions of SPC ratings, we mapped SPC 1 and 2 buildings to the HAZUS pre-code and moderate-code fragility functions, respectively, using the corresponding α and β parameters in Eq. (9). This mapping reflects the fact that SPC 1 and 2 buildings do not comply with the structural provisions of the Alquist Hospital Facilities Seismic Safety Act and are known to be older and more vulnerable structures. While no empirical fragility curves directly link SPC ratings to seismic performance, post-earthquake damage reports from events such as the 1971 San Fernando and 1994 Northridge earthquakes show that hospitals with older structural systems experienced significant damage. Although these observations are not sufficient to derive fragility functions, they support the alignment of SPC 1 and 2 facilities with more vulnerable construction classes, consistent with HAZUS classifications. In contrast, SPC 3, 4, and 5 comply with the Alquist Act. Fragility functions for SPC 5 buildings are obtained by increasing all the α values for high-code structures by 50% higher PGAs. These adjustments were made to represent that hospitals designed to meet the Alquist Act (SPC 5) according to the ASCE 7-16 building code are designed to withstand 50% higher seismic loads than regular buildings, i.e., an importance factor of 1.584. SPC 3 buildings are steel structures that comply with the Alquist Act but are pre-Northridge. We used regular building fragility functions to represent the vulnerability of SPC buildings as pre-Northridge’s non-ductile connections as it takes ~30% less seismic demand to make them reach moderate and extensive levels of damage85, i.e., 0.7 × 1.5 α = ~α. Finally, we modeled SPC 4 buildings with 1.25 α to represent that these buildings have lower performance than SPC 5 buildings (1.5 α). SPC 4 buildings comply with the Alquist Act but can have some structural conditions that make them more prone to damage, e.g., lack of weak beam/strong column, presence of short captive columns86.

We followed a similar approach for the fragility functions of buildings’ non-structural components. We mapped NPC 1, 2, and 3 to pre-code, moderate-code, and high-code fragility functions for acceleration-sensitive non-structural components from HAZUS87. For NPC 4 and 5, we adjusted the fragility functions of high-code fragility functions by increasing the median peak floor acceleration (PFA) to reach different damage states by 25% and 50%, respectively. Unlike structural components, we defined the same fragility functions for all building types because hospitals have similar non-structural components, e.g., equipment for acute care. However, as stated earlier, the input PFA for each hospital building differs and depends on the structural type.

After defining these fragility functions for the portfolio of hospital buildings, we computed realizations of building damage utilizing R2D88. As mentioned, we generated 5000 samples of the buildings’ structural and non-structural damage for each ground-shaking simulation. As stated earlier, we initially tested multiple thresholds of damage, d_s^k and d_n^k (e.g., slight, moderate, extensive damage) to evaluate hospital disruptions (Fig. 3). However, we used the slight damage threshold for most of the analysis later in the study since most hospitals lose functionality at quite early stages of damage. The damage state definitions adopted in this paper for building structural components and non-structural components are consistent with the damage states defined by HAZUS89.

At each building k, we used the Peak Ground Acceleration (PGA) as the shaking intensity random variable I_s^k to estimate structural damage. While spectral accelerations can also be used to improve damage predictability through the inclusion of structural properties, such as period of vibration10, we did not follow this approach here since fragility spectral acceleration-based fragility functions are not available for the diversity of building typologies in the San Francisco Bay Area.

We used PFA as the shaking intensity random variable I_n^k to estimate non-structural damage at building k. Our focus on PFA stems from the fact that acceleration-sensitive non-structural components—such as ceilings, shelves, and mechanical or medical equipment—tend to fail at lower shaking levels than drift-sensitive components like partition walls. Furthermore, in hospitals, acceleration-sensitive components (e.g., x-ray machines) often play a more critical role in maintaining functionality after an earthquake.

PFA varies with height within a building, and total non-structural damage depends on how acceleration-sensitive components are distributed across floors. However, detailed data on the floor-by-floor distribution of non-structural elements are rarely available in regional-scale analyses. To address this limitation, we used a simplified proxy to approximate the variation of PFA with building height while incorporating key building characteristics. Specifically, we assumed a linear distribution of floor accelerations, with the base acceleration set equal to the peak ground acceleration (PGA) and the acceleration at the effective height equal to the spectral acceleration corresponding to the building’s dynamic period. The effective height is estimated for each structural type based on period and height values from the HAZUS exposure model49. We then compute the average PFA across the building height from this linear profile and use an average value across height in our non-structural damage analysis. Further studies can enhance the fidelity of this analysis if higher-resolution information for non-structural components is available, e.g., on each floor.

Bridge vulnerability modeling
This paper assesses highway bridge damage due to both ground shaking and soil liquefaction. To estimate shaking-induced damage, we adopt the methodology developed in HAZUS49, which defines 28 representative bridge archetypes. Each archetype is assigned a fragility function of the form in Eq. (9), using spectral acceleration at a 1-second period as the intensity measure (denoted as i). To account for variations among individual bridges within each archetype, modification factors are applied to the fragility parameter α. These include a three-dimensional modification to capture deck arching effects in multi-span bridges and a skew factor to reflect reduced capacity at skewed deck-pier connections. Additionally, for estimating slight damage, a spectral shape modification converts the intensity measure to an equivalent 0.3-second spectral acceleration, acknowledging that bridges are typically elastic and sensitive to short-period ground motions.

To assess damage from ground failure, HAZUS89 defines fragility curves that use permanent ground deformation (PGD) as the intensity measure. Given the high liquefaction susceptibility in the Bay Area, we adopt the HAZUS-recommended geologic model HAZUS89 to estimate liquefaction-induced PGD at each bridge location. This model first uses empirical correlations between soil types (e.g., intertidal mud, Holocene and Pleistocene alluvium, rock) and liquefaction susceptibility. Liquefaction probability is then estimated based on peak ground acceleration (PGA), earthquake magnitude (to capture shaking duration), and groundwater depth (to reflect pore pressure effects). PGD is subsequently estimated using empirical relationships with the calculated liquefaction probability. We utilize the California statewide geologic map90 and a global groundwater depth model (2010)91 for this analysis. Once PGD is estimated, ground failure-induced bridge damage is determined using HAZUS fragility curves through the R2D software platform.

These fragility curves yield the probability of each bridge reaching damage states—slight, moderate, extensive, or complete—under a given ground motion realization. HAZUS defines the physical characteristics associated with each state (e.g., slight damage involves minor cracking at abutments, while complete damage corresponds to column collapse or loss of bearing support). To estimate post-earthquake traffic performance, we adopt the damage-capacity model from Guo et al. (2017)50, which relates bridge damage to residual free-flow travel speed. Travel time is computed as road length divided by this speed under the assumption that emergency vehicles receive priority and travel at free-flow speed. More realistic travel times could incorporate background traffic using volume-delay relationships such as the Bureau of Public Roads (1964) curve92, though this requires post-disaster traffic data, which remains a key challenge in traffic simulations after major events.

Network model: acute care accessibility modeling
We denote G = (v, e) a graph, where v is the set of |v| vertices and e the set of |e| edges. This graph will represent the infrastructure system of hospitals and roads supporting healthcare access in the Bay Area. Let p ∈ p be a vertex representing the location of a patient needing acute care and p be the set of all patient vertices. Also, let h ∈ h be a vertex representing the location of an acute care hospital and h be the set of all hospital nodes. In this case, p ⊆ v, and h ⊆ v. e = {(u, v) | u, v ∈ v} is the set of |v| edges representing different roads connecting different locations (vertices) in the region. We denote τ(u, v) ∈ R ≥ 0 the travel time between vertices u and v. e = {(u, v) | τ(u, v) < 1 ∀(u, v) ∈ e} for each simulation. Thus, T*(p) is a random variable. We solve Eq. (12) 5000 times using the 5000 Monte Carlo simulations obtained before.

Bay Area’s Transportation System
We study the entire San Francisco Bay, where the transportation network is massive, with |v| = 0.5 million vertices and |e| = 1.5 million edges. The edges in the graph represent the roads in the transportation system, whose information was obtained from the San Francisco Region Roadways95 and OpenStreetMap (OSM)96. We incorporated directional and travel time data into the network models using OSM’s OSMnx library97. We couple the transportation network data to the hospital and the patient data. The 76 hospitals are embedded in the network models by identifying the network’s vertices closest to the hospital locations, forming the set h. In addition, we obtained population data at 1613 zip codes, and we assumed that the number of patients is proportional to the population.

Our goal was to quantify hospital accessibility losses beyond the immediate emergency period, recognizing that hospitals often take months or even years to be repaired. Because people are typically injured within damaged buildings, patient surges after earthquakes generally last only a few days—except in rare cases such as the 2023 Türkiye Earthquake. To focus on long-term access rather than short-term emergency response, we did not model injury locations directly. Instead, we assumed that patient demand is proportional to population distribution and modeled accessibility accordingly. For the Bay Area, we based our analysis on population-weighted access loss and identified the network’s vertices closest to the centroids of census tracts to define the set p (Fig. 6).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents the results from a numerical study designed to evaluate the capacity of hospitals and the anticipated travel times for acute care patients in San Francisco Bay, California, following a potential M7.25 earthquake. This crucial and timely study innovatively integrates a risk model with a transportation network to illustrate the possible cascading effects. However, certain critical assumptions made within the model, which significantly impact the study's conclusions, lack sufficient justification. Details of these assumptions are outlined below. The manuscript requires significant revisions before it can be reconsidered for publication in Nature Communications.\n\nThe authors are advised to address the following while revising their manuscript:\n[Page 5] The definitions adopted for the damage levels are not defined in the manuscript. As a result, it is difficult to interpret the plausibility of the damage probabilities presented in Figure 2 as well as the post-earthquake capacity estimates (in Table 1, Figures 3 and 4). The definitions of the damage states and their impact of the type of damage on the capacity should be explained well.\n[Page 8, Fig. 3, lower left] The legend entry related to markers with small white circles is missing.\n[Page 10, Fig. 4, upper right] The figure legend is missing.\n[Page 11] In the last paragraph, all \"Figure 4\"s should read \"Figure 5\".\n[Page 12] The discussion related to the transportation network is difficult to follow since it requires knowledge of the names of the places. It would be very informative to add labels on the maps (e.g. Figure 1) or to cite the numbers indicated in Figure 4 in the text so that the non-residents can follow the observations related to cascading effects with ease.\n[Page 15] In Equation 1, \"P_IM(I'm)\" should read \"P_IM(im)\"\n[Page 16] It is stated that \"structural and non-structural damage (Dks and Dkn) within a building k are conditionally independent given their respective shaking intensities (Iks and Ikn).\". Physical mechanisms that drive non-structural damage, as well as past reconnaissance observations, indicate the opposite. Given a specific shaking intensity, the non-structural damage is very sensitive to the extent of structural damage. The level of structural damage has a direct influence on the acceleration and deformation demands on the non-structural components as well as the changes in the resistance capacities at the anchorage locations.\n[Page 16] Building functionality is represented using a Bernoulli random variable which can only have two states: building is functional or not functional. This implies that if there is slight non-structural damage in some part of a hospital building, the entire building will become completely dysfunctional. At present, the definition of slight damage adopted in the manuscript is unclear. However, for the typical definition of slight damage, this is not a realistic assumption. This is particularly true after severe disasters where there is a significant demand for urgent acute care. Many of the hospital buildings with slight non-structural damage would continue to operate with some reduced level of functionality. In order to address this issue, the definitions of damage states should be explained. Moreover, the assumption of complete loss of functionality of the entire building needs to be justified based on the provided damage definitions and past experiences. Otherwise, the formulation should be revised accordingly.\n[Page 18] Difficulties associated with the analytical evaluation of \\pi(f) and \\pi(bt) are essentially very similar. The related sentences can be collected together into a single paragraph so as not to repeat very similar issues twice.\n[Page 19] Structural Performance Categories (SPCs) of the hospitals have a critical function in the presented investigation. At present it is unclear if these categories are the revised categories obtained as a result of the HAZUS Reassessment Program for SPC-1 buildings or not. In general, the technical basis of this categorization should be clarified in the manuscript.\n[Page 19] Authors state that \"Following the definitions of SPC ratings (Supplementary Table 1), we mapped SPC 1 and 2 to pre-code and moderate-code fragility functions for regular buildings from HAZUS …\". This is a critical assumption which would have a direct impact on all calculations. The assumed fragility parameters need to be justified. For this purpose, the extent of the structural and non-structural damages observed in hospitals designed and constructed in other parts of the state (or other states with similar design codes) that experienced earthquakes within the last 50 years can be considered as a basis. If the fragility characteristics show a similar trend to the assumed model, the selected parameters can be considered as suitable. At present, the introduced assumptions are not justified based on any empirical or analytical evidence.\n[Page 20] Authors note that they \"utilize a proxy for a representative PFA equal to the spectral acceleration at the building’s period of vibration.\". The assumption of peak floor acceleration being the same as the spectral acceleration at the site of the building is not a suitable one. Such an assumption ignores the height of the building, the type of the system, and any irregularity in the structural layout. These factors significantly influence the resulting floor accelerations.\n[Page 22] It is stated that the number of patients is assumed to be proportional to the population. Past disasters show that the number of acute care patients is typically distributed proportional to the intensity of building damage together with the population density. The building damage is a function of shaking intensity and vulnerability of the residential or commercial building stock. In the proposed approach, it appears that these critical factors are not taken into account while modeling the distribution of patients with acute care needs following an earthquake. This assumption needs to be justified or the approach needs to be revised. The assumptions related to the spatial distribution of patients over the region are expected to have a considerable impact on the calculated travel times and the related conclusions.\n[Page 22] It appears that the potential for any closure of roads after the earthquake is not considered in the proposed framework. Past earthquakes have shown that havoc-related jams, toppling of electric lines and commercial pole signs, landslides, surface fault ruptures, underground pipe ruptures, building façade debris, damages to bridges, flyovers, and tunnels have led to the closure of roads after earthquakes. In urgent cases, the roads are closed as a part of the disaster response operations and only the emergency vehicles are allowed on the main roads. Furthermore, very often, a scarcity of gas is caused after such earthquakes by the demand surge, which cannot be accommodated quickly. As a result, it becomes a common problem to have vehicles on the sides of the roads left without any gas. In the case of California, where electric vehicles are more common as compared to other regions, the post-earthquake functioning of the grid and the likely charging durations may also have a critical impact. In the present investigation, the potential impacts of such effects on the travel time estimates, as well as transportation network connectivity, are not taken into account. These should be noted as a limitation of the study to inform the reader properly about the complexity of the subject matter.\n[Supp. Fig. 3] The damage probabilities are compared against a \"reference\" fragility model for structural wall buildings. However, the original source of this reference model, as well as the related building typology, is unclear. Therefore, it is not easy to interpret the meaning of this comparison.\n(Remarks on code availability)\nI downloaded the code and checked its contents very briefly. It contains the related files. I did not run it to reproduce the results.", "reviewer_2": "As the authors know, one of the most critical elements of any study is the motivation of the work. The authors motivated the work by indicating that, unlike the past studies on hospital networks, this study focuses on a community exposed to earthquakes only within a few kilometers of them. First, the papers cited by the authors include hospitals a few kilometers from the hazard. Second, the justification overall is very weak and does not represent uniqueness. The study is motivated by the hospital being a few kilometers from the hazard, which is irrelevant - not to mention that this was the case in past studies. Furthermore, assessing healthcare networks under earthquakes has been studied quite a bit using more rigorous approaches. It is hard to see valuable contributions in this study.\n\nIn addition to the lack of sufficient motivation, the author did not utilize the state-of-the-art in healthcare resilience analysis and used a simplistic approach in their assessment. For example, it is assumed that damage to the building is a proxy for bed availability and resilience, which is not true. Many recent studies describe healthcare resilience as a function of physical infrastructure, staff, and stuff. So, it appears that the authors are going back in time to use a definition that is no longer recognized in the research community.\n\nMoreover, the paper suffers from many technical issues/mistakes, which causes the analysis to be unsound. For example, their predictions show that many hospitals will experience violent shaking at a scale not seen in over a century under a peak ground acceleration of 0.2. This is not possible. A peak ground acceleration of 0.2 is extremely low and is expected to cause only slight damage. The literature is overwhelmed with studies that show how a 0.2 PGA typically causes slight damage to different archetypal structures. In addition, the authors noted that many hospitals will have a probability of damage above 0.25. What is the significance of 0.25 as a damage probability? and What type of damage corresponds to 0.25 or more? Damage probability ranges from slight to moderate to extensive to complete, and each plays a role in quantifying healthcare functionality. To list that the damage probability is 0.25 has no structural engineering relevance. In earthquake engineering, there is no relevance in saying that many hospitals had a damage probability of more than 0.25. The reviewer recommends that the authors look at various FEMA documents on seismic performance assessment to become more familiar with damage assessment approaches, including the various engineering demand parameters used for seismic evaluation of buildings and hospitals.\n\nConcerning this comment, the authors note that their analysis predicts that 8,501 beds will be lost throughout the Bay, and such predictions are based on slight damage (justified by previous studies that used slight damage to indicate loss of beds). Again, the literature is way past the idea of using damage to indicate bed losses and that stuff, staff, and physical systems should be used to indicate bed losses. In addition, many studies show that hospitals continue to operate beyond slight damage, including the studies referenced by the authors. None of the studies cited by the authors show that hospitals will lose functionality at slight damage. The StEER report cited by the authors indicates that only fully collapsed or severely damaged hospitals were evacuated after the Turkey EQ event. Unfortunately, the authors used this assumption to draw the study's main conclusions. Using slight damage drastically skews the results towards showing significant bed losses, which is very unrealistic. Also, the authors note that services within hospital buildings will be highly disrupted – a statement with no basis since the authors did not model any hospital units or services. Another significant issue is that bridge damage and failure analysis are not included in determining travel time. The travel time calculated in the paper can not be correct due to the lack of bridge failure analysis.\n\nThe methods section also suffers from statements that are either very simplistic and outdated by more detailed analysis, incorrect, or indicate problems with how the study was conducted. For example, the authors suggested that building functionality is modeled with Bernoulli distribution. The state of the art on building functionality (plz see work by Henry Burton or Naiyu Wang) has shown building functionality to be much more complex than this, requiring more details analysis and the inclusion of various probabilities, including the availability of crew workers, the time it takes to issue a permit, material availability, and many other things. These parameters will impact the hospitals' functionality and the staff's viability since their homes could be damaged - criteria that were not included in this study. Assuming a simple Bernoulli function has no basis.\n\nAnother major issue in the methods section is that the authors tried to connect the data collected from the vulnerability rating to the HAZUS fragility. This connection is based on assumptions not validated or supported by previous studies. The authors tried to use ASCE-7 to come up with some numbers that reflect a lack of understanding of the code philosophy. I recommend utilizing fragility functions that reflect the building characteristics; otherwise, the calculated damage does not represent reality.\n\nThe authors also assumed that some hospitals could accept patients if only one bed was functional, which is a weak assumption. If only one bed is functional, then the hospital must be substantially damaged, and if most of the hospital is damaged, then it will be unsafe to utilize. Please check previous studies reporting that many hospitals evacuated, even when they had more than 50% of their capacity due to severe damage. I doubt whether any case study or expert opinion will support the assumption made by the authors.\n\nAnother major issue in this paper is that the authors ignored damage to the transportation network, which is a fundamental component when calculating the estimated demand at different hospitals. Damage to bridges and the road network will significantly change the shortest paths calculated in this study, which can lead to cases where some functional hospitals see less demand due to reduced accessibility. Many previous studies on healthcare systems reported that impact and some even included the dynamic effect of the change in travel time on hospital demand and accessibility.\n\nThe authors also assumed the number of patients proportional to the number of populations. However, considering the variation in patient distribution, especially during disasters, is critical for accurate demand assessment, and again, many studies have already done that. Most earthquake casualties are related to building collapse, a function of the building characteristics and earthquake intensity measured at the building locations. So, the assumption made by the authors has no basis and will significantly impact the results and main conclusions of the study.\n\nOverall, the paper addresses a problem investigated in the past using simple approaches that are not necessarily detailed and, in some cases, infused with incorrect assumptions and/or calculations. Unfortunately, on these grounds, this paper can not be published.\n(Remarks on code availability)\nI evaluated the authors' online sources, and they all have sufficient information.", "reviewer_3": "The manuscript presents a case study on the impacts of a scenario earthquake on the Hayward fault on the San Francisco Bay Area’s hospital capacity. It is very interesting work and implemented using state of the art approaches, giving good weight to the discussion points provided.\n\nThe biggest issue I found with the work was the length of the text that made it rather difficult to read. I understand that the authors wish to discuss their results in detail, but I felt much of the discussion could have been delivered in half the amount of text. I would strongly urge the authors to revise the initial parts of the paper and trim unnecessary sentences or anecdotes that do not contribute to the main points being delivered.\n\nFurthermore, some of the text is written in a manner that seems less like a technical article, and more like a magazine article for non-technical readers. The excessive use of adjectives (i.e. violent shaking) and adverbs (i.e. we rigorously study) and terminology like “we predict” seems a little exaggerated, at least in this Reviewer’s opinion. Reducing these would help the article’s conciseness.\n\nOverall, it is good and interesting work that should be accepted following some minor adjustments.\n\nSome minor observation:\nAbstract:\nCorrect “In East Bay” to “In the East Bay”\nChange “are way higher” to more technical terminology “are much higher”\nPage 1, the term “mass-casualty earthquake” sounds a little dramatic for a technical publication. Consider revising.\nThe authors note that the the Alfred E. Alquist Hospital Seismic Safety Act was enacted in 1973 but twelve Pre-Alquist Act hospital buildings received red tags following the 1994 Northridge earthquake. Does this mean that the act was focused on new hospitals and existing hospitals were left as is? Please comment.\nAlso, the authors write 12 hospitals, but a few lines earlier, 11 were mentioned. Check that these are correct.\nDoes the “California Senate Bill 1953” refer to the year 1953 or just the number 1953? I presume not, so it would be better to specify the year so as to avoid confusion in the timeline of these legislative developments.\nResults:\nIt may be better to specify that “The Bay” refers to the “The Bay Area of San Francisco” for unfamiliar readers.\nStatements like “Our predictions show that many hospitals will experience violent shaking at a scale not seen in over a century.” seem a little dramatic and unnecessary. It also conveys a distorted view to the public that the earthquake shaking can be predicted. In general, words like estimate would be a better reflection of the science behind the methods.\nEquation 1. It seems “I’m” is a typo.\nWould it not make more sense to define the shaking variable as IM = im instead of I = I? It would maintain a consistency with the previous text.\nShould the left hand term of Equation 2a contain the i term as pi(d, i)? The formulation on the right hand side would suggest it should be independent of the intensity and listed simple as pi(d)\nThe authors mention that the damage estimation in Equation 2b assumes independence. Is this realistic? Are there cases where this assumption may not hold? Are there alternative methods that could be adopted? Please comment.\nFigure 6. The term D_1^s appears twice. One of them should be D_1^n.\nAgain, the authors use the term “state of the art” when referring to a ground motion model developed over a decade ago.\n(Remarks on code availability)"}, "author_response": "Overall comment:\nThis manuscript presents the results from a numerical study designed to evaluate the capacity\nof hospitals and the anticipated travel times for acute care patients in San Francisco Bay,\nCalifornia, following a potential M7.25 earthquake. This crucial and timely study innovatively\nintegrates a risk model with a transportation network to illustrate the possible cascading effects.\nHowever, certain critical assumptions made within the model, which significantly impact the\nstudy's conclusions, lack sufficient justification. Details of these assumptions are outlined below.\nThe manuscript requires significant revisions before it can be reconsidered for publication in\nNature Communications.\nOverall response:\nWe thank the reviewer for their thoughtful and constructive comments. We sincerely apologize for\nthe delay in our response—this was due to major revisions made to both the manuscript and the\ncomputational framework to strengthen the analysis and address the issues raised.\nIn particular, we significantly expanded the scope of the study by fully integrating transportation\ninfrastructure into the modeling of post-earthquake hospital accessibility. This addition allowed us\nto identify new critical outcomes—such as the potential isolation of a hospital and a community\n(“urban island”)—that were not captured in the original version of the manuscript.\nWe also conducted new sensitivity analyses to test the robustness of our results under different\nmodeling assumptions, especially those related to damage thresholds and hospital functionality.\nThese changes were made in direct response to the reviewer’s comments, which we found\nextremely helpful in improving the clarity and technical rigor of the work.\nWe carefully addressed each point raised in the review and implemented all suggested revisions.\nReviewer comments are shown in blue, and corresponding changes in the manuscript are\nindicated in red. We are grateful for the reviewer’s input, which has led to a much stronger and\nmore complete study.\nThe authors are advised to address the following while revising their manuscript:\nComment 1: [Page 5] The definitions adopted for the damage levels are not defined in the\nmanuscript. As a result, it is difficult to interpret the plausibility of the damage probabilities\n1\npresented in Figure 2 as well as the post-earthquake capacity estimates (in Table 1, Figures 3\nand 4). The definitions of the damage states and their impact of the type of damage on the\ncapacity should be explained well.\nWe appreciate the reviewer’s comment and agree that clearer definitions of the damage states\nare essential for interpreting the damage probabilities and the post-earthquake capacity\nestimates. In response, we have now added detailed definitions of the damage states for the three\nmost common structural systems in our analysis—Steel Moment Frames, Concrete Shear Walls,\nand Steel Braced Frames—in Supplementary Table 3. We have also included definitions of non-\nstructural damage for suspended ceilings and electrical-mechanical equipment—components\nthat often drive hospital disruptions—in Supplementary Table 4.