7 In an earthquake emergency, injured people require hospital emergency services and timely 8 medical treatment. Earthquake-related patients often have trauma injuries and stress-linked (is- 9 chemic) illnesses that require multiple healthcare procedures, such as minor orthopedic treat- 10 ment, surgical treatment of fractures, and thrombolysis or thrombectomy. Hospital operation 11 models have been proposed to examine these healthcare procedures; however, they exhibit 12 two fundamental gaps that hinder their ability to assess critical service areas after earthquakes. 13 First, these models rest heavily on emergency procedures based on injury severity rather than 14 type. Second, healthcare demands and injury profiles are often modeled after moderate earth- 15 quakes in the United States without including mass casualty data after large earthquakes. This 16 approach has led to an oversimplified representation of the utilization of hospital emergency 17 services and resources, especially for the various profiles of trauma patients after earthquakes 18 globally. This research presents a new hospital operations model based on patient injury type 19 and worldwide earthquake epidemiology data to fill these two gaps. We built the model us- 20 ing discrete event simulations to capture patients’ healthcare metrics that vary rapidly after the 21 earthquake. We then used these metrics to study how healthcare outcomes vary with different 22 levels of functional capacity in specific hospital service areas. Our case study showed that ED- 23 level patients wait 40% longer to receive treatment when half of the examination rooms in the 24 emergency department (ED) are lost and 35% less time if examination rooms increase by 50%. 25 Also, the waiting time for hospital-level procedures reduces up to 65% if the bed occupancy 26 rate drops by 15%, e.g., if reverse triage procedures are activated through a discharge of 15% of 27 patients hospitalized before the earthquake. Our findings provide a valuable tool for decision- 28 making in hospital preparedness as it links expected patient volumes to key healthcare metrics 29 according to hospital functional capacity. 30 Keywords: hospital resources, hospital operations, earthquake casualties, earthquake in- 31 jured, disaster medicine 32 1Departamento de Ingenier ´ıa Estructural y Geot ´ecnica, Pontificia Universidad Cat ´olica de Chile 2Center for Integrated Disaster Risk Management (CIGIDEN), ANID/FONDAP/1522A0005 3Civil and Urban Engineering Department, New York University 4Center for Urban Science and Progress, New York University 5Servicio de Atenci ´on M ´edica de Urgencia (SAMU), Chile Corresponding author: Yvonne Merino, email: ymerino@uc.cl 1 1 Introduction 33 The continued operation of hospitals after earthquakes relies on the functional state of phys- 34 ical systems and the availability of human resources. The interruption of healthcare services 35 after great disasters represents a significant public health concern. Earthquakes can reduce the 36 capacity of hospital networks and hinder their ability to absorb acute care demands (Ceferino, 37 Mitrani-Reiser, Kiremidjian, & Deierlein, 2018; Ceferino et al., 2020a, 2020b). For example, 38 the effects of the 2008 Sichuan Earthquake in China on public health were notable. The injured 39 toll reached 370000 people, and the healthcare infrastructure was severely damaged, including 40 hospitals with modern buildings (Zhao et al., 2009). In Beichuan County ( ≈175000 inhabi- 41 tants, PGA max=1.40g, MMI : IX), the hospitals with tertiary services (i.e., highly specialized 42 resources for hospitalization) experienced structural collapse, and no specialty services were 43 available in the county for two months. Consequently, medical teams from other facilities had 44 to transfer severely injured patients to hospitals in other counties (You et al., 2009). 45 Hospitals must enhance preparedness for earthquakes by providing safe and sufficient in- 46 frastructure to allow continued functionality of medical services, especially those critical dur- 47 ing the emergency response (WHO-PAHO, 2015). Previous models on post-earthquake hospi- 48 tal performance have contributed to understanding the operations needed to treat earthquake- 49 related patients. However, most existing models are based on historical data on hospital demand 50 from injured patients recorded after a few moderate events in the United States (Figure 1), such 51 as the 1994 M 6.7 Northridge Earthquake and the 1989 M 6.9 Loma Prieta Earthquake (Yi 52 et al., 2010). Thus, they do not capture the epidemiological characteristics of large earthquakes 53 (e.g., M >7.0) and other regions across the globe. 