\nTo further address the reviewer’s concern, we conducted a sensitivity analysis evaluating how\nhospital functionality changes under varying damage thresholds. We acknowledge that the actual\nthresholds are more complex in practice and can depend heavily on human decisions influenced\nby factors such as risk perception, preparedness levels, and patient surges. These behavioral\nand operational dimensions are still underexplored in the literature, but we hope our study\nencourages deeper investigation by the research community. We have also discussed these\nchallenges in our related fieldwork-based publication following hospital visits in Turkey [1].\n[1] Ceferino, L., Merino, Y., Pizarro, S. et al. Placing engineering in the earthquake response\nand the survival chain. Nat Commun 15, 4298 (2024). https://doi.org/10.1038/s41467-024-\n48624-3\nModifications to the main manuscript, including sensitivity analysis (line 169):\nOur risk analysis predicts a substantial loss of hospital capacity throughout the\nBay Area following the earthquake scenario (see Methods). We estimate a loss of 8,165\nhospital beds, resulting in only 51% of total acute care beds remaining functional\n(standard deviation: 21%). This significant reduction in capacity is highly uneven across\nthe region (Figure 3, Table 1). Our baseline predictions assume hospitals lose\nfunctionality when structural or non-structural damage exceeds a threshold of slight\ndamage (see Methods). These damage conditions are often shown to disrupt hospital\nservices (see descriptions of multiple damage levels in Supplementary Tables 3 and 4).[\n21, 28–31] We also analyzed more optimistic scenarios with moderate (“favorable”) and\nextensive (“idealistic”) damage thresholds, resulting in increased overall functionality of\n79% and 93%, respectively (Figure 3 and Supplementary Table 5). However, empirical\nevidence supports our baseline assumption, as hospitals often lose operations at early\nstages of damage. [21, 28–31]\n[...] Probability distribution of functional acute care beds under baseline (slight), favorable\n(moderate), and idealistic (extensive) damage thresholds.\nAdditional changes in Supplementary Information:\nSupplementary Table 3. Definitions of structural damage states for most common structural types in the\nhospital building portfolio: S1: Steel Moment Frame; C2: Concrete Shear Walls; S2: Steel Braced Frame.\nThese definitions come from HAZUS and were adopted in this study.4\n[Table Redacted]\n3\ncomponents whose failures often disrupt hospital services. These definitions come from HAZUS and\nw ere adopted in this study.4\n5\n[Table Redacted]\n© OpenStreetMap contributors openstreetmap.org/copyright.\nComment 2: [Page 8, Fig. 3, lower left] The legend entry related to markers with small white\ncircles is missing.\nThank you for catching this. We have added “beds” next to the white circles in the legend. We\nalso added an extra line on the caption:\n“The size of the circles indicates the number of functional beds before and after the\nearthquake.”\nPlease see the new Figure:\nComment 3: [Page 10, Fig. 4, upper right] The figure legend is missing.\nWe added the legend to the pre-earthquake and the post-earthquake cases. We also adjusted\nthe figure’s caption to make it clearer:\nPost-earthquake (Post-EQ) increases in travel time at the zip-code level compared to pre-\nearthquake (Pre-EQ) conditions, highlighting densely populated areas that are most severely\nimpacted.\nPlease see the updated figure:\nFixed\nComment 5: [Page 12] The discussion related to the transportation network is difficult to follow\nsince it requires knowledge of the names of the places. It would be very informative to add\nlabels on the maps (e.g. Figure 1) or to cite the numbers indicated in Figure 4 in the text so that\nthe non-residents can follow the observations related to cascading effects with ease.\nThis is an excellent point. We added the names of the counties in Figure 1. We also adjusted\nthe figure’s caption to make it clearer:\nThe Bay Area's county names are also included for reference.\nPlease see the updated figure:\n© OpenStreetMap contributors openstreetmap.org/copyright.\nComment 6: [Page 15] In Equation 1, \"P_IM(I'm)\" should read \"P_IM(im)\"\nFixed\nComment 7: [Page 16] It is stated that \"structural and non-structural damage (Dks and Dkn)\nwithin a building k are conditionally independent given their respective shaking intensities (Iks\nand Ikn).\". Physical mechanisms that drive non-structural damage, as well as past\nreconnaissance observations, indicate the opposite. Given a specific shaking intensity, the non-\nstructural damage is very sensitive to the extent of structural damage. The level of structural\ndamage has a direct influence on the acceleration and deformation demands on the non-\nstructural components as well as the changes in the resistance capacities at the anchorage\nlocations.\nThis comment touches on an important aspect of the model, and we appreciate it. We spent quite\na bit of time thinking through this assumption when developing our approach. We believe the\nindependence assumption is reasonable in the context of hospital failure, where functionality is\noften lost at early damage stages (e.g., slight damage). At these levels, we think it’s reasonable\nto assume that the structural system hasn’t experienced enough damage to significantly alter the\nbuilding’s dynamic properties or the demands on non-structural components.\nIn other words, since the hospital is assumed to stop functioning once slight damage is reached,\nwe’re operating in a space where the interaction between structural and non-structural damage\n9\nmay be less critical. We didn’t find specific studies that test this hypothesis directly, but we think\nthe assumption is appropriate given how early in the damage process hospitals can fail.\nWe’ve now added a brief explanation in the manuscript to clarify this point and acknowledge\nthat future studies could explore the effects of correlated damage mechanisms in more detail,\nespecially in the later stages of damage (line 393).\nAlthough non-structural damage may not be conditionally independent of structural\ndamage—given that structural damage can alter the dynamic properties of a building\nand, in turn, affect demands on acceleration-sensitive non-structural components—we\nconsider the independence assumption to be reasonable within the failure space of\nhospitals. Specifically, our model assumes that hospital functionality is lost once early\ndamage thresholds (e.g., slight damage) are exceeded; at this stage, structural\ndegradation is unlikely to significantly modify the system’s dynamic characteristics.\nWhile we are not aware of empirical studies explicitly validating this hypothesis, the\nassumption allows us to simplify the model without compromising its ability to capture\nkey failure mechanisms relevant to hospital functionality.\nComment 8: [Page 16] Building functionality is represented using a Bernoulli random variable\nwhich can only have two states: building is functional or not functional. This implies that if there\nis slight non-structural damage in some part of a hospital building, the entire building will\nbecome completely dysfunctional. At present, the definition of slight damage adopted in the\nmanuscript is unclear. However, for the typical definition of slight damage, this is not a realistic\nassumption. This is particularly true after severe disasters where there is a significant demand\nfor urgent acute care. Many of the hospital buildings with slight non-structural damage would\ncontinue to operate with some reduced level of functionality. In order to address this issue, the\ndefinitions of damage states should be explained. Moreover, the assumption of complete loss of\nfunctionality of the entire building needs to be justified based on the provided damage\ndefinitions and past experiences. Otherwise, the formulation should be revised accordingly.\nDear reviewer, thank you for raising this point. Now, we include full descriptions of the damage\nand a sensitivity analysis for different damage thresholds. We believe our response to Comment\n1 should also address this comment.\nComment 9: [Page 18] Difficulties associated with the analytical evaluation of \\pi(f) and \\pi(bt)\nare essentially very similar. The related sentences can be collected together into a single\nparagraph so as not to repeat very similar issues twice.\nThank you very much for the constructive suggestions. This section has been revised to be\nmore concise to the following version (line 450):\nEq. 3 can be analytically evaluated due to closed-form expressions for π(f|i) and π(i), computing\nthe marginal distribution π(f) is not analytically tractable. This is because it involves integrating\nover a set of correlated random variables in i, for which no closed-form marginalization exists.\nNumerical integration methods (e.g., Riemann integration) quickly become computationally\ninfeasible, even for a modest number of buildings. To address this, several approaches have\nbeen proposed to efficiently approximate π(f) in large-scale settings. For example, Ceferino et\nal. demonstrated—both theoretically and empirically—that under certain conditions, Central\nLimit Theorem (CLT)-based approximations can accurately and efficiently estimate π(f).\nHeresi and Miranda showed that similar approximations remain valid even under mild\ncorrelation structures in seismic risk models. However, in situations where the CLT does not\napply, modern risk models often rely on Monte Carlo methods to estimate π(f). In our case, we\nseek to estimate the distribution of bt, the total number of functional beds across hospital\nbuildings, where functionality follows the distribution π(f). Since the number of hospital buildings\nvaries widely—from a few to many—CLT approximations are not generally applicable.\nTherefore, we use Monte Carlo simulation to evaluate π(bt). We implemented this using the\nNHERI SimCenter’s R2D Tool, which enables scalable regional risk assessments. Specifically,\nwe used R2D to generate 5,000 realizations of i and d for both hospitals and bridges, which\nform the basis for evaluating Eq. 2.\nComment 10: [Page 19] Structural Performance Categories (SPCs) of the hospitals have a\ncritical function in the presented investigation. At present, it is unclear if these categories are the\nrevised categories obtained as a result of the HAZUS Reassessment Program for SPC-1\nbuildings or not. In general, the technical basis of this categorization should be clarified.\nThank you for pointing this out. We utilized the official SPC rating from the California\nDepartment of Health Care Access and Information (HCAI). Thus, hospitals that went under the\nreassessment and passed it were considered SPC-2. Fortunately, we did not have to do the\nreassessment analysis as the data provided by HCAI already pointed to the latest building\nrating.\nTo make this clearer, we added this explanation to Supplementary Table 1 for SPC 2:\nSupplementary Table 1. Structural Performance Categories (SPC) according to California’s Department of Health\n11\n[Table Redacted]\nWe also added more clarity to the main manuscript regarding the SPC and made the reference\nto the table shown before (line 117):\nIn this paper, we used the Structural Performance Categories (SPC) and Non-structural\nPerformance Categories (NPC), established and reported by California’s Department of\nHealth Care Access and Information (HCAI), to characterize structural and non-structural\ndeficiencies.[44] Each hospital building receives vulnerability ratings (SPC or NPC)\nranging from 1 to 5, from the most to the least vulnerable. Supplementary Tables 1 and\n2 fully describe SPC and NPC.\nComment 11: [Page 19] Authors state that \"Following the definitions of SPC ratings\n(Supplementary Table 1), we mapped SPC 1 and 2 to pre-code and moderate-code fragility\nfunctions for regular buildings from HAZUS …\". This is a critical assumption which would have a\ndirect impact on all calculations. The assumed fragility parameters need to be justified. For this\npurpose, the extent of the structural and non-structural damages observed in hospitals designed\n12\nand constructed in other parts of the state (or other states with similar design codes) that\nexperienced earthquakes within the last 50 years can be considered as a basis. If the fragility\ncharacteristics show a similar trend to the assumed model, the selected parameters can be\nconsidered as suitable. At present, the introduced assumptions are not justified based on any\nempirical or analytical evidence.\nComment 12: Thank you for raising this important point. We agree that the assumption of\nmapping SPC 1 and 2 to HAZUS pre-code and moderate-code fragility functions plays a central\nrole and needs a clearer justification.\nOur main rationale is that the SPC classification itself was developed by engineers specifically to\nevaluate seismic risk in California hospitals. SPC 1 and 2 buildings are known to be older and\nmore vulnerable structures—mainly designed before modern seismic codes were in place (pre-\n1973)—and have been flagged by the state as not acceptable for continued acute care use in\nfuture earthquakes. These characteristics align closely with the assumptions underlying HAZUS\npre-code and moderate-code fragility functions, which were developed to represent similarly\nvulnerable building stock.\nIn response to your comment, we reviewed post-earthquake damage reports from events such\nas the 1971 San Fernando and 1994 Northridge Earthquakes. In many cases, hospitals with older\nstructural systems—such as non-ductile concrete frames—exhibited significant structural and\nnon-structural damage. Although this information is too limited and variable to develop fragility\nfunctions directly and use them in our models, it does support the idea that SPC 1 and 2 facilities\nrepresent a more vulnerable class of buildings. This general vulnerability is consistent with the\nassumptions behind HAZUS pre-code and moderate-code fragility functions. In fact, HAZUS\nrecommends that “older buildings located in High-Code seismic design areas should be\nevaluated using damage functions for either Moderate-Code buildings or Pre-Code buildings\n(page 5.74 of HAZUS technical manual).\nWe have now added this explanation to the manuscript and cited relevant reconnaissance reports.\nWe also acknowledge the limitation of this assumption and hope that future work will enable the\ndevelopment of empirically calibrated fragility models for SPC-rated hospitals (line 500).\nWe assessed structural damage across a variety of structural system types and five levels\nof structural vulnerability (Figure 3 and Supplementary Figure 1). To represent this range, we\nused and adapted structural fragility functions from HAZUS (FEMA, 2020), also available through\nthe R2D tool (Zsarnóczay et al., 2020). Based on the definitions of SPC ratings (Supplementary\nTable 1), we mapped SPC 1 and 2 buildings to the HAZUS pre-code and moderate-code fragility\nfunctions, respectively, using the corresponding α and β parameters in Equation 1. This mapping\nreflects the fact that SPC 1 and 2 buildings do not comply with the structural provisions of the\nAlquist Hospital Facilities Seismic Safety Act and are known to be older and more vulnerable\nstructures. While no empirical fragility curves directly link SPC ratings to seismic performance,\npost-earthquake damage reports from events such as the 1971 San Fernando and 1994\nNorthridge earthquakes show that hospitals with older structural systems experienced significant\n13\ndamage. Although these observations are not sufficient to derive fragility functions, they support\nthe alignment of SPC 1 and 2 facilities with more vulnerable construction classes, consistent with\nHAZUS classifications.\nComment 12: [Page 20] Authors note that they \"utilize a proxy for a representative PFA equal\nto the spectral acceleration at the building’s period of vibration.\". The assumption of peak floor\nacceleration being the same as the spectral acceleration at the site of the building is not a\nsuitable one. Such an assumption ignores the height of the building, the type of the system, and\nany irregularity in the structural layout. These factors significantly influence the resulting floor\naccelerations.\nThank you for pointing out that floor accelerations are influenced by several building-specific\nfactors. We revised our approach based on this suggestion. A key challenge is that existing\nmethods for estimating peak floor accelerations typically require solving dynamic equations and\nrely on detailed building information. These methods are more suitable for individual building\nanalyses, rather than regional assessments involving large building portfolios (e.g., over 700\nfacilities in our case), where such detailed information (e.g., to capture irregularities) is generally\nunavailable.\nTo improve our model in this regional context, we refined our original approach to better account\nfor building height and structural system. Specifically, we now assume that floor acceleration\nvaries linearly with height, starting from PGA at the base and reaching the spectral acceleration\n(Sa) at the building’s effective height. This approach is consistent with procedures for estimating\nacceleration demands in ASCE 7.\nIn our disaster risk model, both PGA and spectral acceleration are estimated using ground motion\nprediction equations. The spectral acceleration is based on the structural type and height of each\nhospital building, with periods of vibration estimated from the HAZUS exposure model. The\neffective height is computed using the ratio between the equivalent height and total height. We\nuse the HAZUS exposure model to estimate these values, which also depends on structural type\nand number of stories. We then compute the average floor acceleration across the building from\nthis linear profile and use that value in our analysis.\nThis updated method resulted in slightly lower probabilities of non-structural damage compared\nto the previous version of the model, which assumed PFA equal to Sa (i.e., from an equivalent\nsingle-degree-of-freedom system) across the entire building height. The revised estimates are\nlower because the average acceleration across the height is less than Sa, especially since the\neffective height is typically above mid-height.\nWe edited our manuscript according and explained the following (line 551):\non how acceleration-sensitive components are distributed across floors. However,\ndetailed data on the floor-by-floor distribution of non-structural elements are rarely\navailable in regional-scale analyses. To address this limitation, we used a simplified proxy\nto approximate the variation of PFA with building height while incorporating key building\ncharacteristics. Specifically, we assumed a linear distribution of floor accelerations, with\nthe base acceleration set equal to the peak ground acceleration (PGA) and the\nacceleration at the effective height equal to the spectral acceleration corresponding to the\nbuilding’s dynamic period. The effective height is estimated for each structural type based\non period and height values from the HAZUS exposure model. We then compute the\naverage PFA across the building height from this linear profile and use an average value\nacross height in our non-structural damage analysis. Further studies can enhance the\nfidelity of this analysis if higher-resolution information for non-structural components is\navailable, e.g., on each floor.\nComment 13: [Page 22] It is stated that the number of patients is assumed to be proportional to\nthe population. Past disasters show that the number of acute care patients is typically\ndistributed proportional to the intensity of building damage together with the population density.\nThe building damage is a function of shaking intensity and vulnerability of the residential or\ncommercial building stock. In the proposed approach, it appears that these critical factors are\nnot taken into account while modeling the distribution of patients with acute care needs following\nan earthquake. This assumption needs to be justified or the approach needs to be revised. The\nassumptions related to the spatial distribution of patients over the region are expected to have a\nconsiderable impact on the calculated travel times and the related conclusions.\nThank you for pointing this out. We spent significant time considering whether to explicitly model\ninjury distributions from earthquakes in the Bay Area as part of this study. Ultimately, we decided\nnot to proceed for two main reasons.\nFirst, our goal in this analysis was to document hospital accessibility losses beyond the\nemergency response period. Hospitals often remain closed for months or even years after an\nearthquake, and understanding long-term access disruptions is critical for recovery planning.\nPatient surges, on the other hand, typically last only a few days—except under extreme\nconditions, such as the 2023 Türkiye Earthquake, where demand persisted for three weeks.[1]\nWhile we have modeled injuries in other regions with high expected casualties, such as Peru,[2]\nwe expect a much smaller emergency phase in the Bay Area. For this reason, we focused on\npopulation-weighted access losses rather than explicitly modeling injury locations. We have\nclarified this point in the revised manuscript (see line 645).\nrecognizing that hospitals often take months or even years to be repaired. Because people are\ntypically injured within damaged buildings, patient surges after earthquakes generally last only a\nfew days—except in rare extreme cases such as the 2023 Turkiye Earthquake. To focus on long-\nterm access rather than short-term emergency response, we did not model injury locations\ndirectly. Instead, we assumed that patient demand is proportional to population distribution and\nmodeled accessibility accordingly. For the Bay Area, we based our analysis on population-\nweighted access loss and identified the network’s vertices closest to the centroids of census tracts\nto define the set p (Figure 8).\nSecond, the state of the art in earthquake casualty modeling has not advanced significantly in\nrecent decades, and predictions remain highly uncertain—especially in places like California,\nwhere recent damaging earthquakes have not produced large casualty datasets. We are currently\nleading an NSF-funded project (NSF Award #2410291) to address this gap, with a focus on\ndeveloping high-fidelity, empirically grounded casualty models for the Bay Area. This includes\nnew fieldwork and modeling efforts that will inform a dedicated paper focused on spatial injury\ndistributions and emergency care needs. We plan to incorporate the reviewer’s suggestion as part\nof that forthcoming work.\n[1] Ceferino, L., Merino, Y., Pizarro, S. et al. Placing engineering in the earthquake response\nand the survival chain. Nat Commun 15, 4298 (2024). https://doi.org/10.1038/s41467-024-\n48624-3\n[2] Ceferino, L., Mitrani-Reiser, J., Kiremidjian, A. et al. Effective plans for hospital system\nresponse to earthquake emergencies. Nat Commun 11, 4325 (2020).\nhttps://doi.org/10.1038/s41467-020-18072-w\nComment 14: [Page 22] It appears that the potential for any closure of roads after the\nearthquake is not considered in the proposed framework. Past earthquakes have shown that\nhavoc-related jams, toppling of electric lines and commercial pole signs, landslides, surface fault\nruptures, underground pipe ruptures, building façade debris, damages to bridges, flyovers, and\ntunnels have led to the closure of roads after earthquakes. In urgent cases, the roads are closed\nas a part of the disaster response operations and only the emergency vehicles are allowed on\nthe main roads. Furthermore, very often, a scarcity of gas is caused after such earthquakes by\nthe demand surge, which cannot be accommodated quickly. As a result, it becomes a common\nproblem to have vehicles on the sides of the roads left without any gas. In the case of California,\nwhere electric vehicles are more common as compared to other regions, the post-earthquake\nfunctioning of the grid and the likely charging durations may also have a critical impact. In the\npresent investigation, the potential impacts of such effects on the travel time estimates, as well\nas transportation network connectivity, are not taken into account. These should be noted as a\nlimitation of the study to inform the reader properly about the complexity of the subject matter.\nAfter reading your reviews (along with those from the other reviewers), we invested significant\neffort into improving our modeling of transportation infrastructure disruptions in the Bay Area.\nThis became a major component of our revision and is the main reason for the time it took us to\nrespond.\nIn this revised version, we integrated detailed information for over 5,000 bridges in the Bay Area\nand significantly expanded the transportation network model, which now includes approximately\n1.5 million edges and 0.5 million nodes. This refinement substantially increased computational\ndemands: the 5,000 Monte Carlo simulations required for the analysis took about two weeks to\nrun on a laptop equipped with an Apple M2 chip and 64 cores. We ran multiple iterations to\nensure the model was fully debugged and stable.\nThanks to this updated formulation—and your review—we are now able to capture how hospital\nand transportation failures interact to influence post-earthquake hospital accessibility. Our\nrevised analysis highlights several key cascading effects:\n● Widespread transportation failures lead to compound access losses, with travel times\nincreasing by over a factor of 10 in some areas.\n● Some hospitals in the Bay Area may become completely isolated due to bridge failures.\n● Urban communities—particularly in Fremont and Novato—may lose access to essential\nservices due to localized bridge disruptions.\nWe acknowledge that other important factors raised in your comment—such as debris-blocked\nroads, emergency vehicle prioritization, fuel shortages, electric vehicle limitations, and traffic\ncongestion—are not included in this simulation. These are highly relevant and could further\nexacerbate accessibility losses. However, due to a lack of standardized methods and data to\nmodel these phenomena at a regional scale, we did not include them in this analysis. We have\nnow added sentences in the manuscript (in the discussion) explicitly stating these limitations\nand encouraging future work in this direction.\nDespite these limitations, we believe this revised version represents an important step toward\nunderstanding the interdependencies between hospital and transportation networks in post-\nearthquake accessibility. We sincerely thank you for pushing us to deepen the analysis. The\nchanges we made based on your feedback have significantly strengthened the study.\nWe include some of the updated results and manuscript revisions below.\nAbstract (line 15):\nconnectivity data, we analyze 76 hospitals (426 buildings with 16,639 beds) and 5,163 bridges\nwithin a vast network of ∼1.5 million edges and ∼0.5 million nodes [...] Widespread transportation\nfailures further restrict access, increasing regional travel times by 177% and exceeding 1000% in\nparts of East Bay, potentially fully isolating hospitals and entire urban communities. These findings\nunderscore the urgent need for resilient healthcare and transportation infrastructure to mitigate\nlife-threatening disruptions following major earthquakes.\nIntroduction (line 80):\nTo fill this critical gap, we investigate, for the first time, joint failures of healthcare and\ntransportation networks across the San Francisco Bay Area after a major earthquake. By\nexamining diverse urban communities near active seismic faults—often underrepresented in\nprevious studies—this research provides valuable insights into post-earthquake healthcare\naccess, particularly relevant for earthquake-prone regions worldwide with diverse populations\nand similarly vulnerable hospitals and bridges, such as those in the U.S., Japan, and Türkiye.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at this\nscale using publicly available data on both hospital and transportation infrastructure. Whereas\nprior work has focused on individual facilities[20-23] or small systems[42-46]—often relying on\nsynthetic data—our approach couples regional seismic risk models with large-scale network\nanalysis to capture interdependent failures across an entire metropolitan area. By integrating\nvulnerability data from 426 hospital buildings and 5,163 bridges, and simulating disruptions across\na transportation network with approximately 1.5 million edges and 0.5 million nodes, we offer one\nof the most extensive assessments to date of how earthquakes affect healthcare access. This\nstudy advances the state of the art in regional risk modeling globally, offering a scalable,\ncomputationally intensive framework that supports risk-informed decision-making in other high-\nrisk urban areas.\nNew Section on Post-earthquake Bridge Functionality (line 196):\nOur risk analysis model predicts that 1,469 bridges out of 5,163 would be damaged due to the\nearthquake scenario (see Methods). Consequently, 3,693 bridges (72%, standard deviation:\n17%) are expected to remain undamaged and fully operational (Figure 3). Some damaged\nbridges could continue operating, albeit at reduced capacities. Under our “baseline scenario”,\nwhere only bridges with at most slight damage remain operational, a total of 3,964 bridges\n(77%, standard deviation: 15%) would function. In a more optimistic “favorable scenario”, where\nbridges with at most moderate damage also remain partially operational, 4,069 bridges (79%,\nstandard deviation: 14%) could provide service. In an idealistic scenario, which assumes that\nbridges even with extensive damage retain emergency functionality, 4,527 bridges (88%,\nstandard deviation: 11%) would remain operational.\ncontributors openstreetmap.org/copyright.\nSimilar to hospitals, Alameda County faces the most severe transportation impacts (Figure 3,\nTable 2). Under the baseline scenario, Alameda retains only 44% functional bridges (from 642\ndown to 282). Marin County is second most impacted, retaining 64% (from 195 to 125\nbridges). Additionally, estimates of reductions in bridge travel speeds (see Methods)—\ncalculated from their damage probabilities—highlight Alameda’s higher vulnerability due to\nproximity to the Hayward Fault rupture (Figure 3, Table 2).\nFigure 3. [...] Lower left: Probability distribution of fully functional bridges under baseline (slight),\nfavorable (moderate), and idealistic (extensive) damage thresholds. Lower right: Spatial\ndistribution highlighting bridges with post-earthquake travel capacities below 75%. Results\ngenerated from 5,000 Monte Carlo simulations.\nRevised findings on Accessibility (line 223):\nAt a more detailed neighborhood scale, these disruptions are even more pronounced (Figure 4).\nWe identified six densely populated zip codes (each exceeding 15,000 residents, labeled #1 to\n#6 in Figure 4) facing substantial reductions in healthcare access. The most severely impacted is\nNovato (#1, Marin County), where travel times increase nearly 25-fold, from 7.3 to 185.5 minutes,\naffecting approximately 18,000 residents. Similarly, a Fremont zip code (#6, Alameda County)\nwith roughly 66,000 residents experiences an eightfold increase (from 8.4 to 42.2 minutes). Other\nsignificantly impacted zip codes in Richmond (#4), Oakland (#2 and #5, Alameda County), and\nSan Jose (#3, Santa Clara County) face travel time increases of 10, 11, 9, and 11 times their pre-\nearthquake levels, respectively. These results underscore the dramatic reshaping of healthcare\naccess throughout East Bay communities along the earthquake rupture.\nFinally, we explored the relative contributions of hospital and transportation infrastructure\ndisruptions through scenario analyses (Figure 4). We compared the baseline (None, no\ninfrastructure disruptions) against scenarios modeling probabilistic damage only to transportation\ninfrastructure (Transp., hospitals fully resilient), only to hospital infrastructure (Hosp.,\ntransportation fully resilient), and simultaneous probabilistic disruptions to both (Transp. & Hosp.).\nWhen considering disruptions only to transportation infrastructure (Transp.), average Bay Area\ntravel times increase by 41% (from 6.1 to 8.6 minutes), notably less than the combined scenario\n(Transp. & Hosp., 177% increase). Conversely, modeling only hospital infrastructure disruptions\n(Hosp.) yields a 79% increase (from 6.1 to 10.9 minutes), highlighting greater relative fragility in\nhospital networks.\nAt localized urban scales, the compounding effects of simultaneous transportation and hospital\ninfrastructure failures lead to disproportionately severe impacts (Figure 4). For example, as\nmentioned earlier, in the most severely impacted zip code (Novato, labeled #1 in Figure 4), travel\ntimes dramatically increase from 7.3 to 185.5 minutes under combined disruptions (Transp. &\nHosp.), compared to only 14.1 minutes when transportation disruptions are excluded (Hosp. only).