54 The current paradigm for modeling hospital operations assesses healthcare processes based 55 on patients’ injury and illness severity or triage categorization (Basaglia et al., 2022). This 56 modeling criterion can help identify healthcare resource utilization under normal conditions 57 when hospitals expect a regular flow of patients with a wide range of injury profiles. However, 58 this paradigm lacks the granularity of more specific injury and illness types to assess complex 59 emergencies that require the treatment of large fluxes of patients, such as those generated by 60 earthquakes (Gautschi et al., 2008; Mackenzie et al., 2017). 61 Existing models focus on earthquake patients in emergency departments but neglect those 62 requiring hospital-level services, such as hospitalization, intensive care, and dialysis. The latter 63 patients represent an essential group of injured that accounts for most patients’ profiles in 64 several past earthquakes (Bar-On et al., 2013; CDC, 2011; Shi et al., 2010; Tanaka et al., 65 1997; Xie et al., 2008). Thus, neglecting these patients hinders part of our understanding of 66 the relevance of the complex hospital resources needed to assist them, such as hospitalization 67 beds, intensive care units, and dialysis units. Hence, a more comprehensive model for hospital 68 operations is needed to capture key healthcare processes associated with the epidemiology of 69 earthquake patients, aiming to examine better the hospital resources needed to treat patients, 70 especially after large earthquakes. 71 To fill in this gap, we present a new operations model to overcome some existing limitations. 72 The model is based on a proposed classification of expected patients from an extensive review 73 of emergency medicine literature on earthquake injury patterns, validated through interviews 74 2 Figure 1: Total injured for 11 worldwide earthquakes with the highest injured tolls reported (CRED, 2022). The historical events have been separated in two groups according to the avail- ability of their associated epidemiological data. The 1989 Loma Prieta and 1994 Northridge earthquakes are additional to these 11 events. with healthcare experts. As a result, we define seven patient types that represent common 75 injuries and illnesses after major earthquakes and identify the resources needed to support 76 the medical procedures to treat them. This model is designed to allow coupling with risk 77 frameworks for estimating earthquake casualties (Ceferino, Kiremidjian, et al., 2018a, 2018b; 78 Federal Emergency Management Agency (FEMA), 2020), aimed to identify hospital resources 79 required to cope with surging healthcare demands in the aftermath of future major earthquakes. 80 Thus, the proposed model’s application offers decision criteria to develop hospital emergency 81 plans based on medical resources relevant for earthquake-related patients. 82 This paper will proceed with section two, describing the literature review of existing models 83 for hospital performance after large earthquakes and their main applications in disaster risk 84 analysis. Then we describe in section three the methods employed to carry out our model and 85 the details of its parameters. Section four presents the most relevant results of this research, 86 and finally, in section five, we discuss these findings. 87 2 Review of post-earthquake hospital models 88 Simulation models are numerical tools that can be used in operations research to study complex 89 systems that follow a queuing behavior (Aghapour et al., 2019). They are usually employed in 90 the health sector to track stochastic metrics of patient queues and analyze strategies to enhance 91 health outcomes from the design of service flows (Gupta, 2013). In the context of disasters, 92 simulation models in healthcare systems have been increasingly developed in the literature. 93 3 Among the available types of simulation models, discrete event simulation (DES) has been 94 a highly used technique to model emergency healthcare processes under disaster conditions 95 (Gul & Guneri, 2015). DES models are computer-based techniques supporting the dynamic 96 tracking of the state of entities or agents requesting services in a queuing system. For health- 97 care research purposes, the hospital system consists of sets of medical services supported by 98 resources demanded by patients entering the system. 