\nSimilarly, for other highly affected zip codes (labeled #2 to #6 in Figure 4), travel-time ratios\nnotably decrease—from 11, 11, 10, 9, and 8 under combined disruptions, to 6.4, 3.1, 6.1, 4.7, and\n3.4 when transportation disruptions are not considered—highlighting the critical influence of\ncompounding infrastructure failures on healthcare access.\n19\ncontributors openstreetmap.org/copyright.\nFigure 4: Access to functional acute care hospitals in the Bay Area after the earthquake.\nUpper left: Post-earthquake (Post-EQ) increases in travel time at the zip-code level compared to\npre-earthquake (Pre-EQ) conditions, highlighting densely populated areas that are most\nseverely impacted. Upper right: Ratios of post- to pre-earthquake travel times to the closest\nacute care hospitals. Lower right: Distribution of travel times per zip code under four scenarios:\nNone (no infrastructure disruptions), Transp. (only transportation infrastructure is vulnerable),\nHosp. (only hospital infrastructure is vulnerable), and Transp. & Hosp. (both transportation and\nhospital infrastructures are vulnerable). Lower left: Ratios of post- to pre-earthquake travel times\nwhen only hospital infrastructure (Hosp.) is vulnerable. Results generated from 5,000 Monte\nCarlo simulations.\nNew section on Isolated Communities and Hospitals (line 252):\nanalyzed travel volumes to the closest acute care hospitals before and after the earthquake.\nFigure 5 shows pre-earthquake road usage, with line thickness representing travel volume. Roads\nin brown highlight those whose usage falls above the 90th percentile based on pre-earthquake\nconditions, emphasizing the most critical travel routes. As expected, the highest-usage roads prior\nto the earthquake were located near hospitals, especially in densely populated areas with fewer\nhospitals. For instance, communities in Fremont (#6 in Figures 4 and 5) are served by only two\nhospitals, while Richmond (#4) relies on just one.\nFigure 5 also displays post-earthquake road usage, using the same pre-earthquake 90th\npercentile threshold to highlight heavily traveled roads. After the earthquake, patient travel\npatterns shift significantly, with many communities forced to travel longer distances along major\ncorridors. For example, residents in Oakland (#2 and #5 in Figures 4 and 5), who previously relied\non nearby hospitals, will now have to travel west to the San Francisco Peninsula or east to Walnut\nCreek due to simultaneous disruptions in both hospital and transportation infrastructure. These\nshifts help explain the steep increases in travel times observed in East Bay communities along\nthe rupture zone.\nFour major bridges connect the East and West Bay: the Richmond–San Rafael, Oakland–San\nFrancisco Bay, San Mateo–Hayward, and Dumbarton bridges. Before the earthquake, no patients\nneeded to cross these bridges to reach their nearest acute care hospital (Figure 5). After the\nearthquake, however, these bridges become critical, with travel volumes increasing to 3.6, 9.3,\n6.3, and 13.6 times the pre-earthquake 90th percentile values—reflecting the large-scale\nredistribution of healthcare demand.\nOur analysis also revealed a more complex post-disaster phenomenon: micro-scale isolation of\nhospitals and communities due to localized bridge failures. For example, the hospital serving the\nmost severely impacted zip code in Novato (#1 in Figures 4 and 5), which has 64 beds, depends\nentirely on a single bridge for access. If this bridge fails, the hospital becomes inaccessible,\nincreasing travel times from 7.3 to 185.5 minutes for the surrounding population.\nMore concerning, we found that urban neighborhoods near Fremont (#6) could become fully\nisolated (Figure 5). In one area, failure of three bridges would trap one part of the neighborhood;\nin another, a different set of three bridge failures would isolate the remaining part. These\ncommunities would lose access not only to hospitals but also to other essential services such as\ngrocery stores and pharmacies—illustrating how cascading infrastructure failures can sever\nlifeline access in disaster scenarios.\ncontributors openstreetmap.org/copyright.\nFigure 5: Mobility to reach the closest functional acute care hospital in the San Francisco Bay\nArea. Upper left: Pre-earthquake travel volumes to the closest acute care hospitals. Numbers 1\nto 6 indicate the hospitals serving the dense zip codes with the highest post-earthquake\nincreases in travel time. Upper right: Projected travel volumes after the earthquake, showing\nmajor shifts in patient mobility. The red-shaded corridor illustrates how Oakland residents (#2\nand #5) must travel west to the Peninsula or east to Walnut Creek due to hospital and\ntransportation disruptions. Lower left: The hospital serving zip code #1 (Novato) relies entirely\non a single bridge; if the bridge fails, all access to its 64 beds is lost. Lower right: Community\nnear zip code #6 (Fremont), where the southern and northern sections become fully isolated if\nthree different bridges fail in each area. Results are based on 5,000 Monte Carlo simulations of\npost-earthquake patient mobility.\nfragility model for structural wall buildings. However, the original source of this reference model,\nas well as the related building typology, is unclear. Therefore, it is not easy to interpret the\nmeaning of this comparison.\nThank you for pointing this out. We fully agree with the reviewer. This plot was confusing and\ndid not add much relevant information. We removed it.\nComment 16: Reviewer #1 (Remarks on code availability):\nI downloaded the code and checked its contents very briefly. It contains the related files. I did\nnot run it to reproduce the results.\nWe have uploaded updated code to the same data repository. We carefully prepared a README\nwith step-by-step instructions to ensure that all analysis results presented in the paper can be\nreproduced by running the provided code. This updated version contains the new model version.\nReviewer #2 (Remarks to the Author):\nOverall response:\nWe thank the reviewer for their feedback and recognize that the previous version of the\nmanuscript did not sufficiently convey the motivation and contributions of our study. We have\ntaken the comments seriously and used them to substantially revise and strengthen the work.\nWe also note that concerns raised in this review, especially regarding the motivation and novelty\nof the study, were not shared by the other reviewers, whose feedback was more positive and\nencouraging. Nonetheless, we carefully considered all reviewer input and undertook a major\nrevision effort.\nThe delay in resubmission reflects the time required to expand the analysis and clarify our\ncontributions. In particular, we significantly broadened the scope of the study by fully integrating\ntransportation infrastructure into the modeling of post-earthquake hospital accessibility. This\naddition allowed us to identify new critical outcomes—such as the potential isolation of a hospital\nand a community (“urban island”)—that were not captured in the original version. We also\nintroduced new metrics of accessibility, conducted sensitivity analyses, and revised the\nintroduction and discussion to better position the study within the broader literature.\nAll specific responses are provided in blue text, and corresponding changes in the revised\nmanuscript are shown in red. We hope these revisions demonstrate the rigor and value of the\nupdated study.\nComment 1: As the authors know, one of the most critical elements of any study is the\nmotivation of the work. The authors motivated the work by indicating that, unlike the past studies\non hospital networks, this study focuses on a community exposed to earthquakes only within a\nfew kilometers of them. First, the papers cited by the authors include hospitals a few kilometers\nfrom the hazard. Second, the justification overall is very weak and does not represent\nuniqueness. The study is motivated by the hospital being a few kilometers from the hazard,\nwhich is irrelevant - not to mention that this was the case in past studies. Furthermore,\nassessing healthcare networks under earthquakes has been studied quite a bit using more\nrigorous approaches. It is hard to see valuable contributions in this study.\nResponse 1: Thank you very much for the constructive feedback. We appreciate the opportunity\nto clarify the motivation and contribution of our work. We have revised the introduction of the\nmanuscript to better emphasize these points.\nOur motivation stems from the unique combination of challenges present in the San Francisco\nBay Area, including:\n25\n(a) a high concentration of seismically vulnerable hospitals, many of which are pre-1973\nstructures located near active faults;\n(b) a complex and interconnected healthcare network that spans county and jurisdictional\nboundaries; and\n(c) spatially heterogeneous seismic hazards and vulnerabilities across communities.\nThis combination creates critical management challenges. For example, our results show that\nhospitals located near rupture faults face higher risks of damage, and their potential loss would\ndisproportionately reduce access to care in nearby communities. From the perspective of regional\nhealthcare managers (e.g., HCAI, formerly OSHPD), addressing earthquake impacts requires a\nregional risk approach—one that goes beyond individual building assessments to account for\nsystem-wide hospital vulnerabilities and transportation disruptions, as modeled in the current\nversion of this study, to capture changing access patterns across the network.\nWe have clarified in the manuscript (see changes to Introduction below) that the intent is not to\nclaim uniqueness based solely on hospital proximity to faults. Rather, we emphasize that this\nproximity, combined with widespread vulnerability and regional interdependence, demands a\nsystems-level analysis. To our knowledge, this is the first study to evaluate the performance of\na realistic regional healthcare network using publicly available, high-resolution data on both hospital\ninfrastructure and transportation systems.\nIn terms of methodology, we recognize that high-fidelity simulation models have been developed\nto study the earthquake dynamics of individual hospitals. These are valuable for understanding\ndetailed functional disruptions but are not feasible for regional-scale analyses due to their\nintensive data requirements and computational demands. In contrast, our model is designed to\ncapture interdependent failures—such as simultaneous damages to hospitals and critical\nbridges—at a regional scale, while balancing spatial coverage, data availability, and\ncomputational feasibility.\nIn our previous work, we have developed discrete event simulation models to capture detailed\nhospital functionality, which can be coupled with structural models to analyze patient flow and\noperations at the building level [1]. However, applying such models across an entire region\nremains impractical. This study therefore adopts a campus-level functionality model, allowing us\nto compare hospital capacity losses and assess how those losses—combined with bridge\ndamage—affect access to care.\nOur regional modeling approach represents the state of the art in large-scale healthcare system\nanalysis, integrating detailed hospital and transportation vulnerability data, seismic hazard\nmodels, and transportation network connectivities to assess post-earthquake access to care. To\nachieve this level of integration and fidelity using publicly available data, we developed a modeling\nand computational framework capable of simulating interdependent failures across hundreds of\nfacilities and thousands of network links.\nunderscores the technical effort involved in performing this level of analysis and highlights the\npractical challenges of scaling such models to other high-risk urban regions.\nFinally, while we appreciate the reviewer’s concerns, we respectfully disagree with the\nassessment that the study lacks value. We believe the scale, integration, and policy relevance of\nour findings—such as the identification of communities with disparate access to healthcare and\neven isolated hospitals and communities—represent a meaningful contribution to the literature. If\nthere are specific references the reviewer believes have already addressed this problem at a\nsimilar level of scope and resolution, we would be happy to engage with them. Based on our\ncomprehensive literature review, we are confident that this study advances the state of the art in\nregional healthcare system resilience under seismic risk.\nPlease see the new version of the Introduction that is revised to highlight better our contributions\naccording to your comments (lines 50, 57, 63, and 86):\nRecognizing these vulnerabilities, this paper investigates the effects of future earthquakes\non healthcare access in the entire San Francisco Bay Area, California. [...] \nYet, hospitals do not function in isolation—particularly in dense urban areas [...].\nFailures in transportation infrastructure significantly compound healthcare disruptions [...]\nThese interconnected disruptions underscore the urgent need to evaluate joint\nvulnerabilities within healthcare and transportation infrastructure.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at\nthis scale using publicly available data on both hospital and transportation infrastructure.\nWhereas prior work has focused on individual facilities[20-23] or small systems[42-46]—\noften relying on synthetic data—our approach couples regional seismic risk models with\nlarge-scale network analysis to capture interdependent failures across an entire\nmetropolitan area. By integrating vulnerability data from 426 hospital buildings and 5,163\nbridges, and simulating disruptions across a transportation network with approximately 1.5\nmillion edges and 0.5 million nodes, we offer one of the most extensive assessments to\ndate of how earthquakes affect healthcare access. This study advances the state of the\nart in regional risk modeling globally, offering a scalable, computationally intensive\nframework that supports risk-informed decision-making in other high-risk urban areas.\n[1] Merino Y, Ceferino L, Pizarro S, de la Llera JC. Modeling hospital resources based on global\nepidemiology after earthquake-related disasters. Earthquake Spectra. 2024;40(4):2402-2429.\ndoi:10.1177/87552930241262788\nComment 2: In addition to the lack of sufficient motivation, the author did not utilize the state-of-\nthe-art in healthcare resilience analysis and used a simplistic approach in their assessment. For\nexample, it is assumed that damage to the building is a proxy for bed availability and resilience,\nwhich is not true. Many recent studies describe healthcare resilience as a function of physical\ninfrastructure, staff, and stuff. So, it appears that the authors are going back in time to use a\ndefinition that is no longer recognized in the research community.\nWe thank the reviewer for this important point and the opportunity to clarify the scope of our\nmodeling framework. We fully recognize that healthcare resilience is multidimensional, and that\nseminal work—including that of Dr. Mitrani-Reiser—has expanded the definition of hospital\nfunctionality to include structure, staff, and stuff. In fact, we referenced this work in the first version\nof the paper [1].\nAs noted in our literature review, these innovative models have been developed for analyses on\nsingle hospital buildings, where blueprints, space, and staff information are available to construct\na high-fidelity finite element model of the structure and analyze how different spaces of the\nstructure lose functionality. We have actually extended these high-fidelity modeling techniques to\nanalyze single hospitals in Chile using discrete event simulations [2]. These models can often be\nvery computationally expensive and not able to handle uncertainty exploration.\nWhile these models are powerful at the single-building scale, they do not work at the regional\nlevel because of the lack of data and the enormous demands for computational power. We are\nmodeling 76 hospitals with +400 buildings (not just one) in the Bay Area. For these types of\nproblems, we must change the approach as we are not interested in capturing how functionality\nchanges in each specific room of a building but instead in the relative resilience of one hospital\ncampus versus another. We created these regional models for hospitals a few years ago together\nwith Dr. Mitrani (who created the models you are referring to) to analyze effective plans for hospital\nsystem response to earthquake emergencies in the city of Lima, Peru [3]. In the field of regional\nrisk modeling, we create a model based on the available vulnerability information. In the Bay Area,\nwe created a regional risk model based on the available information on structural type, building\nheight, year of construction, structural performance category, and non-structural performance\ncategory. This is the state of the art in regional risk modeling as we are interested at loss of\nfunctionality at the whole hospital campus level and not at each hospital room. We acknowledge,\nthough that these models could be improved if high-resolution information for all hospitals would\nbecome available, which has not happened, unfortunately.\n[1] Jacques CC, McIntosh J, Giovinazzi S, Kirsch TD, Wilson T, Mitrani-Reiser J. Resilience of\nthe Canterbury Hospital System to the 2011 Christchurch Earthquake. Earthquake Spectra.\n2014;30(1):533-554. doi:10.1193/032013EQS074M\n[2] Merino Y, Ceferino L, Pizarro S, de la Llera JC. Modeling hospital resources based on global\nepidemiology after earthquake-related disasters. Earthquake Spectra. 2024;40(4):2402-2429.\ndoi:10.1177/87552930241262788\n28\n[3] Ceferino, L., Mitrani-Reiser, J., Kiremidjian, A. et al. Effective plans for hospital system\nresponse to earthquake emergencies. Nat Commun 11, 4325 (2020).\nhttps://doi.org/10.1038/s41467-020-18072-w\nWe rewrote this part in the introduction to make this point clearer (line 50):\nRecognizing these vulnerabilities, this paper investigates the effects of future\nearthquakes on healthcare access in the entire San Francisco Bay Area, California.\nPrevious research has largely focused on individual hospital vulnerability, using methods\nsuch as structural engineering analyses, performance-based assessments, and fault-tree\nevaluations to examine structural and non-structural damages within isolated\nfacilities.[20–23] Other studies evaluated patient treatment dynamics and medical\nresource demands through flow models and discrete event simulations in post-earthquake\nscenarios but are similarly limited to single-building analyses.[24–27] Yet, hospitals do not\nfunction in isolation—particularly in dense urban areas—as demonstrated by seismic\nevents in Chile, New Zealand, and Japan.[21, 28–31] Failures in individual hospitals can\ntrigger broader network impacts, overwhelming remaining facilities and forcing patients to\ntravel greater distances for care, severely exacerbating health outcomes for critically\ninjured individuals. Thus, understanding healthcare resilience requires examining\ninterconnected failures across healthcare and transportation infrastructure.[32–34]\nComment 3: Moreover, the paper suffers from many technical issues/mistakes, which causes\nthe analysis to be unsound. For example, their predictions show that many hospitals will\nexperience violent shaking at a scale not seen in over a century under a peak ground\nacceleration of 0.2. This is not possible. A peak ground acceleration of 0.2 is extremely low and\nis expected to cause only slight damage. The literature is overwhelmed with studies that show\nhow a 0.2 PGA typically causes slight damage to different archetypal structures.\nComment 3: We appreciate the reviewer’s attention to this point and the opportunity to clarify. It\nwas unclear whether the reviewer’s concern is that 0.2g is not a possible level of ground\nshaking, or that 0.2g does not constitute unusually high shaking for hospitals in the Bay Area.\nTo clarify, we reference 0.2g only as an illustrative example—to note that many hospitals in the\nregion have not experienced even this moderate level of shaking since the 1906 earthquake.\nImportantly, our risk analysis does not rely on this deterministic value. As described in the\nMethods section, our analysis is based on probabilistic seismic hazard models, which sample the\nfull distribution of ground motion intensities across a wide range of scenarios. For damage and\naccessibility assessments, we use spectral acceleration values at building-specific periods rather\nthan PGA.\nTo avoid confusion, we have revised the Methods text to clarify that 0.2g was mentioned purely\nas a historical reference point, and that our modeling approach is fully probabilistic and consistent\nwith established regional risk frameworks (line 469):\nbeen extensively studied to inform resilience policy-making in the Bay Area.47 The rupture\ngeometry was obtained from the Uniform California Earthquake Rupture Forecast\n(UCERF) 2.72 The earthquake ruptures the Hayward South and North sections over a\ntotal length of ∼110 km. Estimates of shallow shear wave velocities (averages at the top\n30 m of soil) are utilized over the entire Bay Area.73 With this information, we built the\njoint probability distribution of shaking intensities π(i) in R2D. We utilized a state-of-the-art\nground motion model74 for shallow crustal earthquakes to estimate medians and\nlogarithm standard deviations of i. i’s uncertainty is divided into two components.75 The\nfirst component captures between-event uncertainty and affects the entire region equally,\nbut it varies per intensity measure type, e.g., peak ground acceleration versus spectral\nacceleration. The first component captures correlation across different intensity\nmeasures.76 The second component captures within-event uncertainty and affects the\nentire region and intensity measure types differently. This component captures spatial\ncorrelation and correlation across different intensity measure types. We use a\ncomputationally efficient method to account for the second component.[62, 77] As stated\nearlier, we sampled 5,000 realizations of i and show expected values E(i) for the entire\nregion (Figure 1).\nWe have also clarified the manuscript to better explain that a PGA of 0.2g is not only plausible,\nbut expected for hospitals located near active faults. For magnitude 7.0 earthquakes at short fault\ndistances—as is the case for many sites along the Hayward Fault—PGAs well above 0.2g are\nconsistent with empirical ground motion prediction equations. As illustrated in Figure 1, several\nhospitals in our study area are within 5 km of the Hayward Fault, making higher levels of ground\nshaking entirely realistic.\nHistorical earthquake records further support this point. While the Bay Area has experienced only\nmoderate earthquakes in recent decades, most of the 76 hospitals in our dataset have not been\nexposed to shaking above 0.2g since the 1906 event. This is the motivation for referencing 0.2g\nin the text: even moderate levels of shaking would represent a significant increase over the\nhistorical experience of many healthcare facilities in the region.\nTo prevent further confusion, we revised the manuscript to clarify that the 0.2g value is used as a\nhistorical reference point, not as a basis for damage estimation. We also emphasize that our\ndamage predictions are derived from spectral acceleration values at building-specific periods, and\nthat the analysis accounts for the close proximity of hospitals to the Hayward Fault and the\ncorresponding hazard expected from a magnitude 7.0 event (line 149).\nWe modeled the rupture geometry (see Methods) and found that 10 acute care hospitals\n30\nwith 2167 beds (13% of the Bay’s total) are within just 5 km of the projected rupture. Our\nshaking intensity estimates indicate that many hospitals could experience levels of\nground motion not observed in recent earthquakes (See Methods). On average, we\npredict 51 hospitals will experience peak ground accelerations above 0.2g (Figure 2). By\ncomparison, the 1989 M 6.9 Loma Prieta Earthquake—previously the strongest since\nthe devastating 1906 M 7.9 San Francisco Earthquake—subjected only 14 hospitals to\nsimilar shaking intensities (Figure 2). Supplementary Figure 2 further contextualizes\nthese findings, illustrating how recent events such as the 2014 Napa Earthquake (M 6.0)\nexposed just three hospitals to significant shaking (>0.2g). In contrast, the historic 1906\nearthquake exposed nearly the entire portfolio (72 out of 76 hospitals)\nComment 4: In addition, the authors noted that many hospitals will have a probability of\ndamage above 0.25. What is the significance of 0.25 as a damage probability? and What type of\ndamage corresponds to 0.25 or more? Damage probability ranges from slight to moderate to\nextensive to complete, and each plays a role in quantifying healthcare functionality. To list that\nthe damage probability is 0.25 has no structural engineering relevance. In earthquake\nengineering, there is no relevance in saying that many hospitals had a damage probability of\nmore than 0.25. The reviewer recommends that the authors look at various FEMA documents\non seismic performance assessment to become more familiar with damage assessment\napproaches, including the various engineering demand parameters used for seismic evaluation\nof buildings and hospitals.\nComment 4: We thank the reviewer for this comment and for recommending the FEMA guidance\ndocuments. These are indeed excellent resources, and we are well acquainted with them. The\nlead author has used FEMA P-58, FEMA P-695, and HAZUS extensively for both research and\nteaching, including in the graduate course “Disaster Risk Analysis” at UC Berkeley. One co-author\nis a risk specialist with years of experience applying these frameworks to develop regional risk\nmodels and policy interventions in collaboration with the World Bank. Another co-author has\ncontributed to the development of NSF-funded tools at the NHERI SimCenter that operationalize\nthese frameworks for both regional and single-building risk assessments. We have referenced\nthese methodologies throughout our work and remain committed to aligning with best practices\nin the field.\nRegarding the reviewer’s specific point: the mention of a damage probability threshold of 0.25\nwas intended solely as an illustrative example—to demonstrate how the likelihood of damage\nincreases with proximity to the fault. It was not used as a cutoff or performance threshold in the\nactual analysis. As detailed in the Methods section, we compute full probability distributions of\nmultiple damage states for each hospital building using fragility functions and combine these with\na fault tree to assess hospital functionality.\nWe understand that our use of the 0.25 value may have caused confusion, and we have revised\nthe manuscript to make it clear that this number was only used for communication purposes, not\nas a substitute for engineering demand parameters or damage state classifications. Our\n31\nunderlying modeling framework is aligned with established seismic performance assessment\napproaches and incorporates state-based damage probabilities in a probabilistic risk analysis. To\nimprove clarity, we revised the Methods section to make this explicit. Below, we provide the\nrevised text in plain format, noting that the full mathematical expressions and formatting appear\nproperly in the main manuscript (line 410):\nHospitals can rapidly lose functionality at early stages of structural and non-structural\ndamage, as observed in the 2023 M 7.8 Kahramanmaraş Earthquake in Turkey, the 2011\nM 6.1 Christchurch Earthquake in New Zealand, and the 2010 M 8.8 Maule Earthquake in\nChile. We consider that damage thresholds, ds and dn, for the structural and non-\nstructural components, respectively, trigger the disruption of hospital functionality—that is,\nif either fails, the hospital loses functionality.\nWe estimate the probabilities of not exceeding these thresholds as:\n● pₖˢ = π(Dₖˢ ≤ ds | Iₖˢ = iₖˢ), and\n● pₖⁿ = π(Dₖⁿ ≤ dn | Iₖⁿ = iₖⁿ),\nwhich can be evaluated using earthquake fragility functions. We then model functionality\nas the intersection of these two events, meaning the hospital component remains\nfunctional only if both structural and non-structural elements perform adequately after the\nearthquake. Since Dₖˢ and Dₖⁿ are assumed conditionally independent, Fₖ (hospital\nbuilding functionality) becomes a Bernoulli random variable with probability pₖˢ × pₖⁿ. Accordingly, the joint probability of functionality given the data d is:\nπ(f | d) = ∏ₖ=1^m [ (pₖˢ × pₖⁿ)^fₖ × (1 - pₖˢ × pₖⁿ)^(1 - fₖ) ] (Equation 4)\nThe functionality of each hospital depends on the structural and non-structural\ncomponents, as described in Equation 4. The hospital portfolio includes various levels of\nSPC (Structural Performance Category) and NPC (Non-structural Performance Category),\nwhich influence the final functionality outcome.\nWe also estimate the probability distribution of the total number of functional beds Bₜ\nacross the region, computed as:\nBₜ = ∑ βₖ × Fₖ (Equation 5)\nwhere βₖ is the number of beds at hospital building k (assumed fully functional before the\nearthquake).\nTo account for hospitals with multiple buildings, we estimate the distribution of the total\nnumber of functional beds Bₕ for hospital h, where 𝓀ₕ is the set of buildings belonging to\nhospital h:\nIn addition, we believe that the previous version of the paper may have overemphasized the\n0.25 value, which may have led some readers to interpret it as a threshold used in the\ncomputation of hospital functionality. To avoid this misunderstanding, we have removed this\nreference from the main text.\nComment 5: Concerning this comment, the authors note that their analysis predicts that 8,501\nbeds will be lost throughout the Bay, and such predictions are based on slight damage (justified\nby previous studies that used slight damage to indicate loss of beds). Again, the literature is way\npast the idea of using damage to indicate bed losses and that stuff, staff, and physical systems\nshould be used to indicate bed losses. In addition, many studies show that hospitals continue to\noperate beyond slight damage, including the studies referenced by the authors. None of the\nstudies cited by the authors show that hospitals will lose functionality at slight damage. The\nStEER report cited by the authors indicates that only fully collapsed or severely damaged\nhospitals were evacuated after the Turkey EQ event. Unfortunately, the authors used this\nassumption to draw the study's main conclusions. Using slight damage drastically skews the\nresults towards showing significant bed losses, which is very unrealistic. Also, the authors note\nthat services within hospital buildings will be highly disrupted – a statement with no basis since\nthe authors did not model any hospital units or services.\nResponse 5:\nWe refer back to our response to Comment 1, where we explain that we do not apply the\n“structure, staff, and stuff” framework in this study because, although valuable, it is not scalable\nto the regional level given current data limitations. While we acknowledge the broader dimensions\nof healthcare resilience, our study focuses on structural and non-structural damage as proxies for\nloss of hospital functionality—an approach consistent with the current state of the art in regional\nseismic risk modeling.\nThe lead author has participated in post-earthquake field investigations in Türkiye, Ecuador, and\nNew Zealand and has directly observed instances where hospitals experienced disruption of\nservices even at slight damage levels. In fact, the lead author coordinated the hospital section of\nthe StEER report on the 2023 Türkiye Earthquake. Contrary to the reviewer’s comment, that\nreport does not state that “only fully collapsed or severely damaged hospitals were evacuated.”\nOur fieldwork, including interviews with hospital staff, documented several cases where hospitals\nwith slight or moderate damage lost functionality or required partial shutdowns due to non-\nstructural failures, dislodged equipment, or internal hazards. These findings are described in our\npeer-reviewed article [1]. We made the following notes on the paper and added references to\nthese cases (line 172):\nstructural damage exceeds a threshold of slight damage—conditions often shown to\ndisrupt hospital services (see Methods).[28-31]\n[1] Ceferino, L., Merino, Y., Pizarro, S. et al. Placing engineering in the earthquake response\nand the survival chain. Nat Commun 15, 4298 (2024). https://doi.org/10.1038/s41467-024-\n48624-3\n[28] Ardagh, M. W. et al. The initial health-system response to the earthquake in Christchurch,\nNew Zealand, in February, 2011. The Lancet 379, 2109–2115 (2012). URL http://dx.doi.org/10.\n1016/S0140-6736(12)60313-4. Publisher: Elsevier Ltd ISBN: 1474-547X (Electronic)\\r0140-\n6736 (Linking).\n[29] Kirsch, T. D. et al. Impact on hospital functions following the 2010 Chilean earthquake.\nDisaster medicine and public health preparedness 4, 122–128 (2010). ArXiv: 1011.1669v3\nISBN: 1938-744X (Electronic)\\r1935-7893 (Linking).