99 Few studies have been carried out to describe hospital operations under earthquake sce- 100 narios aimed at determining metrics to deliver healthcare services. Yi et al., 2010 described 101 hospital operations in the context of earthquakes using DES to determine real-time hospital 102 capacity to treat earthquake-related patients timely to maximize survivability. The proposed 103 patient flows within the hospital were defined based on the main types of patients observed in 104 the aftermath of California’s 1989 and 1994 earthquakes. Their model was able to determine a 105 hospital’s capacity to treat patients from a relationship between the maximum waiting time and 106 the corresponding arrival rates of patients. 107 More recently, Basaglia et al., 2022, proposed an updated hospital model to describe the 108 healthcare response of an idealized hospital in routine conditions and after a major earthquake. 109 Their model accounts for multiple services within the hospital and a detailed collection of the 110 corresponding simulation parameters in both demand scenarios. With this model, they assessed 111 the probability of mortality, identifying delayed treatment as the main factor contributing to 112 fatalities. 113 Other studies in the literature employ DES models for hospital operations to determine 114 hospital performance under the effects of physical damage or decreased functionality after 115 earthquake scenarios. They integrate the seismic response of physical components (i.e., build- 116 ing and contents) and hospital operations due to a sudden increased demand for healthcare. 117 Zhai et al., 2021, developed a post-earthquake hospital model and determined its functionality 118 to assess the availability of physical resources to assist patients from a simplified DES model. 119 Other simulation models have been used to determine the risk of exceeding patients’ waiting 120 times as a function of the earthquake hazard level (Favier et al., 2019). In such research, they 121 assessed the functional state of service areas within the emergency department (ED). 122 This research closes existing gaps by developing a DES model at the entire hospital level 123 instead of the emergency department level, as considered in previous research. In addition, 124 this paper advances existing models by defining treatment processes according to injury type 125 instead of severity to capture medical needs better and quantify medical resources after earth- 126 quakes. We also conduct a thorough review of earthquake epidemiology literature to define 127 expected patient profiles generated by large earthquakes around the globe. Table 1 summarizes 128 the contributions of this paper. 129 3 Methods 130 Our hospital model is based on discrete event simulations (DES) of hospital processes and 131 was developed by integrating empirical data presented in the literature on disaster medicine, 132 with expert elicitation of emergency healthcare staff. The DES model describes the flow of an 133 increased volume of patients arriving at the emergency department (ED) and passing through 134 4 Features of previous hospital models [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] This study Model scope for healthcare processes - ED-level ✓ ✓ ✓ ✓ ✓ ✓ - Hospital-level ✓ ✓ Earthquake-related epidemiology among arriving patients - US EQs ✓ ✓ ✓ - China EQs ✓ ✓ - World EQs excluding China and US ✓ - Non EQs/not specified ✓ Injury type-based approach for healthcare processes✓ ✓ ✓ ✓ Table 1: Overview of the proposed model characteristics relative to previous studies: which are ad- vanced in our model; [1]: Yi et al., 2010; [2]: Basaglia et al., 2022; [3]: Zhai et al., 2021; [4]: Favier et al., 2019; [5]: Romani et al., 2022. different healthcare processes. Sequential combinations of healthcare processes define different 135 paths associated with different types of patients. For example, the healthcare path for a trauma 136 patient with crush syndrome includes the following healthcare processes and resources: triage, 137 examination, laboratory, surgery, intensive care, dialysis, and hospitalization. 138 Arriving patients were studied as an inflow of injured and ill agents divided into seven 139 groups denoted as patient types. The relationships between patient types and the healthcare 140 paths within the hospital were identified by coupling documented medical processes from past 141 earthquakes with specialized knowledge from emergency physicians. Such relationships were 142 validated by interviewing eight experts on emergency hospital operations from different disci- 143 plines. Initially, our target experts were ED physicians; however, additional healthcare profes- 144 sionals contributed significantly to this part of the research. Table 2 summarizes the disciplines 145 and places of elicitation experts who contributed in the validation of this model. 146 Experts consulted Institution Discipline Leader emergency physician SAMU Medicine Operations coordinator LFH Engineering Emergency coordinator SSMSO Nursing Disaster advisor INEE Engineering/Hospital Disaster Risk Regional disaster advisor PAHO Medicine/Hospital Disaster Risk Safe Hospital Program members (6) IMSS Medicine Table 2: Interviewed experts for the model setup: SAMU : Servicio de Atenci ´on M ´edica de Urgen- cia/Metropolitan Urgent Medical Aid Service (Chile); LFH : La Florida Hospital (Chile); SSMSO : Ser- vicio de Salud Metropolitano Sur-Oriente/South-East Metropolitan Healthcare Service (Chile); PAHO : Pan American Health Organization; IMSS : Instituto Mexicano del Seguro Social/Mexican Institute for Social Insurance (Mexico). 5 Once the healthcare paths within the hospital for every patient type were defined, we as- 147 sumed a patient arrival function describing the rate of patients coming into the ED during 148 the first week after the earthquake. According to this function, the simulator stochastically 149 generates arriving patients and randomly assigns the patient a healthcare condition from the 150 previously defined group of patient types. Then, the patient is associated with the correspond- 151 ing path and starts requesting hospital services, i.e., the healthcare processes required to treat 152 every patient type. Each service is developed in a physical space and uses different types of 153 resources. Figure 2 summarizes the steps to perform the model simulations. The following 154 subsections describe the patient profiles considered in the model and the details of the different 155 resources involved in treating them. 156 Figure 2: Flow chart of the pseudo-code for the hospital DES model. 3.1 Demand 157 The proposed model was developed with particular emphasis on the expected profile of the 158 patients that reach large urban hospitals in the aftermath of a destructive earthquake. To do 159 so, we conducted an extensive literature review to identify the most frequent patient profiles 160 and defined seven patient types that account for most earthquake-related injuries and illnesses. 161 They range from frequent trauma conditions to stress-related ischemic conditions. The most 162 common healthcare conditions found in the literature for patients from earthquakes worldwide 163 are the following: 164 •Path 1/Minor injuries : include contusions, lacerations, cuts, among others, which only 165 need basic first aid and ambulatory procedures in the ED, covered by the medical as- 166 sessment performed by an emergency physician in the examination room (Tanaka et al., 167 1997). 168 6 •Path 2/Non-surgical injuries : include injuries that can be treated without a surgical pro- 169 cedure (e.g., dislocations, fractures). They can be treated in a trauma room or examina- 170 tion room, i.e., those where medical staff mobilizes equipment for orthopedic procedures. 171 This patient type usually requires X-ray imaging to support the medical diagnosis. 172 •Path 3/Surgical injuries (extremities) : include soft-tissue injuries or upper and lower 173 limb fractures needing a surgical procedure under general anesthesia in an operating 174 room (e.g., internal fixation, debridement, skin grafting) and a recovery process in a 175 hospitalization bed. This group of patients represents most earthquake-related injured, 176 ranging from 36 to 60% (CDC, 2011; Zhang et al., 2009; Zhang et al., 2014; Xie et al., 177 2008; Bertol et al., 2014). 