\n[30] Shimoto, M. et al. Hospital Evacuation Implications After the 2016 Kumamoto Earthquake.\nDisaster Medicine and Public Health Preparedness 16, 2680–2682 (2022). URL https://www.\ncambridge.org/core/product/identifier/S1935789322000258/type/journal_article.\n[31] Achour, N. & Miyajima, M. Post-earthquake hospital functionality evaluation: The case of\nKumamoto Earthquake 2016. Earthquake Spectra 36,\nWe do recognize that there is uncertainty in defining the precise threshold of functionality loss,\nespecially in crisis settings. In some extreme situations, hospital staff were able to creatively adapt\nby cleaning up debris and isolating safe areas to continue providing care despite building damage.\nThese heroic efforts, while admirable, also underscore the risks involved for both staff and\npatients.\nTo address this uncertainty and better reflect the range of plausible responses, we have added a\nsensitivity analysis that explores alternative (higher) thresholds for functionality loss. We label\nthese scenarios “favorable” and “idealistic,” as we believe they represent optimistic assumptions\nthat may not hold in a context like the Bay Area, where liability, regulatory, and safety concerns\nmay prevent continued operation under damaged conditions (line 169).\nOur risk analysis predicts a substantial loss of hospital capacity throughout the\nBay Area following the earthquake scenario (see Methods). We estimate a loss of 8,165\nhospital beds, resulting in only 51% of total acute care beds remaining functional\n(standard deviation: 21%). This significant reduction in capacity is highly uneven across\nthe region (Figure 3, Table 1). Our baseline predictions assume hospitals lose\nfunctionality when structural or non-structural damage exceeds a threshold of slight\ndamage (see Methods). These damage conditions are often shown to disrupt hospital\nservices (see descriptions of multiple damage levels in Supplementary Tables 3 and 4).[\n21, 28–31] We also analyzed more optimistic scenarios with moderate (“favorable”) and\nextensive (“idealistic”) damage thresholds, resulting in increased overall functionality of\n79% and 93%, respectively (Figure 3 and Supplementary Table 5). However, empirical\n34\nevidence supports our baseline assumption, as hospitals often lose operations at early\nstages of damage. [21, 28–31]\nFigure 3. Post-earthquake functionality of hospitals and bridges across the Bay Area.\n[...] Probability distribution of functional acute care beds under baseline (slight), favorable\n(moderate), and idealistic (extensive) damage thresholds.\nSupplementary Table 5. Predicted post-earthquake hospital bed capacities across Bay Area counties\nunder thresholds of moderate (favorable) and extensive (idealistic) damage scenarios. The numbers in\nparentheses indicate the percentage in proportion to the pre-earthquake capacity.\nFavorable Idealistic\nCounty Mean Std. Dev. Mean Std. Dev.\nAlameda 1,743 (51%) 748 (24%) 2,635 (82%) 554 (17%)\nContra Costa 1,372 (75%) 378 (22%) 1,649 (94%) 188 (11%)\nMarin 482 (71%) 159 (25%) 581 (93%) 84 (13%)\nSan Francisco 3,258 (89%) 502 (14%) 3,547 (98%) 173 (5%)\nSan Mateo 1,269 (86%) 229 (16%) 1,390 (96%) 120 (8%)\nSanta Clara 3,512 (80%) 725 (17%) 4,068 (94%) 346 (8%)\nSolano 636 (88%) 116 (16%) 705 (98%) 50 (7%)\nSonoma 537 (90%) 64 (11%) 573 (98%) 26 (4%)\nTotal 13,129 (79%) 2,583 (16%) 15,492 (93%) 1,271 (8%)\nWe also appreciate that the reviewer is familiar with the “structure, staff, and stuff” model. While\nit brings valuable insight, we note that this framework still does not model human behavior, such\nas staff decision-making or willingness to work in damaged conditions—factors that play a critical\nrole in hospital functionality. To date, these behaviors remain challenging to represent accurately\nin either building-level or regional modeling frameworks. We believe that more research is needed\nin this area to enable their integration into future probabilistic risk models.\nFinally, we note that loss of “stuff” (e.g., medical equipment and supplies) is often directly linked\nto damage to non-structural components or structural failures in specific hospital zones. Even in\nhigh-fidelity single-building models, damage remains the primary driver of functionality loss, as\nconfirmed by our field deployments and multiple case studies.\nComment 6: Another significant issue is that bridge damage and failure analysis are not\nincluded in determining travel time. The travel time calculated in the paper can not be correct\ndue to the lack of bridge failure analysis.\nResponse 6: After reading your reviews (along with those from the other reviewers), we invested\nsignificant effort into improving our modeling of transportation infrastructure disruptions in the Bay\nArea. This became a major component of our revision and is the main reason for the time it took\nus to respond.\nand significantly expanded the transportation network model, which now includes approximately\n1.5 million edges and 0.5 million nodes. This refinement substantially increased computational\ndemands: the 5,000 Monte Carlo simulations required for the analysis took about two weeks to\nrun on a laptop equipped with an Apple M2 chip and 64 cores. We ran multiple iterations to ensure\nthe model was fully debugged and stable.\nThanks to this updated formulation—and your review—we are now able to capture how hospital\nand transportation failures interact to influence post-earthquake hospital accessibility. Our\nrevised analysis highlights several key cascading effects:\n● Widespread transportation failures lead to compound access losses, with travel times\nincreasing by over a factor of 10 in some areas.\n● Some hospitals in the Bay Area may become completely isolated due to bridge failures.\n● Urban communities—particularly in Fremont and Novato—may lose access to essential\nservices due to localized bridge disruptions.\nWe include some of the updated results and manuscript revisions below.\nAbstract (line 15):\nconnectivity data, we analyze 76 hospitals (426 buildings with 16,639 beds) and 5,163 bridges\nwithin a vast network of ∼1.5 million edges and ∼0.5 million nodes [...] Widespread transportation\nfailures further restrict access, increasing regional travel times by 177% and exceeding 1000% in\nparts of East Bay, potentially fully isolating hospitals and entire urban communities. These findings\nunderscore the urgent need for resilient healthcare and transportation infrastructure to mitigate\nlife-threatening disruptions following major earthquakes.\nIntroduction (line 80):\nTo fill this critical gap, we investigate, for the first time, joint failures of healthcare and\ntransportation networks across the San Francisco Bay Area after a major earthquake. By\nexamining diverse urban communities near active seismic faults—often underrepresented in\nprevious studies—this research provides valuable insights into post-earthquake healthcare\naccess, particularly relevant for earthquake-prone regions worldwide with diverse populations\nand similarly vulnerable hospitals and bridges, such as those in the U.S., Japan, and Türkiye.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at this\nscale using publicly available data on both hospital and transportation infrastructure. Whereas\nprior work has focused on individual facilities[20-23] or small systems[42-46]—often relying on\nsynthetic data—our approach couples regional seismic risk models with large-scale network\nanalysis to capture interdependent failures across an entire metropolitan area. By integrating\nvulnerability data from 426 hospital buildings and 5,163 bridges, and simulating disruptions across\na transportation network with approximately 1.5 million edges and 0.5 million nodes, we offer one\nof the most extensive assessments to date of how earthquakes affect healthcare access. This\nstudy advances the state of the art in regional risk modeling globally, offering a scalable,\ncomputationally intensive framework that supports risk-informed decision-making in other high-\nrisk urban areas.\nNew Section on Post-earthquake Bridge Functionality (line 196):\nOur risk analysis model predicts that 1,469 bridges out of 5,163 would be damaged due to the\nearthquake scenario (see Methods). Consequently, 3,693 bridges (72%, standard deviation:\n17%) are expected to remain undamaged and fully operational (Figure 3). Some damaged\nbridges could continue operating, albeit at reduced capacities. Under our “baseline scenario”,\nwhere only bridges with at most slight damage remain operational, a total of 3,964 bridges\n(77%, standard deviation: 15%) would function. In a more optimistic “favorable scenario”, where\nbridges with at most moderate damage also remain partially operational, 4,069 bridges (79%,\nstandard deviation: 14%) could provide service. In an idealistic scenario, which assumes that\nbridges even with extensive damage retain emergency functionality, 4,527 bridges (88%,\nstandard deviation: 11%) would remain operational.\nTable 2). Under the baseline scenario, Alameda retains only 44% functional bridges (from 642\ndown to 282). Marin County is second most impacted, retaining 64% (from 195 to 125 bridges).\nAdditionally, estimates of reductions in bridge travel speeds (see Methods)—calculated from\ntheir damage probabilities—highlight Alameda’s higher vulnerability due to proximity to the\nHayward Fault rupture (Figure 3, Table 2).\ncontributors openstreetmap.org/copyright.\nFigure 3. [...] Lower left: Probability distribution of fully functional bridges under baseline (slight),\nfavorable (moderate), and idealistic (extensive) damage thresholds. Lower right: Spatial\ndistribution highlighting bridges with post-earthquake travel capacities below 75%. Results\ngenerated from 5,000 Monte Carlo simulations.\nRevised findings on Accessibility (line 223):\nAt a more detailed neighborhood scale, these disruptions are even more pronounced (Figure 4).\nWe identified six densely populated zip codes (each exceeding 15,000 residents, labeled #1 to\n#6 in Figure 4) facing substantial reductions in healthcare access. The most severely impacted is\nNovato (#1, Marin County), where travel times increase nearly 25-fold, from 7.3 to 185.5 minutes,\naffecting approximately 18,000 residents. Similarly, a Fremont zip code (#6, Alameda County)\nwith roughly 66,000 residents experiences an eightfold increase (from 8.4 to 42.2 minutes). Other\nsignificantly impacted zip codes in Richmond (#4), Oakland (#2 and #5, Alameda County), and\nSan Jose (#3, Santa Clara County) face travel time increases of 10, 11, 9, and 11 times their pre-\nearthquake levels, respectively. These results underscore the dramatic reshaping of healthcare\naccess throughout East Bay communities along the earthquake rupture.\nFinally, we explored the relative contributions of hospital and transportation infrastructure\ndisruptions through scenario analyses (Figure 4). We compared the baseline (None, no\ninfrastructure disruptions) against scenarios modeling probabilistic damage only to transportation\ninfrastructure (Transp., hospitals fully resilient), only to hospital infrastructure (Hosp.,\ntransportation fully resilient), and simultaneous probabilistic disruptions to both (Transp. & Hosp.).\nWhen considering disruptions only to transportation infrastructure (Transp.), average Bay Area\ntravel times increase by 41% (from 6.1 to 8.6 minutes), notably less than the combined scenario\n(Transp. & Hosp., 177% increase). Conversely, modeling only hospital infrastructure disruptions\n(Hosp.) yields a 79% increase (from 6.1 to 10.9 minutes), highlighting greater relative fragility in\nhospital networks.\ncontributors openstreetmap.org/copyright.\nAt localized urban scales, the compounding effects of simultaneous transportation and hospital\ninfrastructure failures lead to disproportionately severe impacts (Figure 4). For example, as\nmentioned earlier, in the most severely impacted zip code (Novato, labeled #1 in Figure 4),\ntravel times dramatically increase from 7.3 to 185.5 minutes under combined disruptions\n(Transp. & Hosp.), compared to only 14.1 minutes when transportation disruptions are excluded\n(Hosp. only). Similarly, for other highly affected zip codes (labeled #2 to #6 in Figure 4),\ntravel-time ratios notably decrease—from 11, 11, 10, 9, and 8 under combined disruptions, to\n6.4, 3.1, 6.1, 4.7, and 3.4 when transportation disruptions are not considered—highlighting\nthe critical influence of compounding infrastructure failures on healthcare access.\nUpper left: Post-earthquake (Post-EQ) increases in travel time at the zip-code level compared to\npre-earthquake (Pre-EQ) conditions, highlighting densely populated areas that are most\nseverely impacted. Upper right: Ratios of post- to pre-earthquake travel times to the closest\nacute care hospitals. Lower right: Distribution of travel times per zip code under four scenarios:\nNone (no infrastructure disruptions), Transp. (only transportation infrastructure is vulnerable),\nHosp. (only hospital infrastructure is vulnerable), and Transp. & Hosp. (both transportation and\nhospital infrastructures are vulnerable). Lower left: Ratios of post- to pre-earthquake travel times\nwhen only hospital infrastructure (Hosp.) is vulnerable. Results generated from 5,000 Monte\nCarlo simulations.\nNew section on Isolated Communities and Hospitals (line 252):\nanalyzed travel volumes to the closest acute care hospitals before and after the earthquake.\nFigure 5 shows pre-earthquake road usage, with line thickness representing travel volume. Roads\nin brown highlight those whose usage falls above the 90th percentile based on pre-earthquake\nconditions, emphasizing the most critical travel routes. As expected, the highest-usage roads prior\nto the earthquake were located near hospitals, especially in densely populated areas with fewer\nhospitals. For instance, communities in Fremont (#6 in Figures 4 and 5) are served by only two\nhospitals, while Richmond (#4) relies on just one.\nFigure 5 also displays post-earthquake road usage, using the same pre-earthquake 90th\npercentile threshold to highlight heavily traveled roads. After the earthquake, patient travel\npatterns shift significantly, with many communities forced to travel longer distances along major\ncorridors. For example, residents in Oakland (#2 and #5 in Figures 4 and 5), who previously relied\non nearby hospitals, will now have to travel west to the San Francisco Peninsula or east to Walnut\nCreek due to simultaneous disruptions in both hospital and transportation infrastructure. These\nshifts help explain the steep increases in travel times observed in East Bay communities along\nthe rupture zone.\nFour major bridges connect the East and West Bay: the Richmond–San Rafael, Oakland–San\nFrancisco Bay, San Mateo–Hayward, and Dumbarton bridges. Before the earthquake, no patients\nneeded to cross these bridges to reach their nearest acute care hospital (Figure 5). After the\nearthquake, however, these bridges become critical, with travel volumes increasing to 3.6, 9.3,\n6.3, and 13.6 times the pre-earthquake 90th percentile values—reflecting the large-scale\nredistribution of healthcare demand.\nOur analysis also revealed a more complex post-disaster phenomenon: micro-scale isolation of\nhospitals and communities due to localized bridge failures. For example, the hospital serving the\nmost severely impacted zip code in Novato (#1 in Figures 4 and 5), which has 64 beds, depends\nentirely on a single bridge for access. If this bridge fails, the hospital becomes inaccessible,\nincreasing travel times from 7.3 to 185.5 minutes for the surrounding population.\ncontributors openstreetmap.org/copyright.\nMore concerning, we found that urban neighborhoods near Fremont (#6) could become fully\nisolated (Figure 5). In one area, failure of three bridges would trap one part of the neighborhood;\nin another, a different set of three bridge failures would isolate the remaining part. These\ncommunities would lose access not only to hospitals but also to other essential services such as\ngrocery stores and pharmacies—illustrating how cascading infrastructure failures can sever\nlifeline access in disaster scenarios.\nFigure 5: Mobility to reach the closest functional acute care hospital in the San Francisco Bay\nArea. Upper left: Pre-earthquake travel volumes to the closest acute care hospitals. Numbers 1\nto 6 indicate the hospitals serving the dense zip codes with the highest post-earthquake\nincreases in travel time. Upper right: Projected travel volumes after the earthquake, showing\nmajor shifts in patient mobility. The red-shaded corridor illustrates how Oakland residents (#2\nand #5) must travel west to the Peninsula or east to Walnut Creek due to hospital and\ntransportation disruptions. Lower left: The hospital serving zip code #1 (Novato) relies entirely\n44\non a single bridge; if the bridge fails, all access to its 64 beds is lost. Lower right: Community\nnear zip code #6 (Fremont), where the southern and northern sections become fully isolated if\nthree different bridges fail in each area. Results are based on 5,000 Monte Carlo simulations of\npost-earthquake patient mobility.\nfragility model for structural wall buildings. However, the original source of this reference model,\nas well as the related building typology, is unclear. Therefore, it is not easy to interpret the\nmeaning of this comparison.\nThank you for pointing this out. We fully agree with the reviewer. This plot was confusing and\ndid not add much relevant information. We removed it.\nComment 16: Reviewer #1 (Remarks on code availability):\nI downloaded the code and checked its contents very briefly. It contains the related files. I did\nnot run it to reproduce the results.\nWe have uploaded updated code to the same data repository. We carefully prepared a README\nwith step-by-step instructions to ensure that all analysis results presented in the paper can be\nreproduced by running the provided code. This updated version contains the new model version.\nReviewer #2 (Remarks to the Author):\nOverall response:\nWe thank the reviewer for their feedback and recognize that the previous version of the\nmanuscript did not sufficiently convey the motivation and contributions of our study. We have\ntaken the comments seriously and used them to substantially revise and strengthen the work.\nWe also note that concerns raised in this review, especially regarding the motivation and novelty\nof the study, were not shared by the other reviewers, whose feedback was more positive and\nencouraging. Nonetheless, we carefully considered all reviewer input and undertook a major\nrevision effort.\nThe delay in resubmission reflects the time required to expand the analysis and clarify our\ncontributions. In particular, we significantly broadened the scope of the study by fully integrating\ntransportation infrastructure into the modeling of post-earthquake hospital accessibility. This\naddition allowed us to identify new critical outcomes—such as the potential isolation of a hospital\nand a community (“urban island”)—that were not captured in the original version. We also\nintroduced new metrics of accessibility, conducted sensitivity analyses, and revised the\nintroduction and discussion to better position the study within the broader literature.\nAll specific responses are provided in blue text, and corresponding changes in the revised\nmanuscript are shown in red. We hope these revisions demonstrate the rigor and value of the\nupdated study.\nComment 1: As the authors know, one of the most critical elements of any study is the\nmotivation of the work. The authors motivated the work by indicating that, unlike the past studies\non hospital networks, this study focuses on a community exposed to earthquakes only within a\nfew kilometers of them. First, the papers cited by the authors include hospitals a few kilometers\nfrom the hazard. Second, the justification overall is very weak and does not represent\nuniqueness. The study is motivated by the hospital being a few kilometers from the hazard,\nwhich is irrelevant - not to mention that this was the case in past studies. Furthermore,\nassessing healthcare networks under earthquakes has been studied quite a bit using more\nrigorous approaches. It is hard to see valuable contributions in this study.\nResponse 1: Thank you very much for the constructive feedback. We appreciate the opportunity\nto clarify the motivation and contribution of our work. We have revised the introduction of the\nmanuscript to better emphasize these points.\nOur motivation stems from the unique combination of challenges present in the San Francisco\nBay Area, including:\n47\n(a) a high concentration of seismically vulnerable hospitals, many of which are pre-1973\nstructures located near active faults;\n(b) a complex and interconnected healthcare network that spans county and jurisdictional\nboundaries; and\n(c) spatially heterogeneous seismic hazards and vulnerabilities across communities.\nThis combination creates critical management challenges. For example, our results show that\nhospitals located near rupture faults face higher risks of damage, and their potential loss would\ndisproportionately reduce access to care in nearby communities. From the perspective of regional\nhealthcare managers (e.g., HCAI, formerly OSHPD), addressing earthquake impacts requires a\nregional risk approach—one that goes beyond individual building assessments to account for\nsystem-wide hospital vulnerabilities and transportation disruptions, as modeled in the current\nversion of this study, to capture changing access patterns across the network.\nWe have clarified in the manuscript (see changes to Introduction below) that the intent is not to\nclaim uniqueness based solely on hospital proximity to faults. Rather, we emphasize that this\nproximity, combined with widespread vulnerability and regional interdependence, demands a\nsystems-level analysis. To our knowledge, this is the first study to evaluate the performance of\na realistic regional healthcare network using publicly available, high-resolution data on both hospital\ninfrastructure and transportation systems.\nIn terms of methodology, we recognize that high-fidelity simulation models have been developed\nto study the earthquake dynamics of individual hospitals. These are valuable for understanding\ndetailed functional disruptions but are not feasible for regional-scale analyses due to their\nintensive data requirements and computational demands. In contrast, our model is designed to\ncapture interdependent failures—such as simultaneous damages to hospitals and critical\nbridges—at a regional scale, while balancing spatial coverage, data availability, and\ncomputational feasibility.\nIn our previous work, we have developed discrete event simulation models to capture detailed\nhospital functionality, which can be coupled with structural models to analyze patient flow and\noperations at the building level [1]. However, applying such models across an entire region\nremains impractical. This study therefore adopts a campus-level functionality model, allowing us\nto compare hospital capacity losses and assess how those losses—combined with bridge\ndamage—affect access to care.\nOur regional modeling approach represents the state of the art in large-scale healthcare system\nanalysis, integrating detailed hospital and transportation vulnerability data, seismic hazard\nmodels, and transportation network connectivities to assess post-earthquake access to care. To\nachieve this level of integration and fidelity using publicly available data, we developed a modeling\nand computational framework capable of simulating interdependent failures across hundreds of\nfacilities and thousands of network links.\nunderscores the technical effort involved in performing this level of analysis and highlights the\npractical challenges of scaling such models to other high-risk urban regions.\nFinally, while we appreciate the reviewer’s concerns, we respectfully disagree with the\nassessment that the study lacks value. We believe the scale, integration, and policy relevance of\nour findings—such as the identification of communities with disparate access to healthcare and\neven isolated hospitals and communities—represent a meaningful contribution to the literature. If\nthere are specific references the reviewer believes have already addressed this problem at a\nsimilar level of scope and resolution, we would be happy to engage with them. Based on our\ncomprehensive literature review, we are confident that this study advances the state of the art in\nregional healthcare system resilience under seismic risk.\nPlease see the new version of the Introduction that is revised to highlight better our contributions\naccording to your comments (lines 50, 57, 63, and 86):\nRecognizing these vulnerabilities, this paper investigates the effects of future earthquakes\non healthcare access in the entire San Francisco Bay Area, California. [...] \nYet, hospitals do not function in isolation—particularly in dense urban areas [...].\nFailures in transportation infrastructure significantly compound healthcare disruptions [...]\nThese interconnected disruptions underscore the urgent need to evaluate joint\nvulnerabilities within healthcare and transportation infrastructure.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at\nthis scale using publicly available data on both hospital and transportation infrastructure.\nWhereas prior work has focused on individual facilities[20-23] or small systems[42-46]—\noften relying on synthetic data—our approach couples regional seismic risk models with\nlarge-scale network analysis to capture interdependent failures across an entire\nmetropolitan area. By integrating vulnerability data from 426 hospital buildings and 5,163\nbridges, and simulating disruptions across a transportation network with approximately 1.5\nmillion edges and 0.5 million nodes, we offer one of the most extensive assessments to\ndate of how earthquakes affect healthcare access. This study advances the state of the\nart in regional risk modeling globally, offering a scalable, computationally intensive\nframework that supports risk-informed decision-making in other high-risk urban areas.\n[1] Merino Y, Ceferino L, Pizarro S, de la Llera JC. Modeling hospital resources based on global\nepidemiology after earthquake-related disasters. Earthquake Spectra. 2024;40(4):2402-2429.\ndoi:10.1177/87552930241262788\nComment 2: In addition to the lack of sufficient motivation, the author did not utilize the state-of-\nthe-art in healthcare resilience analysis and used a simplistic approach in their assessment. For\nexample, it is assumed that damage to the building is a proxy for bed availability and resilience,\nwhich is not true. Many recent studies describe healthcare resilience as a function of physical\ninfrastructure, staff, and stuff. So, it appears that the authors are going back in time to use a\ndefinition that is no longer recognized in the research community.\nWe thank the reviewer for this important point and the opportunity to clarify the scope of our\nmodeling framework. We fully recognize that healthcare resilience is multidimensional, and that\nseminal work—including that of Dr. Mitrani-Reiser—has expanded the definition of hospital\nfunctionality to include structure, staff, and stuff. In fact, we referenced this work in the first version\nof the paper [1].\nAs noted in our literature review, these innovative models have been developed for analyses on\nsingle hospital buildings, where blueprints, space, and staff information are available to construct\na high-fidelity finite element model of the structure and analyze how different spaces of the\nstructure lose functionality. We have actually extended these high-fidelity modeling techniques to\nanalyze single hospitals in Chile using discrete event simulations [2]. These models can often be\nvery computationally expensive and not able to handle uncertainty exploration.\nWhile these models are powerful at the single-building scale, they do not work at the regional\nlevel because of the lack of data and the enormous demands for computational power. We are\nmodeling 76 hospitals with +400 buildings (not just one) in the Bay Area. For these types of\nproblems, we must change the approach as we are not interested in capturing how functionality\nchanges in each specific room of a building but instead in the relative resilience of one hospital\ncampus versus another. We created these regional models for hospitals a few years ago together\nwith Dr. Mitrani (who created the models you are referring to) to analyze effective plans for hospital\nsystem response to earthquake emergencies in the city of Lima, Peru [3]. In the field of regional\nrisk modeling, we create a model based on the available vulnerability information. In the Bay Area,\nwe created a regional risk model based on the available information on structural type, building\nheight, year of construction, structural performance category, and non-structural performance\ncategory. This is the state of the art in regional risk modeling as we are interested at loss of\nfunctionality at the whole hospital campus level and not at each hospital room. We acknowledge,\nthough that these models could be improved if high-resolution information for all hospitals would\nbecome available, which has not happened, unfortunately.\n[1] Jacques CC, McIntosh J, Giovinazzi S, Kirsch TD, Wilson T, Mitrani-Reiser J. Resilience of\nthe Canterbury Hospital System to the 2011 Christchurch Earthquake. Earthquake Spectra.\n2014;30(1):533-554. doi:10.1193/032013EQS074M\n[2] Merino Y, Ceferino L, Pizarro S, de la Llera JC. Modeling hospital resources based on global\nepidemiology after earthquake-related disasters. Earthquake Spectra. 2024;40(4):2402-2429.\ndoi:10.1177/87552930241262788\n50\n[3] Ceferino, L., Mitrani-Reiser, J., Kiremidjian, A. et al. Effective plans for hospital system\nresponse to earthquake emergencies. Nat Commun 11, 4325 (2020).\nhttps://doi.org/10.1038/s41467-020-18072-w\nWe rewrote this part in the introduction to make this point clearer (line 50):\nRecognizing these vulnerabilities, this paper investigates the effects of future\nearthquakes on healthcare access in the entire San Francisco Bay Area, California.\nPrevious research has largely focused on individual hospital vulnerability, using methods\nsuch as structural engineering analyses, performance-based assessments, and fault-tree\nevaluations to examine structural and non-structural damages within isolated\nfacilities.[20–23] Other studies evaluated patient treatment dynamics and medical\nresource demands through flow models and discrete event simulations in post-earthquake\nscenarios but are similarly limited to single-building analyses.[24–27] Yet, hospitals do not\nfunction in isolation—particularly in dense urban areas—as demonstrated by seismic\nevents in Chile, New Zealand, and Japan.[21, 28–31] Failures in individual hospitals can\ntrigger broader network impacts, overwhelming remaining facilities and forcing patients to\ntravel greater distances for care, severely exacerbating health outcomes for critically\ninjured individuals. Thus, understanding healthcare resilience requires examining\ninterconnected failures across healthcare and transportation infrastructure.[32–34]\nComment 3: Moreover, the paper suffers from many technical issues/mistakes, which causes\nthe analysis to be unsound. For example, their predictions show that many hospitals will\nexperience violent shaking at a scale not seen in over a century under a peak ground\nacceleration of 0.2. This is not possible. A peak ground acceleration of 0.2 is extremely low and\nis expected to cause only slight damage. The literature is overwhelmed with studies that show\nhow a 0.2 PGA typically causes slight damage to different archetypal structures.\nComment 3: We appreciate the reviewer’s attention to this point and the opportunity to clarify. It\nwas unclear whether the reviewer’s concern is that 0.2g is not a possible level of ground\nshaking, or that 0.2g does not constitute unusually high shaking for hospitals in the Bay Area.\nTo clarify, we reference 0.2g only as an illustrative example—to note that many hospitals in the\nregion have not experienced even this moderate level of shaking since the 1906 earthquake.\nImportantly, our risk analysis does not rely on this deterministic value. As described in the\nMethods section, our analysis is based on probabilistic seismic hazard models, which sample the\nfull distribution of ground motion intensities across a wide range of scenarios. For damage and\naccessibility assessments, we use spectral acceleration values at building-specific periods rather\nthan PGA.\nTo avoid confusion, we have revised the Methods text to clarify that 0.2g was mentioned purely\nas a historical reference point, and that our modeling approach is fully probabilistic and consistent\nwith established regional risk frameworks (line 469):\nbeen extensively studied to inform resilience policy-making in the Bay Area.47 The rupture\ngeometry was obtained from the Uniform California Earthquake Rupture Forecast\n(UCERF) 2.72 The earthquake ruptures the Hayward South and North sections over a\ntotal length of ∼110 km. Estimates of shallow shear wave velocities (averages at the top\n30 m of soil) are utilized over the entire Bay Area.73 With this information, we built the\njoint probability distribution of shaking intensities π(i) in R2D. We utilized a state-of-the-art\nground motion model74 for shallow crustal earthquakes to estimate medians and\nlogarithm standard deviations of i. i’s uncertainty is divided into two components.75 The\nfirst component captures between-event uncertainty and affects the entire region equally,\nbut it varies per intensity measure type, e.g., peak ground acceleration versus spectral\nacceleration. The first component captures correlation across different intensity\nmeasures.76 The second component captures within-event uncertainty and affects the\nentire region and intensity measure types differently. This component captures spatial\ncorrelation and correlation across different intensity measure types. We use a\ncomputationally efficient method to account for the second component.[62, 77] As stated\nearlier, we sampled 5,000 realizations of i and show expected values E(i) for the entire\nregion (Figure 1).\nWe have also clarified the manuscript to better explain that a PGA of 0.2g is not only plausible,\nbut expected for hospitals located near active faults. For magnitude 7.0 earthquakes at short fault\ndistances—as is the case for many sites along the Hayward Fault—PGAs well above 0.2g are\nconsistent with empirical ground motion prediction equations. As illustrated in Figure 1, several\nhospitals in our study area are within 5 km of the Hayward Fault, making higher levels of ground\nshaking entirely realistic.\nHistorical earthquake records further support this point. While the Bay Area has experienced only\nmoderate earthquakes in recent decades, most of the 76 hospitals in our dataset have not been\nexposed to shaking above 0.2g since the 1906 event. This is the motivation for referencing 0.2g\nin the text: even moderate levels of shaking would represent a significant increase over the\nhistorical experience of many healthcare facilities in the region.\nTo prevent further confusion, we revised the manuscript to clarify that the 0.2g value is used as a\nhistorical reference point, not as a basis for damage estimation. We also emphasize that our\ndamage predictions are derived from spectral acceleration values at building-specific periods, and\nthat the analysis accounts for the close proximity of hospitals to the Hayward Fault and the\ncorresponding hazard expected from a magnitude 7.0 event (line 149).\nWe modeled the rupture geometry (see Methods) and found that 10 acute care hospitals\n52\nwith 2167 beds (13% of the Bay’s total) are within just 5 km of the projected rupture. Our\nshaking intensity estimates indicate that many hospitals could experience levels of\nground motion not observed in recent earthquakes (See Methods). On average, we\npredict 51 hospitals will experience peak ground accelerations above 0.2g (Figure 2). By\ncomparison, the 1989 M 6.9 Loma Prieta Earthquake—previously the strongest since\nthe devastating 1906 M 7.9 San Francisco Earthquake—subjected only 14 hospitals to\nsimilar shaking intensities (Figure 2). Supplementary Figure 2 further contextualizes\nthese findings, illustrating how recent events such as the 2014 Napa Earthquake (M 6.0)\nexposed just three hospitals to significant shaking (>0.2g). In contrast, the historic 1906\nearthquake exposed nearly the entire portfolio (72 out of 76 hospitals)\nComment 4: In addition, the authors noted that many hospitals will have a probability of\ndamage above 0.25. What is the significance of 0.25 as a damage probability? and What type of\ndamage corresponds to 0.25 or more? Damage probability ranges from slight to moderate to\nextensive to complete, and each plays a role in quantifying healthcare functionality. To list that\nthe damage probability is 0.25 has no structural engineering relevance. In earthquake\nengineering, there is no relevance in saying that many hospitals had a damage probability of\nmore than 0.25. The reviewer recommends that the authors look at various FEMA documents\non seismic performance assessment to become more familiar with damage assessment\napproaches, including the various engineering demand parameters used for seismic evaluation\nof buildings and hospitals.\nComment 4: We thank the reviewer for this comment and for recommending the FEMA guidance\ndocuments. These are indeed excellent resources, and we are well acquainted with them. The\nlead author has used FEMA P-58, FEMA P-695, and HAZUS extensively for both research and\nteaching, including in the graduate course “Disaster Risk Analysis” at UC Berkeley. One co-author\nis a risk specialist with years of experience applying these frameworks to develop regional risk\nmodels and policy interventions in collaboration with the World Bank. Another co-author has\ncontributed to the development of NSF-funded tools at the NHERI SimCenter that operationalize\nthese frameworks for both regional and single-building risk assessments. We have referenced\nthese methodologies throughout our work and remain committed to aligning with best practices\nin the field.\nRegarding the reviewer’s specific point: the mention of a damage probability threshold of 0.25\nwas intended solely as an illustrative example—to demonstrate how the likelihood of damage\nincreases with proximity to the fault. It was not used as a cutoff or performance threshold in the\nactual analysis. As detailed in the Methods section, we compute full probability distributions of\nmultiple damage states for each hospital building using fragility functions and combine these with\na fault tree to assess hospital functionality.\nWe understand that our use of the 0.25 value may have caused confusion, and we have revised\nthe manuscript to make it clear that this number was only used for communication purposes, not\nas a substitute for engineering demand parameters or damage state classifications. Our\n53\nunderlying modeling framework is aligned with established seismic performance assessment\napproaches and incorporates state-based damage probabilities in a probabilistic risk analysis. To\nimprove clarity, we revised the Methods section to make this explicit. Below, we provide the\nrevised text in plain format, noting that the full mathematical expressions and formatting appear\nproperly in the main manuscript (line 410):\nHospitals can rapidly lose functionality at early stages of structural and non-structural\ndamage, as observed in the 2023 M 7.8 Kahramanmaraş Earthquake in Turkey, the 2011\nM 6.1 Christchurch Earthquake in New Zealand, and the 2010 M 8.8 Maule Earthquake in\nChile. We consider that damage thresholds, ds and dn, for the structural and non-\nstructural components, respectively, trigger the disruption of hospital functionality—that is,\nif either fails, the hospital loses functionality.\nWe estimate the probabilities of not exceeding these thresholds as:\n● pₖˢ = π(Dₖˢ ≤ ds | Iₖˢ = iₖˢ), and\n● pₖⁿ = π(Dₖⁿ ≤ dn | Iₖⁿ = iₖⁿ),\nwhich can be evaluated using earthquake fragility functions. We then model functionality\nas the intersection of these two events, meaning the hospital component remains\nfunctional only if both structural and non-structural elements perform adequately after the\nearthquake. Since Dₖˢ and Dₖⁿ are assumed conditionally independent, Fₖ (hospital\nbuilding functionality) becomes a Bernoulli random variable with probability pₖˢ × pₖⁿ. Accordingly, the joint probability of functionality given the data d is:\nπ(f | d) = ∏ₖ=1^m [ (pₖˢ × pₖⁿ)^fₖ × (1 - pₖˢ × pₖⁿ)^(1 - fₖ) ] (Equation 4)\nThe functionality of each hospital depends on the structural and non-structural\ncomponents, as described in Equation 4. The hospital portfolio includes various levels of\nSPC (Structural Performance Category) and NPC (Non-structural Performance Category),\nwhich influence the final functionality outcome.\nWe also estimate the probability distribution of the total number of functional beds Bₜ\nacross the region, computed as:\nBₜ = ∑ βₖ × Fₖ (Equation 5)\nwhere βₖ is the number of beds at hospital building k (assumed fully functional before the\nearthquake).\nTo account for hospitals with multiple buildings, we estimate the distribution of the total\nnumber of functional beds Bₕ for hospital h, where 𝓀ₕ is the set of buildings belonging to\nhospital h:\nIn addition, we believe that the previous version of the paper may have overemphasized the\n0.25 value, which may have led some readers to interpret it as a threshold used in the\ncomputation of hospital functionality. To avoid this misunderstanding, we have removed this\nreference from the main text.\nComment 5: Concerning this comment, the authors note that their analysis predicts that 8,501\nbeds will be lost throughout the Bay, and such predictions are based on slight damage (justified\nby previous studies that used slight damage to indicate loss of beds). Again, the literature is way\npast the idea of using damage to indicate bed losses and that stuff, staff, and physical systems\nshould be used to indicate bed losses. In addition, many studies show that hospitals continue to\noperate beyond slight damage, including the studies referenced by the authors. None of the\nstudies cited by the authors show that hospitals will lose functionality at slight damage. The\nStEER report cited by the authors indicates that only fully collapsed or severely damaged\nhospitals were evacuated after the Turkey EQ event. Unfortunately, the authors used this\nassumption to draw the study's main conclusions. Using slight damage drastically skews the\nresults towards showing significant bed losses, which is very unrealistic. Also, the authors note\nthat services within hospital buildings will be highly disrupted – a statement with no basis since\nthe authors did not model any hospital units or services.\nResponse 5:\nWe refer back to our response to Comment 1, where we explain that we do not apply the\n“structure, staff, and stuff” framework in this study because, although valuable, it is not scalable\nto the regional level given current data limitations. While we acknowledge the broader dimensions\nof healthcare resilience, our study focuses on structural and non-structural damage as proxies for\nloss of hospital functionality—an approach consistent with the current state of the art in regional\nseismic risk modeling.\nThe lead author has participated in post-earthquake field investigations in Türkiye, Ecuador, and\nNew Zealand and has directly observed instances where hospitals experienced disruption of\nservices even at slight damage levels. In fact, the lead author coordinated the hospital section of\nthe StEER report on the 2023 Türkiye Earthquake. Contrary to the reviewer’s comment, that\nreport does not state that “only fully collapsed or severely damaged hospitals were evacuated.”\nOur fieldwork, including interviews with hospital staff, documented several cases where hospitals\nwith slight or moderate damage lost functionality or required partial shutdowns due to non-\nstructural failures, dislodged equipment, or internal hazards. These findings are described in our\npeer-reviewed article [1]. We made the following notes on the paper and added references to\nthese cases (line 172):\nstructural damage exceeds a threshold of slight damage—conditions often shown to\ndisrupt hospital services (see Methods).[28-31]\n[1] Ceferino, L., Merino, Y., Pizarro, S. et al. Placing engineering in the earthquake response\nand the survival chain. Nat Commun 15, 4298 (2024). https://doi.org/10.1038/s41467-024-\n48624-3\n[28] Ardagh, M. W. et al. The initial health-system response to the earthquake in Christchurch,\nNew Zealand, in February, 2011. The Lancet 379, 2109–2115 (2012). URL http://dx.doi.org/10.\n1016/S0140-6736(12)60313-4. Publisher: Elsevier Ltd ISBN: 1474-547X (Electronic)\\r0140-\n6736 (Linking).\n[29] Kirsch, T. D. et al. Impact on hospital functions following the 2010 Chilean earthquake.\nDisaster medicine and public health preparedness 4, 122–128 (2010). ArXiv: 1011.1669v3\nISBN: 1938-744X (Electronic)\\r1935-7893 (Linking).\n[30] Shimoto, M. et al. Hospital Evacuation Implications After the 2016 Kumamoto Earthquake.\nDisaster Medicine and Public Health Preparedness 16, 2680–2682 (2022). URL https://www.\ncambridge.org/core/product/identifier/S1935789322000258/type/journal_article.\n[31] Achour, N. & Miyajima, M. Post-earthquake hospital functionality evaluation: The case of\nKumamoto Earthquake 2016. Earthquake Spectra 36,\nWe do recognize that there is uncertainty in defining the precise threshold of functionality loss,\nespecially in crisis settings. In some extreme situations, hospital staff were able to creatively adapt\nby cleaning up debris and isolating safe areas to continue providing care despite building damage.\nThese heroic efforts, while admirable, also underscore the risks involved for both staff and\npatients.\nTo address this uncertainty and better reflect the range of plausible responses, we have added a\nsensitivity analysis that explores alternative (higher) thresholds for functionality loss. We label\nthese scenarios “favorable” and “idealistic,” as we believe they represent optimistic assumptions\nthat may not hold in a context like the Bay Area, where liability, regulatory, and safety concerns\nmay prevent continued operation under damaged conditions (line 169).\nOur risk analysis predicts a substantial loss of hospital capacity throughout the\nBay Area following the earthquake scenario (see Methods). We estimate a loss of 8,165\nhospital beds, resulting in only 51% of total acute care beds remaining functional\n(standard deviation: 21%). This significant reduction in capacity is highly uneven across\nthe region (Figure 3, Table 1). Our baseline predictions assume hospitals lose\nfunctionality when structural or non-structural damage exceeds a threshold of slight\ndamage (see Methods). These damage conditions are often shown to disrupt hospital\nservices (see descriptions of multiple damage levels in Supplementary Tables 3 and 4).[\n21, 28–31] We also analyzed more optimistic scenarios with moderate (“favorable”) and\nextensive (“idealistic”) damage thresholds, resulting in increased overall functionality of\n79% and 93%, respectively (Figure 3 and Supplementary Table 5). However, empirical\n56\nevidence supports our baseline assumption, as hospitals often lose operations at early\nstages of damage. [21, 28–31]\nFigure 3. Post-earthquake functionality of hospitals and bridges across the Bay Area.\n[...] Probability distribution of functional acute care beds under baseline (slight), favorable\n(moderate), and idealistic (extensive) damage thresholds.\nSupplementary Table 5. Predicted post-earthquake hospital bed capacities across Bay Area counties\nunder thresholds of moderate (favorable) and extensive (idealistic) damage scenarios. The numbers in\nparentheses indicate the percentage in proportion to the pre-earthquake capacity.\nFavorable Idealistic\nCounty Mean Std. Dev. Mean Std. Dev.\nAlameda 1,743 (51%) 748 (24%) 2,635 (82%) 554 (17%)\nContra Costa 1,372 (75%) 378 (22%) 1,649 (94%) 188 (11%)\nMarin 482 (71%) 159 (25%) 581 (93%) 84 (13%)\nSan Francisco 3,258 (89%) 502 (14%) 3,547 (98%) 173 (5%)\nSan Mateo 1,269 (86%) 229 (16%) 1,390 (96%) 120 (8%)\nSanta Clara 3,512 (80%) 725 (17%) 4,068 (94%) 346 (8%)\nSolano 636 (88%) 116 (16%) 705 (98%) 50 (7%)\nSonoma 537 (90%) 64 (11%) 573 (98%) 26 (4%)\nTotal 13,129 (79%) 2,583 (16%) 15,492 (93%) 1,271 (8%)\nWe also appreciate that the reviewer is familiar with the “structure, staff, and stuff” model. While\nit brings valuable insight, we note that this framework still does not model human behavior, such\nas staff decision-making or willingness to work in damaged conditions—factors that play a critical\nrole in hospital functionality. To date, these behaviors remain challenging to represent accurately\nin either building-level or regional modeling frameworks. We believe that more research is needed\nin this area to enable their integration into future probabilistic risk models.\nFinally, we note that loss of “stuff” (e.g., medical equipment and supplies) is often directly linked\nto damage to non-structural components or structural failures in specific hospital zones. Even in\nhigh-fidelity single-building models, damage remains the primary driver of functionality loss, as\nconfirmed by our field deployments and multiple case studies.\nComment 6: Another significant issue is that bridge damage and failure analysis are not\nincluded in determining travel time. The travel time calculated in the paper can not be correct\ndue to the lack of bridge failure analysis.\nResponse 6: After reading your reviews (along with those from the other reviewers), we invested\nsignificant effort into improving our modeling of transportation infrastructure disruptions in the Bay\nArea. This became a major component of our revision and is the main reason for the time it took\nus to respond.\nand significantly expanded the transportation network model, which now includes approximately\n1.5 million edges and 0.5 million nodes. This refinement substantially increased computational\ndemands: the 5,000 Monte Carlo simulations required for the analysis took about two weeks to\nrun on a laptop equipped with an Apple M2 chip and 64 cores. We ran multiple iterations to ensure\nthe model was fully debugged and stable.\nThanks to this updated formulation—and your review—we are now able to capture how hospital\nand transportation failures interact to influence post-earthquake hospital accessibility. Our\nrevised analysis highlights several key cascading effects:\n● Widespread transportation failures lead to compound access losses, with travel times\nincreasing by over a factor of 10 in some areas.\n● Some hospitals in the Bay Area may become completely isolated due to bridge failures.\n● Urban communities—particularly in Fremont and Novato—may lose access to essential\nservices due to localized bridge disruptions.\nWe include some of the updated results and manuscript revisions below.\nAbstract (line 15):\nconnectivity data, we analyze 76 hospitals (426 buildings with 16,639 beds) and 5,163 bridges\nwithin a vast network of ∼1.5 million edges and ∼0.5 million nodes [...] Widespread transportation\nfailures further restrict access, increasing regional travel times by 177% and exceeding 1000% in\nparts of East Bay, potentially fully isolating hospitals and entire urban communities. These findings\nunderscore the urgent need for resilient healthcare and transportation infrastructure to mitigate\nlife-threatening disruptions following major earthquakes.\nIntroduction (line 80):\nTo fill this critical gap, we investigate, for the first time, joint failures of healthcare and\ntransportation networks across the San Francisco Bay Area after a major earthquake. By\nexamining diverse urban communities near active seismic faults—often underrepresented in\nprevious studies—this research provides valuable insights into post-earthquake healthcare\naccess, particularly relevant for earthquake-prone regions worldwide with diverse populations\nand similarly vulnerable hospitals and bridges, such as those in the U.S., Japan, and Türkiye.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at this\nscale using publicly available data on both hospital and transportation infrastructure. Whereas\nprior work has focused on individual facilities[20-23] or small systems[42-46]—often relying on\nsynthetic data—our approach couples regional seismic risk models with large-scale network\nanalysis to capture interdependent failures across an entire metropolitan area. By integrating\nvulnerability data from 426 hospital buildings and 5,163 bridges, and simulating disruptions across\na transportation network with approximately 1.5 million edges and 0.5 million nodes, we offer one\nof the most extensive assessments to date of how earthquakes affect healthcare access. This\nstudy advances the state of the art in regional risk modeling globally, offering a scalable,\ncomputationally intensive framework that supports risk-informed decision-making in other high-\nrisk urban areas.\nNew Section on Post-earthquake Bridge Functionality (line 196):\nOur risk analysis model predicts that 1,469 bridges out of 5,163 would be damaged due to the\nearthquake scenario (see Methods). Consequently, 3,693 bridges (72%, standard deviation:\n17%) are expected to remain undamaged and fully operational (Figure 3). Some damaged\nbridges could continue operating, albeit at reduced capacities. Under our “baseline scenario”,\nwhere only bridges with at most slight damage remain operational, a total of 3,964 bridges\n(77%, standard deviation: 15%) would function. In a more optimistic “favorable scenario”, where\nbridges with at most moderate damage also remain partially operational, 4,069 bridges (79%,\nstandard deviation: 14%) could provide service. In an idealistic scenario, which assumes that\ncontributors openstreetmap.org/copyright.\nbridges even with extensive damage retain emergency functionality, 4,527 bridges (88%,\nstandard deviation: 11%) would remain operational.\nSimilar to hospitals, Alameda County faces the most severe transportation impacts (Figure 3,\nTable 2). Under the baseline scenario, Alameda retains only 44% functional bridges (from 642\ndown to 282). Marin County is second most impacted, retaining 64% (from 195 to 125 bridges).\nAdditionally, estimates of reductions in bridge travel speeds (see Methods)—calculated from\ntheir damage probabilities—highlight Alameda’s higher vulnerability due to proximity to the\nHayward Fault rupture (Figure 3, Table 2).\nFigure 3. [...] Lower left: Probability distribution of fully functional bridges under baseline (slight),\nfavorable (moderate), and idealistic (extensive) damage thresholds. Lower right: Spatial\ndistribution highlighting bridges with post-earthquake travel capacities below 75%. Results\ngenerated from 5,000 Monte Carlo simulations.\nRevised findings on Accessibility (line 223):\nAt a more detailed neighborhood scale, these disruptions are even more pronounced (Figure 4).\nWe identified six densely populated zip codes (each exceeding 15,000 residents, labeled #1 to\n#6 in Figure 4) facing substantial reductions in healthcare access. The most severely impacted is\nNovato (#1, Marin County), where travel times increase nearly 25-fold, from 7.3 to 185.5 minutes,\naffecting approximately 18,000 residents. Similarly, a Fremont zip code (#6, Alameda County)\nwith roughly 66,000 residents experiences an eightfold increase (from 8.4 to 42.2 minutes). Other\nsignificantly impacted zip codes in Richmond (#4), Oakland (#2 and #5, Alameda County), and\nSan Jose (#3, Santa Clara County) face travel time increases of 10, 11, 9, and 11 times their pre-\nearthquake levels, respectively. These results underscore the dramatic reshaping of healthcare\naccess throughout East Bay communities along the earthquake rupture.\nFinally, we explored the relative contributions of hospital and transportation infrastructure\ndisruptions through scenario analyses (Figure 4). We compared the baseline (None, no\ninfrastructure disruptions) against scenarios modeling probabilistic damage only to transportation\ninfrastructure (Transp., hospitals fully resilient), only to hospital infrastructure (Hosp.,\ntransportation fully resilient), and simultaneous probabilistic disruptions to both (Transp. & Hosp.).\nWhen considering disruptions only to transportation infrastructure (Transp.), average Bay Area\ntravel times increase by 41% (from 6.1 to 8.6 minutes), notably less than the combined scenario\n(Transp. & Hosp., 177% increase). Conversely, modeling only hospital infrastructure disruptions\n(Hosp.) yields a 79% increase (from 6.1 to 10.9 minutes), highlighting greater relative fragility in\nhospital networks.\ninfrastructure failures lead to disproportionately severe impacts (Figure 4). For example, as\nmentioned earlier, in the most severely impacted zip code (Novato, labeled #1 in Figure 4),\ntravel times dramatically increase from 7.3 to 185.5 minutes under combined disruptions\n(Transp. & Hosp.), compared to only 14.1 minutes when transportation disruptions are excluded\n(Hosp. only). Similarly, for other highly affected zip codes (labeled #2 to #6 in Figure 4),\ntravel-time ratios notably decrease—from 11, 11, 10, 9, and 8 under combined disruptions, to\n6.4, 3.1, 6.1, 4.7, and 3.4 when transportation disruptions are not considered—highlighting\nthe critical influence of compounding infrastructure failures on healthcare access.\ncontributors openstreetmap.org/copyright.\nFigure 4: Access to functional acute care hospitals in the Bay Area after the earthquake.\nUpper left: Post-earthquake (Post-EQ) increases in travel time at the zip-code level compared to\npre-earthquake (Pre-EQ) conditions, highlighting densely populated areas that are most\nseverely impacted. Upper right: Ratios of post- to pre-earthquake travel times to the closest\nacute care hospitals. Lower right: Distribution of travel times per zip code under four scenarios:\nNone (no infrastructure disruptions), Transp. (only transportation infrastructure is vulnerable),\nHosp. (only hospital infrastructure is vulnerable), and Transp. & Hosp. (both transportation and\nhospital infrastructures are vulnerable). Lower left: Ratios of post- to pre-earthquake travel times\nwhen only hospital infrastructure (Hosp.) is vulnerable. Results generated from 5,000 Monte\nCarlo simulations.\nNew section on Isolated Communities and Hospitals (line 252):\nanalyzed travel volumes to the closest acute care hospitals before and after the earthquake.\nFigure 5 shows pre-earthquake road usage, with line thickness representing travel volume. Roads\nin brown highlight those whose usage falls above the 90th percentile based on pre-earthquake\nconditions, emphasizing the most critical travel routes. As expected, the highest-usage roads prior\nto the earthquake were located near hospitals, especially in densely populated areas with fewer\nhospitals. For instance, communities in Fremont (#6 in Figures 4 and 5) are served by only two\nhospitals, while Richmond (#4) relies on just one.\nFigure 5 also displays post-earthquake road usage, using the same pre-earthquake 90th\npercentile threshold to highlight heavily traveled roads. After the earthquake, patient travel\npatterns shift significantly, with many communities forced to travel longer distances along major\ncorridors. For example, residents in Oakland (#2 and #5 in Figures 4 and 5), who previously relied\non nearby hospitals, will now have to travel west to the San Francisco Peninsula or east to Walnut\nCreek due to simultaneous disruptions in both hospital and transportation infrastructure. These\nshifts help explain the steep increases in travel times observed in East Bay communities along\nthe rupture zone.\nFour major bridges connect the East and West Bay: the Richmond–San Rafael, Oakland–San\nFrancisco Bay, San Mateo–Hayward, and Dumbarton bridges. Before the earthquake, no patients\nneeded to cross these bridges to reach their nearest acute care hospital (Figure 5). After the\nearthquake, however, these bridges become critical, with travel volumes increasing to 3.6, 9.3,\n6.3, and 13.6 times the pre-earthquake 90th percentile values—reflecting the large-scale\nredistribution of healthcare demand.\nOur analysis also revealed a more complex post-disaster phenomenon: micro-scale isolation of\nhospitals and communities due to localized bridge failures. For example, the hospital serving the\nmost severely impacted zip code in Novato (#1 in Figures 4 and 5), which has 64 beds, depends\nentirely on a single bridge for access. If this bridge fails, the hospital becomes inaccessible,\nincreasing travel times from 7.3 to 185.5 minutes for the surrounding population.\nMore concerning, we found that urban neighborhoods near Fremont (#6) could become fully\nisolated (Figure 5). In one area, failure of three bridges would trap one part of the neighborhood;\nin another, a different set of three bridge failures would isolate the remaining part. These\ncommunities would lose access not only to hospitals but also to other essential services such as\ngrocery stores and pharmacies—illustrating how cascading infrastructure failures can sever\nlifeline access in disaster scenarios.\ncontributors openstreetmap.org/copyright.\nFigure 5: Mobility to reach the closest functional acute care hospital in the San Francisco Bay\nArea. Upper left: Pre-earthquake travel volumes to the closest acute care hospitals. Numbers 1\nto 6 indicate the hospitals serving the dense zip codes with the highest post-earthquake\nincreases in travel time. Upper right: Projected travel volumes after the earthquake, showing\nmajor shifts in patient mobility. The red-shaded corridor illustrates how Oakland residents (#2\nand #5) must travel west to the Peninsula or east to Walnut Creek due to hospital and\ntransportation disruptions. Lower left: The hospital serving zip code #1 (Novato) relies entirely\non a single bridge; if the bridge fails, all access to its 64 beds is lost. Lower right: Community\nnear zip code #6 (Fremont), where the southern and northern sections become fully isolated if\nthree different bridges fail in each area. Results are based on 5,000 Monte Carlo simulations of\npost-earthquake patient mobility.\nfragility model for structural wall buildings. However, the original source of this reference model,\nas well as the related building typology, is unclear. Therefore, it is not easy to interpret the\nmeaning of this comparison.\nThank you for pointing this out. We fully agree with the reviewer. This plot was confusing and\ndid not add much relevant information. We removed it.\nComment 16: Reviewer #1 (Remarks on code availability):\nI downloaded the code and checked its contents very briefly. It contains the related files. I did\nnot run it to reproduce the results.\nWe have uploaded updated code to the same data repository. We carefully prepared a README\nwith step-by-step instructions to ensure that all analysis results presented in the paper can be\nreproduced by running the provided code. This updated version contains the new model version.\nReviewer #2 (Remarks to the Author):\nOverall response:\nWe thank the reviewer for their feedback and recognize that the previous version of the\nmanuscript did not sufficiently convey the motivation and contributions of our study. We have\ntaken the comments seriously and used them to substantially revise and strengthen the work.\nWe also note that concerns raised in this review, especially regarding the motivation and novelty\nof the study, were not shared by the other reviewers, whose feedback was more positive and\nencouraging. Nonetheless, we carefully considered all reviewer input and undertook a major\nrevision effort.\nThe delay in resubmission reflects the time required to expand the analysis and clarify our\ncontributions. In particular, we significantly broadened the scope of the study by fully integrating\ntransportation infrastructure into the modeling of post-earthquake hospital accessibility. This\naddition allowed us to identify new critical outcomes—such as the potential isolation of a hospital\nand a community (“urban island”)—that were not captured in the original version. We also\nintroduced new metrics of accessibility, conducted sensitivity analyses, and revised the\nintroduction and discussion to better position the study within the broader literature.\nAll specific responses are provided in blue text, and corresponding changes in the revised\nmanuscript are shown in red. We hope these revisions demonstrate the rigor and value of the\nupdated study.\nComment 1: As the authors know, one of the most critical elements of any study is the\nmotivation of the work. The authors motivated the work by indicating that, unlike the past studies\non hospital networks, this study focuses on a community exposed to earthquakes only within a\nfew kilometers of them. First, the papers cited by the authors include hospitals a few kilometers\nfrom the hazard. Second, the justification overall is very weak and does not represent\nuniqueness. The study is motivated by the hospital being a few kilometers from the hazard,\nwhich is irrelevant - not to mention that this was the case in past studies. Furthermore,\nassessing healthcare networks under earthquakes has been studied quite a bit using more\nrigorous approaches. It is hard to see valuable contributions in this study.\nResponse 1: Thank you very much for the constructive feedback. We appreciate the opportunity\nto clarify the motivation and contribution of our work. We have revised the introduction of the\nmanuscript to better emphasize these points.\nOur motivation stems from the unique combination of challenges present in the San Francisco\nBay Area, including:\n67\n(a) a high concentration of seismically vulnerable hospitals, many of which are pre-1973\nstructures located near active faults;\n(b) a complex and interconnected healthcare network that spans county and jurisdictional\nboundaries; and\n(c) spatially heterogeneous seismic hazards and vulnerabilities across communities.\nThis combination creates critical management challenges. For example, our results show that\nhospitals located near rupture faults face higher risks of damage, and their potential loss would\ndisproportionately reduce access to care in nearby communities. From the perspective of regional\nhealthcare managers (e.g., HCAI, formerly OSHPD), addressing earthquake impacts requires a\nregional risk approach—one that goes beyond individual building assessments to account for\nsystem-wide hospital vulnerabilities and transportation disruptions, as modeled in the current\nversion of this study, to capture changing access patterns across the network.\nWe have clarified in the manuscript (see changes to Introduction below) that the intent is not to\nclaim uniqueness based solely on hospital proximity to faults. Rather, we emphasize that this\nproximity, combined with widespread vulnerability and regional interdependence, demands a\nsystems-level analysis. To our knowledge, this is the first study to evaluate the performance of\na realistic regional healthcare network using publicly available, high-resolution data on both hospital\ninfrastructure and transportation systems.\nIn terms of methodology, we recognize that high-fidelity simulation models have been developed\nto study the earthquake dynamics of individual hospitals. These are valuable for understanding\ndetailed functional disruptions but are not feasible for regional-scale analyses due to their\nintensive data requirements and computational demands. In contrast, our model is designed to\ncapture interdependent failures—such as simultaneous damages to hospitals and critical\nbridges—at a regional scale, while balancing spatial coverage, data availability, and\ncomputational feasibility.\nIn our previous work, we have developed discrete event simulation models to capture detailed\nhospital functionality, which can be coupled with structural models to analyze patient flow and\noperations at the building level [1]. However, applying such models across an entire region\nremains impractical. This study therefore adopts a campus-level functionality model, allowing us\nto compare hospital capacity losses and assess how those losses—combined with bridge\ndamage—affect access to care.\nOur regional modeling approach represents the state of the art in large-scale healthcare system\nanalysis, integrating detailed hospital and transportation vulnerability data, seismic hazard\nmodels, and transportation network connectivities to assess post-earthquake access to care. To\nachieve this level of integration and fidelity using publicly available data, we developed a modeling\nand computational framework capable of simulating interdependent failures across hundreds of\nfacilities and thousands of network links.\nunderscores the technical effort involved in performing this level of analysis and highlights the\npractical challenges of scaling such models to other high-risk urban regions.\nFinally, while we appreciate the reviewer’s concerns, we respectfully disagree with the\nassessment that the study lacks value. We believe the scale, integration, and policy relevance of\nour findings—such as the identification of communities with disparate access to healthcare and\neven isolated hospitals and communities—represent a meaningful contribution to the literature. If\nthere are specific references the reviewer believes have already addressed this problem at a\nsimilar level of scope and resolution, we would be happy to engage with them. Based on our\ncomprehensive literature review, we are confident that this study advances the state of the art in\nregional healthcare system resilience under seismic risk.\nPlease see the new version of the Introduction that is revised to highlight better our contributions\naccording to your comments (lines 50, 57, 63, and 86):\nRecognizing these vulnerabilities, this paper investigates the effects of future earthquakes\non healthcare access in the entire San Francisco Bay Area, California. [...] \nYet, hospitals do not function in isolation—particularly in dense urban areas [...].\nFailures in transportation infrastructure significantly compound healthcare disruptions [...]\nThese interconnected disruptions underscore the urgent need to evaluate joint\nvulnerabilities within healthcare and transportation infrastructure.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at\nthis scale using publicly available data on both hospital and transportation infrastructure.\nWhereas prior work has focused on individual facilities[20-23] or small systems[42-46]—\noften relying on synthetic data—our approach couples regional seismic risk models with\nlarge-scale network analysis to capture interdependent failures across an entire\nmetropolitan area. By integrating vulnerability data from 426 hospital buildings and 5,163\nbridges, and simulating disruptions across a transportation network with approximately 1.5\nmillion edges and 0.5 million nodes, we offer one of the most extensive assessments to\ndate of how earthquakes affect healthcare access. This study advances the state of the\nart in regional risk modeling globally, offering a scalable, computationally intensive\nframework that supports risk-informed decision-making in other high-risk urban areas.\n[1] Merino Y, Ceferino L, Pizarro S, de la Llera JC. Modeling hospital resources based on global\nepidemiology after earthquake-related disasters. Earthquake Spectra. 2024;40(4):2402-2429.\ndoi:10.1177/87552930241262788\nComment 2: In addition to the lack of sufficient motivation, the author did not utilize the state-of-\nthe-art in healthcare resilience analysis and used a simplistic approach in their assessment. For\nexample, it is assumed that damage to the building is a proxy for bed availability and resilience,\nwhich is not true. Many recent studies describe healthcare resilience as a function of physical\ninfrastructure, staff, and stuff. So, it appears that the authors are going back in time to use a\ndefinition that is no longer recognized in the research community.\nWe thank the reviewer for this important point and the opportunity to clarify the scope of our\nmodeling framework. We fully recognize that healthcare resilience is multidimensional, and that\nseminal work—including that of Dr. Mitrani-Reiser—has expanded the definition of hospital\nfunctionality to include structure, staff, and stuff. In fact, we referenced this work in the first version\nof the paper [1].\nAs noted in our literature review, these innovative models have been developed for analyses on\nsingle hospital buildings, where blueprints, space, and staff information are available to construct\na high-fidelity finite element model of the structure and analyze how different spaces of the\nstructure lose functionality. We have actually extended these high-fidelity modeling techniques to\nanalyze single hospitals in Chile using discrete event simulations [2]. These models can often be\nvery computationally expensive and not able to handle uncertainty exploration.\nWhile these models are powerful at the single-building scale, they do not work at the regional\nlevel because of the lack of data and the enormous demands for computational power. We are\nmodeling 76 hospitals with +400 buildings (not just one) in the Bay Area. For these types of\nproblems, we must change the approach as we are not interested in capturing how functionality\nchanges in each specific room of a building but instead in the relative resilience of one hospital\ncampus versus another. We created these regional models for hospitals a few years ago together\nwith Dr. Mitrani (who created the models you are referring to) to analyze effective plans for hospital\nsystem response to earthquake emergencies in the city of Lima, Peru [3]. In the field of regional\nrisk modeling, we create a model based on the available vulnerability information. In the Bay Area,\nwe created a regional risk model based on the available information on structural type, building\nheight, year of construction, structural performance category, and non-structural performance\ncategory. This is the state of the art in regional risk modeling as we are interested at loss of\nfunctionality at the whole hospital campus level and not at each hospital room. We acknowledge,\nthough that these models could be improved if high-resolution information for all hospitals would\nbecome available, which has not happened, unfortunately.\n[1] Jacques CC, McIntosh J, Giovinazzi S, Kirsch TD, Wilson T, Mitrani-Reiser J. Resilience of\nthe Canterbury Hospital System to the 2011 Christchurch Earthquake. Earthquake Spectra.\n2014;30(1):533-554. doi:10.1193/032013EQS074M\n[2] Merino Y, Ceferino L, Pizarro S, de la Llera JC. Modeling hospital resources based on global\nepidemiology after earthquake-related disasters. Earthquake Spectra. 2024;40(4):2402-2429.\ndoi:10.1177/87552930241262788\n69\n[3] Ceferino, L., Mitrani-Reiser, J., Kiremidjian, A. et al. Effective plans for hospital system\nresponse to earthquake emergencies. Nat Commun 11, 4325 (2020).\nhttps://doi.org/10.1038/s41467-020-18072-w\nWe rewrote this part in the introduction to make this point clearer (line 50):\nRecognizing these vulnerabilities, this paper investigates the effects of future\nearthquakes on healthcare access in the entire San Francisco Bay Area, California.\nPrevious research has largely focused on individual hospital vulnerability, using methods\nsuch as structural engineering analyses, performance-based assessments, and fault-tree\nevaluations to examine structural and non-structural damages within isolated\nfacilities.[20–23] Other studies evaluated patient treatment dynamics and medical\nresource demands through flow models and discrete event simulations in post-earthquake\nscenarios but are similarly limited to single-building analyses.[24–27] Yet, hospitals do not\nfunction in isolation—particularly in dense urban areas—as demonstrated by seismic\nevents in Chile, New Zealand, and Japan.[21, 28–31] Failures in individual hospitals can\ntrigger broader network impacts, overwhelming remaining facilities and forcing patients to\ntravel greater distances for care, severely exacerbating health outcomes for critically\ninjured individuals. Thus, understanding healthcare resilience requires examining\ninterconnected failures across healthcare and transportation infrastructure.[32–34]\nComment 3: Moreover, the paper suffers from many technical issues/mistakes, which causes\nthe analysis to be unsound. For example, their predictions show that many hospitals will\nexperience violent shaking at a scale not seen in over a century under a peak ground\nacceleration of 0.2. This is not possible. A peak ground acceleration of 0.2 is extremely low and\nis expected to cause only slight damage. The literature is overwhelmed with studies that show\nhow a 0.2 PGA typically causes slight damage to different archetypal structures.\nComment 3: We appreciate the reviewer’s attention to this point and the opportunity to clarify. It\nwas unclear whether the reviewer’s concern is that 0.2g is not a possible level of ground\nshaking, or that 0.2g does not constitute unusually high shaking for hospitals in the Bay Area.\nTo clarify, we reference 0.2g only as an illustrative example—to note that many hospitals in the\nregion have not experienced even this moderate level of shaking since the 1906 earthquake.\nImportantly, our risk analysis does not rely on this deterministic value. As described in the\nMethods section, our analysis is based on probabilistic seismic hazard models, which sample the\nfull distribution of ground motion intensities across a wide range of scenarios. For damage and\naccessibility assessments, we use spectral acceleration values at building-specific periods rather\nthan PGA.\nTo avoid confusion, we have revised the Methods text to clarify that 0.2g was mentioned purely\nas a historical reference point, and that our modeling approach is fully probabilistic and consistent\nwith established regional risk frameworks (line 469):\nbeen extensively studied to inform resilience policy-making in the Bay Area.47 The rupture\ngeometry was obtained from the Uniform California Earthquake Rupture Forecast\n(UCERF) 2.72 The earthquake ruptures the Hayward South and North sections over a\ntotal length of ∼110 km. Estimates of shallow shear wave velocities (averages at the top\n30 m of soil) are utilized over the entire Bay Area.73 With this information, we built the\njoint probability distribution of shaking intensities π(i) in R2D. We utilized a state-of-the-art\nground motion model74 for shallow crustal earthquakes to estimate medians and\nlogarithm standard deviations of i. i’s uncertainty is divided into two components.75 The\nfirst component captures between-event uncertainty and affects the entire region equally,\nbut it varies per intensity measure type, e.g., peak ground acceleration versus spectral\nacceleration. The first component captures correlation across different intensity\nmeasures.76 The second component captures within-event uncertainty and affects the\nentire region and intensity measure types differently. This component captures spatial\ncorrelation and correlation across different intensity measure types. We use a\ncomputationally efficient method to account for the second component.[62, 77] As stated\nearlier, we sampled 5,000 realizations of i and show expected values E(i) for the entire\nregion (Figure 1).\nWe have also clarified the manuscript to better explain that a PGA of 0.2g is not only plausible,\nbut expected for hospitals located near active faults. For magnitude 7.0 earthquakes at short fault\ndistances—as is the case for many sites along the Hayward Fault—PGAs well above 0.2g are\nconsistent with empirical ground motion prediction equations. As illustrated in Figure 1, several\nhospitals in our study area are within 5 km of the Hayward Fault, making higher levels of ground\nshaking entirely realistic.\nHistorical earthquake records further support this point. While the Bay Area has experienced only\nmoderate earthquakes in recent decades, most of the 76 hospitals in our dataset have not been\nexposed to shaking above 0.2g since the 1906 event. This is the motivation for referencing 0.2g\nin the text: even moderate levels of shaking would represent a significant increase over the\nhistorical experience of many healthcare facilities in the region.\nTo prevent further confusion, we revised the manuscript to clarify that the 0.2g value is used as a\nhistorical reference point, not as a basis for damage estimation. We also emphasize that our\ndamage predictions are derived from spectral acceleration values at building-specific periods, and\nthat the analysis accounts for the close proximity of hospitals to the Hayward Fault and the\ncorresponding hazard expected from a magnitude 7.0 event (line 149).\nWe modeled the rupture geometry (see Methods) and found that 10 acute care hospitals\n71\nwith 2167 beds (13% of the Bay’s total) are within just 5 km of the projected rupture. Our\nshaking intensity estimates indicate that many hospitals could experience levels of\nground motion not observed in recent earthquakes (See Methods). On average, we\npredict 51 hospitals will experience peak ground accelerations above 0.2g (Figure 2). By\ncomparison, the 1989 M 6.9 Loma Prieta Earthquake—previously the strongest since\nthe devastating 1906 M 7.9 San Francisco Earthquake—subjected only 14 hospitals to\nsimilar shaking intensities (Figure 2). Supplementary Figure 2 further contextualizes\nthese findings, illustrating how recent events such as the 2014 Napa Earthquake (M 6.0)\nexposed just three hospitals to significant shaking (>0.2g). In contrast, the historic 1906\nearthquake exposed nearly the entire portfolio (72 out of 76 hospitals)\nComment 4: In addition, the authors noted that many hospitals will have a probability of\ndamage above 0.25. What is the significance of 0.25 as a damage probability? and What type of\ndamage corresponds to 0.25 or more? Damage probability ranges from slight to moderate to\nextensive to complete, and each plays a role in quantifying healthcare functionality. To list that\nthe damage probability is 0.25 has no structural engineering relevance. In earthquake\nengineering, there is no relevance in saying that many hospitals had a damage probability of\nmore than 0.25. The reviewer recommends that the authors look at various FEMA documents\non seismic performance assessment to become more familiar with damage assessment\napproaches, including the various engineering demand parameters used for seismic evaluation\nof buildings and hospitals.\nComment 4: We thank the reviewer for this comment and for recommending the FEMA guidance\ndocuments. These are indeed excellent resources, and we are well acquainted with them. The\nlead author has used FEMA P-58, FEMA P-695, and HAZUS extensively for both research and\nteaching, including in the graduate course “Disaster Risk Analysis” at UC Berkeley. One co-author\nis a risk specialist with years of experience applying these frameworks to develop regional risk\nmodels and policy interventions in collaboration with the World Bank. Another co-author has\ncontributed to the development of NSF-funded tools at the NHERI SimCenter that operationalize\nthese frameworks for both regional and single-building risk assessments. We have referenced\nthese methodologies throughout our work and remain committed to aligning with best practices\nin the field.\nRegarding the reviewer’s specific point: the mention of a damage probability threshold of 0.25\nwas intended solely as an illustrative example—to demonstrate how the likelihood of damage\nincreases with proximity to the fault. It was not used as a cutoff or performance threshold in the\nactual analysis. As detailed in the Methods section, we compute full probability distributions of\nmultiple damage states for each hospital building using fragility functions and combine these with\na fault tree to assess hospital functionality.\nWe understand that our use of the 0.25 value may have caused confusion, and we have revised\nthe manuscript to make it clear that this number was only used for communication purposes, not\nas a substitute for engineering demand parameters or damage state classifications. Our\n72\nunderlying modeling framework is aligned with established seismic performance assessment\napproaches and incorporates state-based damage probabilities in a probabilistic risk analysis. To\nimprove clarity, we revised the Methods section to make this explicit. Below, we provide the\nrevised text in plain format, noting that the full mathematical expressions and formatting appear\nproperly in the main manuscript (line 410):\nHospitals can rapidly lose functionality at early stages of structural and non-structural\ndamage, as observed in the 2023 M 7.8 Kahramanmaraş Earthquake in Turkey, the 2011\nM 6.1 Christchurch Earthquake in New Zealand, and the 2010 M 8.8 Maule Earthquake in\nChile. We consider that damage thresholds, ds and dn, for the structural and non-\nstructural components, respectively, trigger the disruption of hospital functionality—that is,\nif either fails, the hospital loses functionality.\nWe estimate the probabilities of not exceeding these thresholds as:\n● pₖˢ = π(Dₖˢ ≤ ds | Iₖˢ = iₖˢ), and\n● pₖⁿ = π(Dₖⁿ ≤ dn | Iₖⁿ = iₖⁿ),\nwhich can be evaluated using earthquake fragility functions. We then model functionality\nas the intersection of these two events, meaning the hospital component remains\nfunctional only if both structural and non-structural elements perform adequately after the\nearthquake. Since Dₖˢ and Dₖⁿ are assumed conditionally independent, Fₖ (hospital\nbuilding functionality) becomes a Bernoulli random variable with probability pₖˢ × pₖⁿ. Accordingly, the joint probability of functionality given the data d is:\nπ(f | d) = ∏ₖ=1^m [ (pₖˢ × pₖⁿ)^fₖ × (1 - pₖˢ × pₖⁿ)^(1 - fₖ) ] (Equation 4)\nThe functionality of each hospital depends on the structural and non-structural\ncomponents, as described in Equation 4. The hospital portfolio includes various levels of\nSPC (Structural Performance Category) and NPC (Non-structural Performance Category),\nwhich influence the final functionality outcome.\nWe also estimate the probability distribution of the total number of functional beds Bₜ\nacross the region, computed as:\nBₜ = ∑ βₖ × Fₖ (Equation 5)\nwhere βₖ is the number of beds at hospital building k (assumed fully functional before the\nearthquake).\nTo account for hospitals with multiple buildings, we estimate the distribution of the total\nnumber of functional beds Bₕ for hospital h, where 𝓀ₕ is the set of buildings belonging to\nhospital h:\nIn addition, we believe that the previous version of the paper may have overemphasized the\n0.25 value, which may have led some readers to interpret it as a threshold used in the\ncomputation of hospital functionality. To avoid this misunderstanding, we have removed this\nreference from the main text.\nComment 5: Concerning this comment, the authors note that their analysis predicts that 8,501\nbeds will be lost throughout the Bay, and such predictions are based on slight damage (justified\nby previous studies that used slight damage to indicate loss of beds). Again, the literature is way\npast the idea of using damage to indicate bed losses and that stuff, staff, and physical systems\nshould be used to indicate bed losses. In addition, many studies show that hospitals continue to\noperate beyond slight damage, including the studies referenced by the authors. None of the\nstudies cited by the authors show that hospitals will lose functionality at slight damage. The\nStEER report cited by the authors indicates that only fully collapsed or severely damaged\nhospitals were evacuated after the Turkey EQ event. Unfortunately, the authors used this\nassumption to draw the study's main conclusions. Using slight damage drastically skews the\nresults towards showing significant bed losses, which is very unrealistic. Also, the authors note\nthat services within hospital buildings will be highly disrupted – a statement with no basis since\nthe authors did not model any hospital units or services.\nResponse 5:\nWe refer back to our response to Comment 1, where we explain that we do not apply the\n“structure, staff, and stuff” framework in this study because, although valuable, it is not scalable\nto the regional level given current data limitations. While we acknowledge the broader dimensions\nof healthcare resilience, our study focuses on structural and non-structural damage as proxies for\nloss of hospital functionality—an approach consistent with the current state of the art in regional\nseismic risk modeling.\nThe lead author has participated in post-earthquake field investigations in Türkiye, Ecuador, and\nNew Zealand and has directly observed instances where hospitals experienced disruption of\nservices even at slight damage levels. In fact, the lead author coordinated the hospital section of\nthe StEER report on the 2023 Türkiye Earthquake. Contrary to the reviewer’s comment, that\nreport does not state that “only fully collapsed or severely damaged hospitals were evacuated.”\nOur fieldwork, including interviews with hospital staff, documented several cases where hospitals\nwith slight or moderate damage lost functionality or required partial shutdowns due to non-\nstructural failures, dislodged equipment, or internal hazards. These findings are described in our\npeer-reviewed article [1]. We made the following notes on the paper and added references to\nthese cases (line 172):\nstructural damage exceeds a threshold of slight damage—conditions often shown to\ndisrupt hospital services (see Methods).[28-31]\n[1] Ceferino, L., Merino, Y., Pizarro, S. et al. Placing engineering in the earthquake response\nand the survival chain. Nat Commun 15, 4298 (2024). https://doi.org/10.1038/s41467-024-\n48624-3\n[28] Ardagh, M. W. et al. The initial health-system response to the earthquake in Christchurch,\nNew Zealand, in February, 2011. The Lancet 379, 2109–2115 (2012). URL http://dx.doi.org/10.\n1016/S0140-6736(12)60313-4. Publisher: Elsevier Ltd ISBN: 1474-547X (Electronic)\\r0140-\n6736 (Linking).\n[29] Kirsch, T. D. et al. Impact on hospital functions following the 2010 Chilean earthquake.\nDisaster medicine and public health preparedness 4, 122–128 (2010). ArXiv: 1011.1669v3\nISBN: 1938-744X (Electronic)\\r1935-7893 (Linking).\n[30] Shimoto, M. et al. Hospital Evacuation Implications After the 2016 Kumamoto Earthquake.\nDisaster Medicine and Public Health Preparedness 16, 2680–2682 (2022). URL https://www.\ncambridge.org/core/product/identifier/S1935789322000258/type/journal_article.\n[31] Achour, N. & Miyajima, M. Post-earthquake hospital functionality evaluation: The case of\nKumamoto Earthquake 2016. Earthquake Spectra 36,\nWe do recognize that there is uncertainty in defining the precise threshold of functionality loss,\nespecially in crisis settings. In some extreme situations, hospital staff were able to creatively adapt\nby cleaning up debris and isolating safe areas to continue providing care despite building damage.\nThese heroic efforts, while admirable, also underscore the risks involved for both staff and\npatients.\nTo address this uncertainty and better reflect the range of plausible responses, we have added a\nsensitivity analysis that explores alternative (higher) thresholds for functionality loss. We label\nthese scenarios “favorable” and “idealistic,” as we believe they represent optimistic assumptions\nthat may not hold in a context like the Bay Area, where liability, regulatory, and safety concerns\nmay prevent continued operation under damaged conditions (line 169).\nOur risk analysis predicts a substantial loss of hospital capacity throughout the\nBay Area following the earthquake scenario (see Methods). We estimate a loss of 8,165\nhospital beds, resulting in only 51% of total acute care beds remaining functional\n(standard deviation: 21%). This significant reduction in capacity is highly uneven across\nthe region (Figure 3, Table 1). Our baseline predictions assume hospitals lose\nfunctionality when structural or non-structural damage exceeds a threshold of slight\ndamage (see Methods). These damage conditions are often shown to disrupt hospital\nservices (see descriptions of multiple damage levels in Supplementary Tables 3 and 4).[\n21, 28–31] We also analyzed more optimistic scenarios with moderate (“favorable”) and\nextensive (“idealistic”) damage thresholds, resulting in increased overall functionality of\n79% and 93%, respectively (Figure 3 and Supplementary Table 5). However, empirical\n75\nevidence supports our baseline assumption, as hospitals often lose operations at early\nstages of damage. [21, 28–31]\nFigure 3. Post-earthquake functionality of hospitals and bridges across the Bay Area.\n[...] Probability distribution of functional acute care beds under baseline (slight), favorable\n(moderate), and idealistic (extensive) damage thresholds.\nSupplementary Table 5. Predicted post-earthquake hospital bed capacities across Bay Area counties\nunder thresholds of moderate (favorable) and extensive (idealistic) damage scenarios. The numbers in\nparentheses indicate the percentage in proportion to the pre-earthquake capacity.\nFavorable Idealistic\nCounty Mean Std. Dev. Mean Std. Dev.\nAlameda 1,743 (51%) 748 (24%) 2,635 (82%) 554 (17%)\nContra Costa 1,372 (75%) 378 (22%) 1,649 (94%) 188 (11%)\nMarin 482 (71%) 159 (25%) 581 (93%) 84 (13%)\nSan Francisco 3,258 (89%) 502 (14%) 3,547 (98%) 173 (5%)\nSan Mateo 1,269 (86%) 229 (16%) 1,390 (96%) 120 (8%)\nSanta Clara 3,512 (80%) 725 (17%) 4,068 (94%) 346 (8%)\nSolano 636 (88%) 116 (16%) 705 (98%) 50 (7%)\nSonoma 537 (90%) 64 (11%) 573 (98%) 26 (4%)\nTotal 13,129 (79%) 2,583 (16%) 15,492 (93%) 1,271 (8%)\nWe also appreciate that the reviewer is familiar with the “structure, staff, and stuff” model. While\nit brings valuable insight, we note that this framework still does not model human behavior, such\nas staff decision-making or willingness to work in damaged conditions—factors that play a critical\nrole in hospital functionality. To date, these behaviors remain challenging to represent accurately\nin either building-level or regional modeling frameworks. We believe that more research is needed\nin this area to enable their integration into future probabilistic risk models.\nFinally, we note that loss of “stuff” (e.g., medical equipment and supplies) is often directly linked\nto damage to non-structural components or structural failures in specific hospital zones. Even in\nhigh-fidelity single-building models, damage remains the primary driver of functionality loss, as\nconfirmed by our field deployments and multiple case studies.\nComment 6: Another significant issue is that bridge damage and failure analysis are not\nincluded in determining travel time. The travel time calculated in the paper can not be correct\ndue to the lack of bridge failure analysis.\nResponse 6: After reading your reviews (along with those from the other reviewers), we invested\nsignificant effort into improving our modeling of transportation infrastructure disruptions in the Bay\nArea. This became a major component of our revision and is the main reason for the time it took\nus to respond.\nand significantly expanded the transportation network model, which now includes approximately\n1.5 million edges and 0.5 million nodes. This refinement substantially increased computational\ndemands: the 5,000 Monte Carlo simulations required for the analysis took about two weeks to\nrun on a laptop equipped with an Apple M2 chip and 64 cores. We ran multiple iterations to ensure\nthe model was fully debugged and stable.\nThanks to this updated formulation—and your review—we are now able to capture how hospital\nand transportation failures interact to influence post-earthquake hospital accessibility. Our\nrevised analysis highlights several key cascading effects:\n● Widespread transportation failures lead to compound access losses, with travel times\nincreasing by over a factor of 10 in some areas.\n● Some hospitals in the Bay Area may become completely isolated due to bridge failures.\n● Urban communities—particularly in Fremont and Novato—may lose access to essential\nservices due to localized bridge disruptions.\nWe include some of the updated results and manuscript revisions below.\nAbstract (line 15):\nconnectivity data, we analyze 76 hospitals (426 buildings with 16,639 beds) and 5,163 bridges\nwithin a vast network of ∼1.5 million edges and ∼0.5 million nodes [...] Widespread transportation\nfailures further restrict access, increasing regional travel times by 177% and exceeding 1000% in\nparts of East Bay, potentially fully isolating hospitals and entire urban communities. These findings\nunderscore the urgent need for resilient healthcare and transportation infrastructure to mitigate\nlife-threatening disruptions following major earthquakes.\nIntroduction (line 80):\nTo fill this critical gap, we investigate, for the first time, joint failures of healthcare and\ntransportation networks across the San Francisco Bay Area after a major earthquake. By\nexamining diverse urban communities near active seismic faults—often underrepresented in\nprevious studies—this research provides valuable insights into post-earthquake healthcare\naccess, particularly relevant for earthquake-prone regions worldwide with diverse populations\nand similarly vulnerable hospitals and bridges, such as those in the U.S., Japan, and Türkiye.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at this\nscale using publicly available data on both hospital and transportation infrastructure. Whereas\nprior work has focused on individual facilities[20-23] or small systems[42-46]—often relying on\nsynthetic data—our approach couples regional seismic risk models with large-scale network\nanalysis to capture interdependent failures across an entire metropolitan area. By integrating\nvulnerability data from 426 hospital buildings and 5,163 bridges, and simulating disruptions across\na transportation network with approximately 1.5 million edges and 0.5 million nodes, we offer one\nof the most extensive assessments to date of how earthquakes affect healthcare access. This\nstudy advances the state of the art in regional risk modeling globally, offering a scalable,\ncomputationally intensive framework that supports risk-informed decision-making in other high-\nrisk urban areas.\nNew Section on Post-earthquake Bridge Functionality (line 196):\nOur risk analysis model predicts that 1,469 bridges out of 5,163 would be damaged due to the\nearthquake scenario (see Methods). Consequently, 3,693 bridges (72%, standard deviation:\n17%) are expected to remain undamaged and fully operational (Figure 3). Some damaged\nbridges could continue operating, albeit at reduced capacities. Under our “baseline scenario”,\nwhere only bridges with at most slight damage remain operational, a total of 3,964 bridges\n(77%, standard deviation: 15%) would function. In a more optimistic “favorable scenario”, where\nbridges with at most moderate damage also remain partially operational, 4,069 bridges (79%,\nstandard deviation: 14%) could provide service. In an idealistic scenario, which assumes that\ncontributors openstreetmap.org/copyright.\nbridges even with extensive damage retain emergency functionality, 4,527 bridges (88%,\nstandard deviation: 11%) would remain operational.\nSimilar to hospitals, Alameda County faces the most severe transportation impacts (Figure 3,\nTable 2). Under the baseline scenario, Alameda retains only 44% functional bridges (from 642\ndown to 282). Marin County is second most impacted, retaining 64% (from 195 to 125 bridges).\nAdditionally, estimates of reductions in bridge travel speeds (see Methods)—calculated from\ntheir damage probabilities—highlight Alameda’s higher vulnerability due to proximity to the\nHayward Fault rupture (Figure 3, Table 2).\nFigure 3. [...] Lower left: Probability distribution of fully functional bridges under baseline (slight),\nfavorable (moderate), and idealistic (extensive) damage thresholds. Lower right: Spatial\ndistribution highlighting bridges with post-earthquake travel capacities below 75%. Results\ngenerated from 5,000 Monte Carlo simulations.\nRevised findings on Accessibility (line 223):\nAt a more detailed neighborhood scale, these disruptions are even more pronounced (Figure 4).\nWe identified six densely populated zip codes (each exceeding 15,000 residents, labeled #1 to\n#6 in Figure 4) facing substantial reductions in healthcare access. The most severely impacted is\nNovato (#1, Marin County), where travel times increase nearly 25-fold, from 7.3 to 185.5 minutes,\naffecting approximately 18,000 residents. Similarly, a Fremont zip code (#6, Alameda County)\nwith roughly 66,000 residents experiences an eightfold increase (from 8.4 to 42.2 minutes). Other\nsignificantly impacted zip codes in Richmond (#4), Oakland (#2 and #5, Alameda County), and\nSan Jose (#3, Santa Clara County) face travel time increases of 10, 11, 9, and 11 times their pre-\nearthquake levels, respectively. These results underscore the dramatic reshaping of healthcare\naccess throughout East Bay communities along the earthquake rupture.\nFinally, we explored the relative contributions of hospital and transportation infrastructure\ndisruptions through scenario analyses (Figure 4). We compared the baseline (None, no\ninfrastructure disruptions) against scenarios modeling probabilistic damage only to transportation\ninfrastructure (Transp., hospitals fully resilient), only to hospital infrastructure (Hosp.,\ntransportation fully resilient), and simultaneous probabilistic disruptions to both (Transp. & Hosp.).\nWhen considering disruptions only to transportation infrastructure (Transp.), average Bay Area\ntravel times increase by 41% (from 6.1 to 8.6 minutes), notably less than the combined scenario\n(Transp. & Hosp., 177% increase). Conversely, modeling only hospital infrastructure disruptions\n(Hosp.) yields a 79% increase (from 6.1 to 10.9 minutes), highlighting greater relative fragility in\nhospital networks.\ninfrastructure failures lead to disproportionately severe impacts (Figure 4). For example, as\nmentioned earlier, in the most severely impacted zip code (Novato, labeled #1 in Figure 4),\ntravel times dramatically increase from 7.3 to 185.5 minutes under combined disruptions\n(Transp. & Hosp.), compared to only 14.1 minutes when transportation disruptions are excluded\n(Hosp. only). Similarly, for other highly affected zip codes (labeled #2 to #6 in Figure 4),\ntravel-time ratios notably decrease—from 11, 11, 10, 9, and 8 under combined disruptions, to\n6.4, 3.1, 6.1, 4.7, and 3.4 when transportation disruptions are not considered—highlighting\nthe critical influence of compounding infrastructure failures on healthcare access.\ncontributors openstreetmap.org/copyright.\nFigure 4: Access to functional acute care hospitals in the Bay Area after the earthquake.\nUpper left: Post-earthquake (Post-EQ) increases in travel time at the zip-code level compared to\npre-earthquake (Pre-EQ) conditions, highlighting densely populated areas that are most\nseverely impacted. Upper right: Ratios of post- to pre-earthquake travel times to the closest\nacute care hospitals. Lower right: Distribution of travel times per zip code under four scenarios:\nNone (no infrastructure disruptions), Transp. (only transportation infrastructure is vulnerable),\nHosp. (only hospital infrastructure is vulnerable), and Transp. & Hosp. (both transportation and\nhospital infrastructures are vulnerable). Lower left: Ratios of post- to pre-earthquake travel times\nwhen only hospital infrastructure (Hosp.) is vulnerable. Results generated from 5,000 Monte\nCarlo simulations.\nNew section on Isolated Communities and Hospitals (line 252):\nanalyzed travel volumes to the closest acute care hospitals before and after the earthquake.\nFigure 5 shows pre-earthquake road usage, with line thickness representing travel volume. Roads\nin brown highlight those whose usage falls above the 90th percentile based on pre-earthquake\nconditions, emphasizing the most critical travel routes. As expected, the highest-usage roads prior\nto the earthquake were located near hospitals, especially in densely populated areas with fewer\nhospitals. For instance, communities in Fremont (#6 in Figures 4 and 5) are served by only two\nhospitals, while Richmond (#4) relies on just one.\nFigure 5 also displays post-earthquake road usage, using the same pre-earthquake 90th\npercentile threshold to highlight heavily traveled roads. After the earthquake, patient travel\npatterns shift significantly, with many communities forced to travel longer distances along major\ncorridors. For example, residents in Oakland (#2 and #5 in Figures 4 and 5), who previously relied\non nearby hospitals, will now have to travel west to the San Francisco Peninsula or east to Walnut\nCreek due to simultaneous disruptions in both hospital and transportation infrastructure. These\nshifts help explain the steep increases in travel times observed in East Bay communities along\nthe rupture zone.\nFour major bridges connect the East and West Bay: the Richmond–San Rafael, Oakland–San\nFrancisco Bay, San Mateo–Hayward, and Dumbarton bridges. Before the earthquake, no patients\nneeded to cross these bridges to reach their nearest acute care hospital (Figure 5). After the\nearthquake, however, these bridges become critical, with travel volumes increasing to 3.6, 9.3,\n6.3, and 13.6 times the pre-earthquake 90th percentile values—reflecting the large-scale\nredistribution of healthcare demand.\nOur analysis also revealed a more complex post-disaster phenomenon: micro-scale isolation of\nhospitals and communities due to localized bridge failures. For example, the hospital serving the\nmost severely impacted zip code in Novato (#1 in Figures 4 and 5), which has 64 beds, depends\nentirely on a single bridge for access. If this bridge fails, the hospital becomes inaccessible,\nincreasing travel times from 7.3 to 185.5 minutes for the surrounding population.\nMore concerning, we found that urban neighborhoods near Fremont (#6) could become fully\nisolated (Figure 5). In one area, failure of three bridges would trap one part of the neighborhood;\nin another, a different set of three bridge failures would isolate the remaining part. These\ncommunities would lose access not only to hospitals but also to other essential services such as\ngrocery stores and pharmacies—illustrating how cascading infrastructure failures can sever\nlifeline access in disaster scenarios.\ncontributors openstreetmap.org/copyright.\nFigure 5: Mobility to reach the closest functional acute care hospital in the San Francisco Bay\nArea. Upper left: Pre-earthquake travel volumes to the closest acute care hospitals. Numbers 1\nto 6 indicate the hospitals serving the dense zip codes with the highest post-earthquake\nincreases in travel time. Upper right: Projected travel volumes after the earthquake, showing\nmajor shifts in patient mobility. The red-shaded corridor illustrates how Oakland residents (#2\nand #5) must travel west to the Peninsula or east to Walnut Creek due to hospital and\ntransportation disruptions. Lower left: The hospital serving zip code #1 (Novato) relies entirely\non a single bridge; if the bridge fails, all access to its 64 beds is lost. Lower right: Community\nnear zip code #6 (Fremont), where the southern and northern sections become fully isolated if\nthree different bridges fail in each area. Results are based on 5,000 Monte Carlo simulations of\npost-earthquake patient mobility.\nand outdated by more detailed analysis, incorrect, or indicate problems with how the study was\nconducted. For example, the authors suggested that building functionality is modeled with\nBernoulli distribution. The state of the art on building functionality (plz see work by Henry Burton\nor Naiyu Wang) has shown building functionality to be much more complex than this, requiring\nmore details analysis and the inclusion of various probabilities, including the availability of crew\nworkers, the time it takes to issue a permit, material availability, and many other things. These\nparameters will impact the hospitals' functionality and the staff's viability since their homes could\nbe damaged - criteria that were not included in this study. Assuming a simple Bernoulli function\nhas no basis.\nResponse 7: We thank the reviewer for the opportunity to clarify our modeling approach and the\nrole of the Bernoulli distribution in our framework. We fully agree that the evolution of hospital\nfunctionality after an earthquake depends on a wide range of factors beyond structural integrity,\nincluding crew availability, permitting timelines, material logistics, and staff viability. These\nconsiderations are especially relevant for modeling long-term recovery trajectories, where the full\nrestoration of services can take multiple years. For example, following major earthquakes such\nas the 2010 Chile Earthquake and the 2023 Türkiye Earthquake, the repair of residential and\nhealthcare buildings often took 1 to 4 years, depending on the severity of damage, logistical\nconstraints, and institutional capacity.\nIn contrast, our study focuses on a regional, scenario-based assessment of hospital system\nfunctionality and accessibility during the first days to months following a major earthquake. Within\nthis timeframe, building functionality is estimated based on damage to structural and non-\nstructural components, which serve as proxies for immediate operability. This approach is\nconsistent with established practices in regional seismic risk modeling and is appropriate for\nidentifying where healthcare access is likely to be most compromised in the aftermath of a major\nevent.\nTo support this analysis, we model hospital building functionality using correlated Bernoulli\nrandom variables, not independent ones. These variables are derived from fragility-based\nexceedance probabilities informed by spatially correlated ground motions and component\ndamage. Simulating from high-dimensional correlated Bernoulli distributions is computationally\nintensive—especially at the scale of this study, which includes 76 hospital campuses and over\n5,000 bridges—and requires careful approximations to ensure tractability. We have clarified these\naspects in the revised Methods section (line 421).\nThis formulation reflects our focus on estimating hospital functionality during the\ninitial post-earthquake period, where service disruption is most directly tied to structural\nand non-structural damage. Rather than modeling the full trajectory of hospital\nrecovery\\cite{Burton2016}—which depends on permitting, logistics, and staffing—we\nassess whether each building is likely to remain operational immediately after the event.\nTo enable this analysis across hundreds of facilities and correlated scenarios, we use\nBernoulli random variables derived from fragility-based exceedance probabilities,\naccounting for spatial dependencies in seismic intensity and building response (Figure 7).\nWe are also familiar with the recovery modeling frameworks developed by Henry Burton and\nNaiyu Wang. In fact, the lead author has previously collaborated with Henry Burton [1], using the\nsame structural modeling techniques that underpin Burton’s recovery framework [2]. While these\nframeworks provide valuable insights into building-level recovery and time-dependent\nfunctionality, they also rely on limit-state exceedance representations and fault-tree logic—\nconcepts that closely align with our modeling structure. For example, Burton’s framework uses\nthree discrete functionality states (none, partial, full), whereas we adopt a binary representation\nthat is appropriate for our study’s scope, scale, and data constraints. Moreover, many of Burton’s\nrecovery paths transition directly from no functionality to full functionality, which is conceptually\nsimilar to the transitions used in our study.\n[1] Burton, Deierlein, Lallemant, and Lin. \"Framework for incorporating probabilistic building\nperformance in the assessment of community seismic resilience.\" Journal of Structural\nEngineering 142.8 (2016): C4015007.\n[2] Lallemant, Burton, Ceferino, Zullock, and Kiremidjian. \"A framework and case study for\nearthquake vulnerability assessment of incrementally expanding buildings.\" Earthquake spectra\n33.4 (2017): 1369-1384.\nWe acknowledge that a binary Bernoulli model does not capture partial functionality within\nindividual buildings, but our framework allows for partial functionality at the hospital campus level,\nsince each campus includes multiple buildings evaluated with different random variables. This\nstructure enables us to estimate the proportion of functional capacity at each hospital across\nsimulated scenarios.\nTo further address the reviewer’s concern, we have added a sensitivity analysis (see response to\nComment 5 and Supplementary Note 4) that explores how varying functionality thresholds affect\naccessibility outcomes.\nComment 8: Another major issue in the methods section is that the authors tried to connect the\ndata collected from the vulnerability rating to the HAZUS fragility. This connection is based on\nassumptions not validated or supported by previous studies. The authors tried to use ASCE-7 to\ncome up with some numbers that reflect a lack of understanding of the code philosophy. I\nrecommend utilizing fragility functions that reflect the building characteristics; otherwise, the\ncalculated damage does not represent reality.\nResponse 8: Thank you very much for the helpful feedback. We would like to clarify how the\nfragility functions used in our study are linked to building characteristics and why we believe this\napproach is appropriate for a regional-scale hospital risk assessment.\nThe fragility functions applied in our model do reflect key building characteristics, including\nstructural system type, effective building height, and the official Structural Performance\nCategories (SPC) and Non-structural Performance Categories (NPC) assigned to each hospital\nby the California Department of Health Care Access and Information (HCAI). These SPC and\nNPC ratings reflect engineering assessments of seismic vulnerability and are widely used by the\nState of California to inform seismic upgrade policies.\nIn line with the guidance provided in the FEMA HAZUS Technical Manual (Section 5.7: Guidance\nfor Expert Users), buildings “deemed not to conform to modern code provisions should be\nassigned a lower seismic design level or defined as Pre-Code buildings if not seismically\ndesigned.” Following this recommendation, we mapped SPC 1 buildings to pre-code fragilities,\nSPC 2–3 to moderate-code, and SPC 4–5 to high-code fragility curves. This mapping approach\nis consistent with prior studies and allows us to leverage the extensive fragility data provided in\nHAZUS while making transparent assumptions about code conformance.\nWe acknowledge that this method involves simplifications and introduces uncertainty. However,\nsuch approximations are common in regional seismic risk modeling, where detailed high-\nresolution building-by-building structural data are typically unavailable. To address this, we\nincorporate Monte Carlo simulations to propagate uncertainties in damage and functionality\nestimates across the building portfolio. In addition, we conducted a sensitivity analysis to explore\nhow varying damage thresholds influence our hospital functionality outcomes (see response to\ncomment 5.\nWe also want to clarify that we did not derive fragility functions from ASCE 7 provisions, but only\nreferenced ASCE 7 to support our assumptions about differences in design intent across building\ncode eras. The fragility functions themselves are based on HAZUS and were adjusted according\nto the SPC/NPC mapping logic.\nTo ensure transparency, we have added more detail to the Methods section (see \"Hospital\nVulnerability Modeling\") and Supplementary Table 1 describing how SPC 2 buildings were\nclassified based on official HCAI reassessments. We also added Supplementary Table 3, which\nincludes definitions of the damage states for the three most common structural systems in our\ndataset—Steel Moment Frames, Concrete Shear Walls, and Steel Braced Frames—and\nSupplementary Table 4, which defines non-structural damage for elements like suspended\nceilings and mechanical/electrical equipment, which often drive hospital service disruptions. We\nadded the following (line 117):\nIn this paper, we used the Structural Performance Categories (SPC) and Non-structural\nPerformance Categories (NPC), established and reported by California’s Department of\nHealth Care Access and Information (HCAI), to characterize structural and non-structural\ndeficiencies.[44] Each hospital building receives vulnerability ratings (SPC or NPC)\nranging from 1 to 5, from the most to the least vulnerable. Supplementary Tables 1 and\n2 fully describe SPC and NPC.\nSupplementary Table 3. Definitions of structural damage states for most common structural types in the\nhospital building portfolio: S1: Steel Moment Frame; C2: Concrete Shear Walls; S2: Steel Braced Frame.\nThese definitions come from HAZUS and were adopted in this study.4\n[Table Redacted]\nSupplementary Table 4. Definitions of non-structural damage states for two acceleration-sensitive\ncomponents whose failures often disrupt hospital services. These definitions come from HAZUS and\nw ere adopted in this study.4\n[Table Redacted]\nWe also detailed further SPC 2:\nSupplementary Table 1. Structural Performance Categories (SPC) according to California’s Department of Health\n[Table Redacted]\nComment 9: The authors also assumed that some hospitals could accept patients if only one\nbed was functional, which is a weak assumption. If only one bed is functional, then the hospital\nmust be substantially damaged, and if most of the hospital is damaged, then it will be unsafe to\nutilize. Please check previous studies reporting that many hospitals evacuated, even when they\nhad more than 50% of their capacity due to severe damage. I doubt whether any case study or\nexpert opinion will support the assumption made by the authors.\nResponse 9: We fully agree that treating a hospital as operational with just one functional bed\ndoes not reflect realistic clinical or safety conditions. In response to this concern, we have updated\nour model to require that hospitals retain at least 50% of their functional bed capacity to be\nconsidered able to receive patients.\nThis change was motivated by both prior studies and field observations. For example, during post-\nearthquake reconnaissance following the 2023 Kahramanmaraş earthquakes in Türkiye, the lead\nauthor visited several hospitals that were evacuated or rendered inoperable despite partial\nstructural integrity. Closure decisions were often based on internal system damage, safety\nassessments, or operational concerns—not merely bed availability. Similar outcomes were\nreported after the 2010 Chile and 1994 Northridge earthquakes, where hospitals with remaining\ncapacity still ceased operations due to broader functional limitations.\nWhile our model does not explicitly simulate these decision-making factors, they highlight the\nimportance of establishing more conservative functionality thresholds. This is why we adopted the\n50% bed capacity rule and also explored sensitivity to different damage thresholds in our updated\ntravel time analysis (see response to Comment 6). These revisions are reflected in the\nmanuscript. Please note that the equation formatting here is adapted for Google Docs and may\ndiffer slightly from the typeset version in the manuscript. For the full mathematical expression and\nformal notation, we kindly refer the reviewer to the main manuscript (line 619).\nIn the post-earthquake scenario, all hospitals are assumed to be functional. Then,\nEquation 11 finds the shortest time to reach an acute care hospital p (see Figure 8).\nIn an earthquake scenario, we adjust Equation 11 to:\nT = min { t(h) | h ∈ ĥ }**\nwhere ĥ = { h | Bh > 0.5 × βh for all h ∈ ĥ }, to account for the reduction in hospital\ncapacity. In this case, ĥ is the set of hospitals that retain more than 50% of their pre-\nearthquake bed capacity (βh). This means that, in our model, a hospital must have at\nleast 50% of its beds functional (Bh > 0.5 × βh) in order to be considered available to\nreceive new patients. Studies on hospital disaster resilience during earthquakes suggest\nthat a significant reduction in functional bed availability can severely strain hospital\noperations, particularly in accommodating new patients in the emergency department.²⁷\n⁹⁷\nComment 10: Another major issue in this paper is that the authors ignored damage to the\ntransportation network, which is a fundamental component when calculating the estimated\ndemand at different hospitals. Damage to bridges and the road network will significantly change\nthe shortest paths calculated in this study, which can lead to cases where some functional\nhospitals see less demand due to reduced accessibility. Many previous studies on healthcare\nsystems reported that impact and some even included the dynamic effect of the change in travel\ntime on hospital demand and accessibility.\nResponse 10: Thanks for the constructive comment. We believe we have address this on the\nresponse to comment 6\nComment 11: The authors also assumed the number of patients proportional to the number of\npopulations. However, considering the variation in patient distribution, especially during\ndisasters, is critical for accurate demand assessment, and again, many studies have already\ndone that. Most earthquake casualties are related to building collapse, a function of the building\ncharacteristics and earthquake intensity measured at the building locations. So, the assumption\nmade by the authors has no basis and will significantly impact the results and main conclusions\nof the study.\nResponse 11:\nWe thank the reviewer for raising this important point. We spent significant time considering\nwhether to explicitly model injury distributions from earthquakes in the Bay Area as part of this\nstudy. While we have modeled spatial injury distributions in other regions with high expected\ncasualties—such as Peru[1]—we ultimately decided not to include this component here for two\nmain reasons.\nFirst, our focus is on hospital accessibility in the days to a few months following a major\nearthquake, rather than the immediate emergency response phase. While surges of severely\ninjured patients are critical in the early aftermath, they typically last only a few days—except in\nrare large-scale disasters such as the 2023 Türkiye Earthquake, where demand persisted for\nseveral weeks.¹ In the Bay Area, where building code compliance is higher, we expect a shorter\nemergency phase and lower injury loads. Our goal was to evaluate accessibility during the\ntransitional period when hospitals may still be closed or operating below capacity, and when\nroutine or follow-up care becomes increasingly important. To model this, we used population-\nweighted demand, assigning it to the network based on census tract centroids (Figure 8). We\nadded an explanation to the manuscript (line 645):\nOur goal was to quantify hospital accessibility losses beyond the immediate\nemergency period, recognizing that hospitals often take months or even years to be\nrepaired. Because people are typically injured within damaged buildings, patient surges\nafter earthquakes generally last only a few days—except in rare extreme cases such as\nthe 2023 Turkiye Earthquake. To focus on long-term access rather than short-term\nemergency response, we did not model injury locations directly. Instead, we assumed that\npatient demand is proportional to population distribution and modeled accessibility\naccordingly. For the Bay Area, we based our analysis on population-weighted access loss\nand identified the network’s vertices closest to the centroids of census tracts to define the\nset p (Figure 8).\nSecond, the state of the art in spatially explicit casualty modeling remains limited—especially in\nCalifornia, where recent damaging earthquakes have not produced large empirical injury\ndatasets. To address this gap, we are currently leading an NSF-funded project (NSF Award\n#2410291) to develop high-resolution, empirically grounded casualty models for the Bay Area.\nThis includes ongoing fieldwork, structural modeling, and healthcare systems simulation. We plan\nto incorporate the reviewer’s suggestion as part of that forthcoming work.\n[1] Ceferino, L., Merino, Y., Pizarro, S. et al. Placing engineering in the earthquake response\nand the survival chain. Nat Commun 15, 4298 (2024). https://doi.org/10.1038/s41467-024-\n48624-3\nComment 12: Overall, the paper addresses a problem investigated in the past using simple\napproaches that are not necessarily detailed and, in some cases, infused with incorrect\nassumptions and/or calculations. Unfortunately, on these grounds, this paper can not be\npublished.\nResponse 12: We appreciate the reviewer’s feedback and the opportunity to clarify the novelty\nand rigor of our work. We respectfully disagree with the assessment that this study revisits prior\nwork using simple or incorrect approaches. As outlined in our responses to earlier comments,\nwe have taken care to develop a regionally scalable, computationally intensive model that\nintegrates structural and non-structural fragility modeling, correlated damage simulations across\nmore than 5,000 infrastructure elements, and accessibility calculations on disrupted\ntransportation networks—including bridge failures.\nWhile our approach is necessarily approximate in some respects—as is common in regional risk\nmodeling—we have been careful to follow established methodologies (e.g., HAZUS-based\nfragility models, Monte Carlo simulation), and we have incorporated improvements in model\nfidelity compared to previous studies. For example, we use official SPC and NPC classifications\nfor hospital buildings, spatially correlated damage fields, and we explicitly model threshold-based\nhospital capacity loss and rerouting under bridge disruptions. In response to earlier reviewer\ncomments, we have also:\n● Revised our hospital functionality threshold to 50% capacity, based on field observations\nand supporting literature.\n● Clarified and expanded our modeling of hospital vulnerability, including mapping\nprocedures and fragility assumptions.\n● Added a sensitivity analysis to assess the effects of alternative damage thresholds.\n● Emphasized that our focus is on post-emergency accessibility over the weeks and months\nfollowing an earthquake, rather than short-term surge demand (e.g., couple of days).\n● Analyzed the transportation infrastructure risks, capturing more realistic travel times and\nidentifying a potentially isolated hospital and community.\nWe believe these revisions significantly strengthen the manuscript and address concerns\nregarding assumptions and scope. We have been transparent about our modeling choices and\nlimitations, and have taken steps to validate them against prior studies and post-earthquake\nobservations (e.g., fieldwork in Türkiye, Chile, and California).\nWe respectfully hope the reviewer will reconsider the value of this contribution, especially in light\nof these clarifications and improvements.\nComment 13: Reviewer #2 (Remarks on code availability):\nI evaluated the authors' online sources, and they all have sufficient information.\nResponse 13:\nThank you.\nReviewer #3\nReviewer #3 (Remarks to the Author):\nComment 1: The manuscript presents a case study on the impacts of a scenario earthquake on\nthe Hayward fault on the San Francisco Bay Area’s hospital capacity. It is very interesting work\nand implemented using state of the art approaches, giving good weight to the discussion points\nprovided.\nComment 2: We thank the reviewer for their thoughtful and encouraging feedback. We are\ngrateful for the recognition of our work’s relevance and the implementation of state-of-the-art\napproaches, and we are especially glad that the discussion points resonated.\nWe sincerely apologize for the delay in submitting our response. A major revision was undertaken\nto expand the analysis and address reviewer suggestions thoroughly, which required substantial\ntime and computational effort.\nFirst, we have made significant improvements to the manuscript’s structure and presentation. We\nstreamlined the introduction and results sections to improve clarity, reduced redundancy, and\nensured a concise and technically focused tone. We also revised scientific estimates for\nconsistency and precision and addressed editorial corrections to improve the overall readability\nand professionalism of the paper.\nMost notably, we expanded the scope of the analysis to explicitly incorporate transportation\ninfrastructure disruptions, including bridge failures. This addition allowed us to assess hospital\naccessibility in greater detail and revealed the potential for complete isolation of both a hospital\nand a community following a major Hayward Fault earthquake. We believe this significantly\nenhances both the rigor and real-world applicability of the study. We provide more detail on this\nmajor addition at the end of our response.\nTo help the reviewer navigate our response, we have marked our replies in blue and used red\ntext in the manuscript to indicate the changes. We hope the reviewer finds the revised version\neven more impactful and technically complete, and we truly appreciate the supportive and\nconstructive review.\nComment 2: The biggest issue I found with the work was the length of the text that made it\nrather difficult to read. I understand that the authors wish to discuss their results in detail, but I\nfelt much of the discussion could have been delivered in half the amount of text. I would strongly\nurge the authors to revise the initial parts of the paper and trim unnecessary sentences or\nanecdotes that do not contribute to the main points being delivered.\nResponse 2: Thank you for this comment. We reduced the main text from ~5,000 words to\n4,000 words. We wanted to reduce it further but the addition of the transportation network\nrequired us to add more text.\nComment 3: Furthermore, some of the text is written in a manner that seems less like a\ntechnical article, and more like a magazine article for non-technical readers. The excessive use\nof adjectives (i.e. violent shaking) and adverbs (i.e. we rigorously study) and terminology like\n“we predict” seems a little exaggerated, at least in this Reviewer’s opinion. Reducing these\nwould help the article’s conciseness.\nResponse 3: We revised the manuscript to reduce the use of adjectives, adverbs, and informal\nexpressions such as “violent shaking,” and “we rigorously study” and “we predict.” Several\nsentences were re‑written to eliminate redundant phrasing. We avoided all the above mentioned\nadjectives and the current manuscript looks more concise.\nComment 4: Overall, it is good and interesting work that should be accepted following some\nminor adjustments.\nResponse 4: Thank you. We have reviewed the paper according to all these comments.\nSome minor observation:\nComment 5: Abstract:\nCorrect “In East Bay” to “In the East Bay”\nResponse 5: Change executed\nComment 5: Change “are way higher” to more technical terminology “are much higher”\nResponse 6: Change executed\nComment 6: Page 1, the term “mass-casualty earthquake” sounds a little dramatic for a\ntechnical publication. Consider revising.\nResponse 6: We changed it to “major”.\nComment 7: The authors note that Alfred E. Alquist Hospital Seismic Safety Act was enacted\nin 1973 but twelve Pre-Alquist Act hospital buildings received red tags following the 1994\nNorthridge earthquake. Does this mean that the act was focused on new hospitals and existing\nhospitals were left as is? Please comment.\nResponse 7: Yes, the 1973 Alquist Act applied only to new hospital construction. As described\nin the manuscript, it was the 1994 Northridge Earthquake that revealed the vulnerability of older\nhospital buildings and prompted the passage of Senate Bill 1953, which introduced retrofit\nrequirements for existing facilities. As shown in Figure 1, many hospitals have yet to complete\nthese retrofits. The current deadline is 2030, but many are unlikely to meet it. We have revised\nthe text to clarify this timeline and policy progression (line 34).\nIn the U.S., even moderate earthquakes have severely disrupted healthcare access. The\nin forced evacuations, two structural collapses, and more than 40 fatalities.¹³ These\ntragedies prompted legislative action, notably the Alfred E. Alquist Hospital Seismic\nSafety Act of 1973, mandating stronger, more resilient hospital infrastructure. However,\nthe law primarily applied to new hospital construction and did not require immediate\nretrofits of existing facilities built before 1973. The law emphasizes that hospitals must\nbe capable of protecting vulnerable patients and providing critical medical services\nimmediately after disasters, highlighting the importance of resilience planning in disaster-\nprone regions.¹³\nIn 1994, the M 6.7 Northridge Earthquake severely disrupted healthcare services,¹⁴\nforcing evacuations at eight acute care hospitals in Los Angeles County and causing\naround USD 3 billion in losses.¹⁵ Twelve hospital buildings constructed before the Alquist\nAct were deemed unsafe for occupancy. Post-Alquist Act buildings experienced less\nstructural damage, but non-structural damage was still extensive.¹⁶ These disruptions\nprompted California Senate Bill 1953 (passed in 1994), mandating significant retrofits to\nacute care hospitals by 2030.¹⁷ ¹⁸ Notably, many hospitals face financial barriers that\nmay prevent them from meeting these critical resilience goals.¹⁹\nComment 8: Also, the authors write 12 hospitals, but a few lines earlier, 11 were mentioned.\nCheck that these are correct.\nResponse 8: We corrected this (paragraph is in the previous response). It should have been\ntwelve. Thank you for pointing this out.\nComment 9: Does the “California Senate Bill 1953” refer to the year 1953 or just the number\n1953? I presume not, so it would be better to specify the year so as to avoid confusion in the\ntimeline of these legislative developments.\nResponse 9: This is just the number of the Bill. It was enacted in 1994. We added a\nclarification:\nThese disruptions prompted California Senate Bill 1953 (passed in 1994), [...]\nResults:\nComment 10 :It may be better to specify that “The Bay” refers to the “The Bay Area of San\nFrancisco” for unfamiliar readers.\nWe iterated this in the entire manuscript. We refer to it as the San Francisco Bay Area throughout\nthe paper.\nComment 11: Statements like “Our predictions show that many hospitals will experience violent\nshaking at a scale not seen in over a century.” seem a little dramatic and unnecessary. It also\nconveys a distorted view to the public that the earthquake shaking can be predicted. In general,\nwords like estimate would be a better reflection of the science behind the methods.\nResponse 11: We agree. We changed it to (line 150):\nOur shaking intensity estimates indicate that many hospitals could experience levels of\nground motion not observed in recent earthquakes\nComment 12: Equation 1. It seems “I’m” is a typo.\nResponse 12: We have corrected the notation:\nComment 13: Would it not make more sense to define the shaking variable as IM = im instead\nof I = I? It would maintain a consistency with the previous text.\nResponse 13: We thank the reviewer for the thoughtful suggestion. In regional risk modeling,\nespecially when simulating thousands of assets and correlated realizations, the dimensionality of\nthe random variable space becomes quite large. To manage this complexity and maintain\nnotational tractability, we adopt a convention of using concise single-letter variable names, such\nas I for intensity measures. This approach facilitates the presentation of joint distributions,\nconditional probabilities, and integrals involving multiple variables across infrastructure elements.\nWhile we agree that using IM could align more explicitly with “intensity measure,” we believe that\nthe definition of I is clearly stated and consistently applied throughout the manuscript, and that\nthe more compact notation is better suited to the mathematical structure of the regional\nframework. To make this clearer to the reader, we have revised the text in the Methods section\nto briefly explain our rationale for choosing a concise notation (line 366).\nWe also define the shaking variable I, instead of IM, and call Iₖˢ and Iₖⁿ the shaking\nmeasures affecting structural and non-structural damage of building k. We use the more\nconcise notation I rather than IM to improve the readability of expressions in high-\ndimensional regional models, where large sets of correlated variables are simulated.\nComment 14: Should the left hand term of Equation 2a contain the i term as pi(d, i)? The\nformulation on the right hand side would suggest it should be independent of the intensity and\nlisted simple as pi(d)\nResponse 14: We included the term i on the left-hand side of Equation 2a to indicate that p(d, i)\nrepresents the joint probability distribution of damage and ground shaking intensity. The equation\nfollows the standard chain rule: p(d, i) = p(d | i) · p(i), where p(d | i) corresponds to the fragility\nfunctions used in regional risk modeling. This formulation does not assume independence; rather,\nit captures the dependence of damage on intensity. The purpose is to illustrate how fragility\nfunctions are defined and how spatial correlation in damage arises from the underlying correlated\nground motions. We have clarified this point in the revised manuscript in the Methods section (line\n380).\nThis formulation follows the chain rule of probability, where Equation 2a represents\nthe joint distribution of damage and intensity. Equation 2b assumes that, conditional on\nshaking intensity, the damage at each building is independent—an assumption that\nsimplifies regional modeling. This allows the conditional joint distribution π(d | i) to be\nexpressed as the product of per-building fragility functions. While this assumes no direct\ninteraction between buildings once shaking is known, the spatial correlation of ground\nmotion in π(i) introduces dependence across damage outcomes.\nComment 15: The authors mention that the damage estimation in Equation 2b assumes\nindependence. Is this realistic? Are there cases where this assumption may not hold? Are there\nalternative methods that could be adopted? Please comment.\nResponse 15: We thank the reviewer for raising this important point. We carefully considered the\nindependence assumption when developing our model. Because hospitals in our framework are\nassumed to lose functionality at early damage stages (e.g., slight damage), we believe it is\nreasonable to assume conditional independence between structural and non-structural damage—\nsince interaction effects are likely minimal before major degradation occurs. While we are not\naware of empirical studies that directly validate this assumption, it aligns with observations from\npast events where hospitals were disrupted even at low damage states. We have added a brief\nexplanation to the manuscript to clarify this point and note that future work could explore how\ncorrelated damage mechanisms may affect functionality, particularly at later stages (line 393).\nAlthough non-structural damage may not be conditionally independent of structural\ndamage—given that structural damage can alter the dynamic properties of a building\nand, in turn, affect demands on acceleration-sensitive non-structural components—we\nconsider the independence assumption to be reasonable within the failure space of\nhospitals. Specifically, our model assumes that hospital functionality is lost once early\ndamage thresholds (e.g., slight damage) are exceeded; at this stage, structural\ndegradation is unlikely to significantly modify the system’s dynamic characteristics.\nWhile we are not aware of empirical studies explicitly validating this hypothesis, the\nassumption allows us to simplify the model without compromising its ability to capture\nkey failure mechanisms relevant to hospital functionality.\nComment 16: Figure 6. The term D_1^s appears twice. One of them should be D_1^n.\nResponse 16: We fixed it. Thank you for catching this. Se the iterated figure (D_1^n appears\nnext to D_1^s)\nComment 17: Again, the authors use the term “state of the art” when referring to a ground\nmotion model developed over a decade ago.\nResponse 17: We removed state-of-the-art. The iterated text says (line 475):\nWe utilized a ground motion model for shallow crustal earthquakes to estimate the\nmedians and logarithmic standard deviations of i.\nAdditional major edits: As mentioned earlier, we made substantial revisions to the\ncomputational analysis in response to feedback from the review process. Most notably, we\nincorporated transportation infrastructure failures into the modeling framework. This\nenhancement allowed us to better assess post-earthquake hospital accessibility and identify\nspecific hospitals and communities that could become isolated due to bridge or road damage.\nThese changes significantly improved the realism and scope of the study. A summary of the\nupdates and corresponding modifications to the manuscript is provided below.\nAbstract (line 15):\nBy integrating seismic hazard with hospital and transportation infrastructure’s vulnerability and\nconnectivity data, we analyze 76 hospitals (426 buildings with 16,639 beds) and 5,163 bridges\nwithin a vast network of ∼1.5 million edges and ∼0.5 million nodes [...] Widespread transportation\nfailures further restrict access, increasing regional travel times by 177% and exceeding 1000% in\nparts of East Bay, potentially fully isolating hospitals and entire urban communities. These findings\nunderscore the urgent need for resilient healthcare and transportation infrastructure to mitigate\nlife-threatening disruptions following major earthquakes.\nIntroduction (line 80):\nTo fill this critical gap, we investigate, for the first time, joint failures of healthcare and\ntransportation networks across the San Francisco Bay Area after a major earthquake. By\nexamining diverse urban communities near active seismic faults—often underrepresented in\nprevious studies—this research provides valuable insights into post-earthquake healthcare\naccess, particularly relevant for earthquake-prone regions worldwide with diverse populations\nand similarly vulnerable hospitals and bridges, such as those in the U.S., Japan, and Türkiye.\nTo our knowledge, this is the first study to evaluate post-earthquake healthcare access at this\nscale using publicly available data on both hospital and transportation infrastructure. Whereas\nprior work has focused on individual facilities[20-23] or small systems[42-46]—often relying on\nsynthetic data—our approach couples regional seismic risk models with large-scale network\nanalysis to capture interdependent failures across an entire metropolitan area. By integrating\nvulnerability data from 426 hospital buildings and 5,163 bridges, and simulating disruptions across\na transportation network with approximately 1.5 million edges and 0.5 million nodes, we offer one\nof the most extensive assessments to date of how earthquakes affect healthcare access. This\nstudy advances the state of the art in regional risk modeling globally, offering a scalable,\ncomputationally intensive framework that supports risk-informed decision-making in other high-\nrisk urban areas.\nNew Section on Post-earthquake Bridge Functionality (line 196):\nOur risk analysis model predicts that 1,469 bridges out of 5,163 would be damaged due to the\nearthquake scenario (see Methods). Consequently, 3,693 bridges (72%, standard deviation:\n17%) are expected to remain undamaged and fully operational (Figure 3). Some damaged\nbridges could continue operating, albeit at reduced capacities. Under our “baseline scenario”,\nwhere only bridges with at most slight damage remain operational, a total of 3,964 bridges\n(77%, standard deviation: 15%) would function. In a more optimistic “favorable scenario”, where\nbridges with at most moderate damage also remain partially operational, 4,069 bridges (79%,\nstandard deviation: 14%) could provide service. In an idealistic scenario, which assumes that\nEditorial Note: The map data in figure 3 of this Peer Review file is from\n© OpenStreetMap contributors openstreetmap.org/copyright.\nbridges even with extensive damage retain emergency functionality, 4,527 bridges (88%,\nstandard deviation: 11%) would remain operational.\nSimilar to hospitals, Alameda County faces the most severe transportation impacts (Figure 3,\nTable 2). Under the baseline scenario, Alameda retains only 44% functional bridges (from 642\ndown to 282). Marin County is second most impacted, retaining 64% (from 195 to 125 bridges).\nAdditionally, estimates of reductions in bridge travel speeds (see Methods)—calculated from\ntheir damage probabilities—highlight Alameda’s higher vulnerability due to proximity to the\nHayward Fault rupture (Figure 3, Table 2).\nFigure 3. [...] Lower left: Probability distribution of fully functional bridges under baseline (slight),\nfavorable (moderate), and idealistic (extensive) damage thresholds. Lower right: Spatial\ndistribution highlighting bridges with post-earthquake travel capacities below 75%. Results\ngenerated from 5,000 Monte Carlo simulations.\nRevised findings on Accessibility (line 223):\nAt a more detailed neighborhood scale, these disruptions are even more pronounced (Figure 4).\nWe identified six densely populated zip codes (each exceeding 15,000 residents, labeled #1 to\n#6 in Figure 4) facing substantial reductions in healthcare access. The most severely impacted is\nNovato (#1, Marin County), where travel times increase nearly 25-fold, from 7.3 to 185.5 minutes,\naffecting approximately 18,000 residents. Similarly, a Fremont zip code (#6, Alameda County)\nwith roughly 66,000 residents experiences an eightfold increase (from 8.4 to 42.2 minutes). Other\nsignificantly impacted zip codes in Richmond (#4), Oakland (#2 and #5, Alameda County), and\nSan Jose (#3, Santa Clara County) face travel time increases of 10, 11, 9, and 11 times their pre-\nearthquake levels, respectively. These results underscore the dramatic reshaping of healthcare\naccess throughout East Bay communities along the earthquake rupture.\nFinally, we explored the relative contributions of hospital and transportation infrastructure\ndisruptions through scenario analyses (Figure 4). We compared the baseline (None, no\ninfrastructure disruptions) against scenarios modeling probabilistic damage only to transportation\ninfrastructure (Transp., hospitals fully resilient), only to hospital infrastructure (Hosp.,\ntransportation fully resilient), and simultaneous probabilistic disruptions to both (Transp. & Hosp.).\nWhen considering disruptions only to transportation infrastructure (Transp.), average Bay Area\ntravel times increase by 41% (from 6.1 to 8.6 minutes), notably less than the combined scenario\n(Transp. & Hosp., 177% increase). Conversely, modeling only hospital infrastructure disruptions\n(Hosp.) yields a 79% increase (from 6.1 to 10.9 minutes), highlighting greater relative fragility in\nhospital networks.\nAt localized urban scales, the compounding effects of simultaneous transportation and hospital\ninfrastructure failures lead to disproportionately severe impacts (Figure 4). For example, as\nmentioned earlier, in the most severely impacted zip code (Novato, labeled #1 in Figure 4),\ntravel times dramatically increase from 7.3 to 185.5 minutes under combined disruptions\n(Transp. & Hosp.), compared to only 14.1 minutes when transportation disruptions are excluded\n(Hosp. only). Similarly, for other highly affected zip codes (labeled #2 to #6 in Figure 4),\ntravel-time ratios notably decrease—from 11, 11, 10, 9, and 8 under combined disruptions, to\n6.4, 3.1, 6.1, 4.7, and 3.4 when transportation disruptions are not considered—highlighting\nthe critical influence of compounding infrastructure failures on healthcare access.\nEditorial Note: The map data in figure 4 of this Peer Review file is from © OpenStreetMap\ncontributors openstreetmap.org/copyright.\nFigure 4: Access to functional acute care hospitals in the Bay Area after the earthquake.\nUpper left: Post-earthquake (Post-EQ) increases in travel time at the zip-code level compared to\npre-earthquake (Pre-EQ) conditions, highlighting densely populated areas that are most\nseverely impacted. Upper right: Ratios of post- to pre-earthquake travel times to the closest\nacute care hospitals. Lower right: Distribution of travel times per zip code under four scenarios:\nNone (no infrastructure disruptions), Transp. (only transportation infrastructure is vulnerable),\nHosp. (only hospital infrastructure is vulnerable), and Transp. & Hosp. (both transportation and\nhospital infrastructures are vulnerable). Lower left: Ratios of post- to pre-earthquake travel times\nwhen only hospital infrastructure (Hosp.) is vulnerable. Results generated from 5,000 Monte\nCarlo simulations.\nNew section on Isolated Communities and Hospitals (line 252):\nTo understand the drivers behind the sharp increases in travel times observed earlier, we\nanalyzed travel volumes to the closest acute care hospitals before and after the earthquake.\nFigure 5 shows pre-earthquake road usage, with line thickness representing travel volume. Roads\nin brown highlight those whose usage falls above the 90th percentile based on pre-earthquake\nconditions, emphasizing the most critical travel routes. As expected, the highest-usage roads prior\nto the earthquake were located near hospitals, especially in densely populated areas with fewer\nhospitals. For instance, communities in Fremont (#6 in Figures 4 and 5) are served by only two\nhospitals, while Richmond (#4) relies on just one.\nFigure 5 also displays post-earthquake road usage, using the same pre-earthquake 90th\npercentile threshold to highlight heavily traveled roads. After the earthquake, patient travel\npatterns shift significantly, with many communities forced to travel longer distances along major\ncorridors. For example, residents in Oakland (#2 and #5 in Figures 4 and 5), who previously relied\non nearby hospitals, will now have to travel west to the San Francisco Peninsula or east to Walnut\nCreek due to simultaneous disruptions in both hospital and transportation infrastructure. These\nshifts help explain the steep increases in travel times observed in East Bay communities along\nthe rupture zone.\nFour major bridges connect the East and West Bay: the Richmond–San Rafael, Oakland–San\nFrancisco Bay, San Mateo–Hayward, and Dumbarton bridges. Before the earthquake, no patients\nneeded to cross these bridges to reach their nearest acute care hospital (Figure 5). After the\nearthquake, however, these bridges become critical, with travel volumes increasing to 3.6, 9.3,\n6.3, and 13.6 times the pre-earthquake 90th percentile values—reflecting the large-scale\nredistribution of healthcare demand.\nOur analysis also revealed a more complex post-disaster phenomenon: micro-scale isolation of\nhospitals and communities due to localized bridge failures. For example, the hospital serving the\nmost severely impacted zip code in Novato (#1 in Figures 4 and 5), which has 64 beds, depends\nentirely on a single bridge for access. If this bridge fails, the hospital becomes inaccessible,\nincreasing travel times from 7.3 to 185.5 minutes for the surrounding population.\nMore concerning, we found that urban neighborhoods near Fremont (#6) could become fully\nisolated (Figure 5). In one area, failure of three bridges would trap one part of the neighborhood;\nin another, a different set of three bridge failures would isolate the remaining part. These\ncommunities would lose access not only to hospitals but also to other essential services such as\ngrocery stores and pharmacies—illustrating how cascading infrastructure failures can sever\nlifeline access in disaster scenarios.\nEditorial Note: The map data in figure 5 of this Peer Review file is from © OpenStreetMap\ncontributors openstreetmap.org/copyright.\nFigure 5: Mobility to reach the closest functional acute care hospital in the San Francisco Bay\nArea. Upper left: Pre-earthquake travel volumes to the closest acute care hospitals. Numbers 1\nto 6 indicate the hospitals serving the dense zip codes with the highest post-earthquake\nincreases in travel time. Upper right: Projected travel volumes after the earthquake, showing\nmajor shifts in patient mobility. The red-shaded corridor illustrates how Oakland residents (#2\nand #5) must travel west to the Peninsula or east to Walnut Creek due to hospital and\ntransportation disruptions. Lower left: The hospital serving zip code #1 (Novato) relies entirely\non a single bridge; if the bridge fails, all access to its 64 beds is lost. Lower right: Community\nnear zip code #6 (Fremont), where the southern and northern sections become fully isolated if\nthree different bridges fail in each area. Results are based on 5,000 Monte Carlo simulations of\npost-earthquake patient mobility.\nReviewer #1\nComment 1: This manuscript presents a numerical investigation into the anticipated hospital\ncapacity and patient travel times in the San Francisco Bay Area, California, following a simulated\nM7.25 earthquake. The study focuses on expected travel times during the earthquake's recovery\nphase. A key innovation lies in integrating a risk model with a transportation network to elucidate\npotential cascading effects. The results demonstrate that the fragility of both healthcare facilities\nand transportation infrastructure significantly contributes to the probable elongation of patient\ntravel times.\nCompared to a previous iteration, this manuscript has undergone a comprehensive revision.\nSeveral critical assumptions employed in the earlier version have been relaxed, and the impact\nof the remaining assumptions is thoroughly discussed. A limitation of the study is the use of\nrelatively generic vulnerability models to estimate the probability of specific damage levels for\neach hospital, given the expected ground shaking. While individual hospital buildings may exhibit\nfragility characteristics that deviate from these generic models, this approach provides a\nreasonable approximation considering the large number of buildings considered. Overall, the\nmanuscript is suitable for publication in Nature Communications.\nResponse 1: We sincerely thank the reviewer for their thoughtful and constructive comments\nthroughout the revision process. Their feedback was instrumental in improving the quality of our\nmanuscript. We agree that incorporating more refined structural models would enhance the\nfidelity of our regional analysis. Over the coming years, our research group will focus on\ndeveloping computational methods that scale structurally detailed models to regional levels, as\nwell as collecting building-specific data to support the construction of these models. We are\ngrateful for the reviewer’s insights and support.\nComment 2: The code reaches 3.4GB and exceeds the 2GB transfer limit set by the server. It\nis not practical to download and try to run it on the local computer. It would be much more\nconvenient if the file size was reduced.\nResponse 2: DesignSafe allows for downloading each file individually (see screenshot below).\nThat way, other researchers can download the scripts and files they are interested in without\nexceeding transfer limits. We added a line in the Code and Data Availability Statements pointing\nto this. Thank you for catching it.\nReviewer #2:\nComment 1: I had the chance to reread the paper and review the author's responses to my\noriginal comment. I appreciate how the authors have elaborated on their work and clarified their\ncontribution, and this manuscript is an improved version of what they submitted originally. For\nexample, adding bridge failure analysis is a significant improvement. The authors also provided\nvarious clarifications on issues. They explained different confusing elements, including, for\nexample, that their intent was not to use a value of 0.2 PGA as an indicator of significant\ndamage to the buildings, and how a probability of 0.25 was not used as a cut-off for damage.\nSimilarly, the use of HAZSU fragilities and their adjustment according to the SPC/NPC mapping\nprovided a clearer reflection on the actions taken to obtain damage fragilities. However, it is\nessential to note that the validity of HAZSU facilities has been a subject of extensive\ndiscussions within the earthquake community. It is good to see, however, that they have been\nadjusted based on some logic.\nWhile these improvements helped the paper in general, I still consider the analysis simplistic in\nmany ways, and I struggled to see the novelty of the work. As a case study, the findings are\nindeed important and relevant to the city of San Francisco. However, I remain unconvinced\nabout the novelty of the work and the study's motivation. Integrating transportation infrastructure\ninto the modeling of post-earthquake hospital accessibility has been done numerous times, and\npublications with a similar motive appear in many journals worldwide, not only for seismic\napplications but also for almost all other natural hazards. The authors further elaborated on the\nstudy's motivation, noting that the San Francisco Bay area's uniqueness is characterized by a\nhigh concentration of seismically vulnerable hospitals, a complex and interconnected healthcare\nnetwork that spans county and jurisdictional boundaries, and spatially heterogeneous seismic\nhazards and vulnerabilities across communities. These three elements are not unique to San\nFrancisco. In fact, most major cities around the world exhibit similar characteristics, including a\ncomplex network of aging infrastructure. So, in my opinion, the argued uniqueness represents a\nform of baseline risk environment rather than a novel or case-specific anomaly. The authors\nfurther noted that the uniqueness is in that \"this is the first study to evaluate the performance of\na realistic regional healthcare network using publicly available, high-resolution data on both\nhospital infrastructure and transportation systems.\". As I noted, numerous studies have\ninvestigated accessibility to healthcare on a large scale, which limits the uniqueness of your\nstudy (please see some examples below). Of course, the studies listed below are not \"exactly\"\nsimilar to yours in any way. Still, the overall idea of examining accessibility to healthcare\nsystems on a large scale remains the same.\nPost-earthquake health care service accessibility assessment framework and its application in a\nmedium-sized city: 10.1016/j.ress.2022.108782\nAccessibility of medical services following an earthquake: A case study of traffic and economic\naspects affecting the Istanbul\nroadway: https://www.sciencedirect.com/science/article/abs/pii/S2212420918305314\nMeasuring spatiotemporal accessibility to healthcare with multimodal transport modes in the\ndynamic traffic environment: https://www.degruyterbrill.com/document/doi/10.1515/geo-2022-\n0461/html?lang=en\nI appreciated the elaboration on the intent of the paper by the authors and I also recognize the\ncomputational demand in integrating staff, stuff, and supplies in calculating bed availability at a\nsingle room level, which is the state of the art, as opposed to your approach where you\nassumed hospital damage as a proxy for bed availability. A better approximation would have\nbeen to perform that integration at the hospital level, rather than at the single-room level. Not\nonly would this be computationally reasonable, but it would also give you a much better\napproximation of bed availability. Similarly, modeling building functionality as a Bernoulli\nprocess and not considering the state-of-the-art that integrates various elements to determine\nthe functionality level adds to the uncertainty of the results. This gross approximation, combined\nwith the hospital bed approximation, increases the uncertainty level in the results presented,\nrendering them somewhat questionable.\nResponse 1: We thank the reviewer for their thoughtful comments and for engaging deeply with\nour manuscript throughout all rounds of review. We carefully reviewed the suggested references\nand have incorporated two of them into the revised manuscript: the case study in Istanbul\ninvolving eight hospitals [1], and the simulation-based study in a medium-sized Chinese city [2].\nWe did not include the third reference, as it does not focus on earthquake-related disruptions,\nwhich are central to our study of post-earthquake healthcare accessibility. Nonetheless, we\nappreciate the recommendation and found it valuable for understanding broader methodological\napproaches.\nIn response to the reviewer’s concerns about the framing of our study’s novelty, we have\nrevised the Introduction substantially. We have removed the initial claims regarding the\nuniqueness of our study and, instead, contextualize our contribution more carefully within the\nexisting literature. We highlight how our study complements prior work while emphasizing the\nspecific regional characteristics and data-driven elements of our San Francisco Bay Area\nanalysis. Our revised framing focuses on the practical implications and transferability of our\nmodeling framework rather than its singularity.\nWe also appreciate the reviewer’s comments on structural modeling fidelity and acknowledge\nthe limitations of using generic fragility functions and simplified assumptions (e.g., Bernoulli\nprocess for functionality). We agree that better approximations for hospital bed availability—\nsuch as integrating hospital-level data—would improve model realism and reduce uncertainty.\nMoving forward, our group is actively pursuing research efforts that aim to (1) scale structurally\ndetailed models to regional levels, and (2) collect and integrate building-specific and hospital\noperational data to improve future analyses.\nWe are grateful for the reviewer’s insights, which have helped us strengthen both the framing\nand technical direction of our study.\n[1] Post-earthquake health care service accessibility assessment framework and its application\nin a medium-sized city: 10.1016/j.ress.2022.108782\n[2] Accessibility of medical services following an earthquake: A case study of traffic and\neconomic aspects affecting the Istanbul\nroadway: https://www.sciencedirect.com/science/article/abs/pii/S2212420918305314\nNew part of the Introduction:\nPast research has examined hospital seismic risk primarily at the building scale. Studies have\nused structural engineering methods, fault-tree analyses, and performance-based assessments\nto evaluate damage in isolated facilities.23–26 Others have used flow models and discrete-event\nsimulations to explore patient care delays and medical bottlenecks in single-hospital\nscenarios.27–30 While valuable, these studies often overlook how failures can propagate across\nurban systems.\nIn parallel, a growing body of work has started to model access to hospital services at the\nregional scale. Studies in Lima, Peru,31, 32 and Butte County, California,33 have shown that even\nsmall reductions in overall healthcare capacity can significantly affect local access to care. More\nrecent efforts have begun to jointly consider disruptions to both healthcare and transportation\nsystems, e.g., in Istanbul, T¨urkiye,34 and in a synthetic medium-sized city in China.35 We\ncontribute to this growing literature by modeling these compounding effects at scale across the\nSan Francisco Bay Area using detailed, real-world datasets on hospital and bridge\ninfrastructure.\nRecent earthquakes in Chile, New Zealand, and Japan have also underscored the importance\nof treating hospitals as part of broader interdependent systems.24, 36–39 Failures at one facility\ncan cascade across a regional network—overwhelming nearby hospitals, increasing patient\ntravel distances, and worsening health outcomes. To support resilience planning across large\nmetropolitan areas, there is a need for region-wide models grounded in real exposure data that\ncapture operational interdependencies between healthcare and transportation infrastructure.40–42\nDeveloping such models remains challenging due to limited data, computational demands, and\nregional variation in infrastructure.\nIn this work, we evaluate post-earthquake healthcare access across the entire San Francisco\nBay Area by simulating joint disruptions in healthcare and transportation systems. We integrate\nseismic risk models with regional-scale network analysis using publicly available data on 426\nhospital buildings and 5,163 bridges across a transportation network comprising approximately\n1.5 million edges and 0.5 million nodes. Our study contributes to the growing field of integrated\ndisaster risk modeling by providing one of the most extensive simulations to date of\ninterdependent failures affecting healthcare access after an earthquake. Although grounded in\nthe San Francisco Bay Area, our study highlights systemic barriers to accessing healthcare after\nearthquakes under conditions common to many dense urban regions—such as high seismic\nrisk, aging infrastructure, complex emergency response systems, and population disparities.\nThese findings underscore the need for integrated planning approaches that account for\ninfrastructure interdependencies and can inform resilience policy in similarly exposed\nmetropolitan areas\nReviewer #3:\nComment 1: The authors have addressed all comments by this reviewer\nResponse 1: The authors thank reviewer #3 for all the comments that helped us make the\npaper better."}]

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