178 •Path 4/Surgical injuries (non-extremities) : include injuries or fractures in the head, 179 neck, thorax, and pelvis for which major surgery in an operating room is needed. Ad- 180 ditionally, intensive care is carried out after such procedure in most cases, especially for 181 patients with spinal cord injury (Gautschi et al., 2008). These fractures represented more 182 than 20% of total fractures observed after the 1995 Kobe earthquake. For this earthquake, 183 11% of trauma patients required intensive care units (ICU) as a resource (Tanaka et al., 184 1997). Evidence from past disasters suggests that older people are more likely to suffer 185 these type of trauma condition (Zhang et al., 2014). 186 •Path 5/Crush syndrome : represents a critical condition developed by most patients 187 who have suffered crush injuries during earthquakes and did not reach medical facili- 188 ties promptly. This condition requires intensive care in most cases. Also, subsequent 189 hemodialysis procedures are often needed for patients with renal failure, a common 190 complication after prolonged muscle compressions (Xie et al., 2008; Yang et al., 2009). 191 (Tanaka et al., 1997) showed that for 70% of patients who developed crush syndrome, 192 their injuries were caused by house collapse, requiring ICU resources, and hemodialysis 193 in 33% of the cases. 194 •Path 6/Amputation : is required when patients experience a severe musculoskeletal 195 trauma. Amputation rates in past large earthquakes have reached up to 16% (CDC, 2011; 196 PAHO, 2011; Xie et al., 2008; Yang et al., 2009). Trauma patients needing amputation 197 procedures usually access the hospital’s ED through resuscitation processes, thus using 198 the shock room (Wolfson, 2012). The amputation procedure requires major surgery and 199 subsequent intensive care. 200 •Path 7/Ischemic disease : includes myocardial infarction. This is the most frequent 201 stress-related disease in the aftermath of earthquakes, e.g., 1995 Kobe Earthquake in 202 Japan (Tanaka et al., 1997), 2010 Maule Earthquake in Chile (P. Molina, personal com- 203 munication, October 2021). In most cases, this condition is treated in a catheteriza- 204 tion laboratory, performing a hemodynamics surgery (i.e. thrombectomy). When the 205 catheterization laboratory is unavailable, the thrombolysis treatment is performed in a 206 conventional examination room by providing a clot-busting drug. 207 7 Table 3 presents a distribution of injuries/illnesses-related patient types, following the av- 208 erage patterns documented from past events. As seen in the proposed distribution, the leading 209 medical specialty is trauma, and most injuries require surgical treatments (75%). Other milder 210 trauma conditions represent 15%, and less cases (5%) account for myocardial infarction. To 211 account for crush injuries, the renal specialty has been included for 5% of patients, according 212 to the data available in the literature. 213 Patient type Injury/Illness Medical Specialty Distribution (%) 1 [MI] Minor injury Trauma 10 2 [NS] Non-surgical injury Trauma 5 3 [SE] Surgical injury (extremities) Trauma 55 4 [SN] Surgical injury (non-extremities) Trauma 15 5 [CS] Crush syndrome Trauma/renal 5 6 [AM] Amputation Trauma 5 7 [ID] Ischemic disease Medicine 5 Table 3: Earthquake-related patient types proposed for the assessment of healthcare demand in the hospital. Specialties for every type are included as well as the respective percentage relative to the total patient volume. The increased demand for healthcare services in the initial phases of the response to the 214 aftermaths of the earthquake was assumed as a time-dependent distribution of patient arrivals 215 at the hospital. The model follows the time scales proposed in previous research frameworks 216 for emergency medical teams deployed to support the healthcare response after earthquakes 217 (Lind et al., 2012). The first two phases are defined in days and weeks; phase 1 has been 218 proposed as the first 72 hours, and phase 2 as the range between days 4 to 21 ( <3 weeks). The 219 arrivals of injured patients were simulated over the first seven days after the earthquake, with 220 most of them arriving during the first stage ( <72 hours), according to the arrivals data reported 221 by hospitals in past earthquakes (Bulut et al., 2005; Ganjouei et al., 2008; Yang et al., 2009). 222 The patient arrivals obey to a non-homogeneous Poisson process. The Poisson distribution 223 of arrivals accounts for uncertainties of inter-arrival times of injured people. An arrivals pattern 224 was defined on a basis of the average daily patient volume recorded in past earthquakes (Bulut 225 et al., 2005; Chen et al., 2001; Ganjouei et al., 2008; McArthur et al., 2000; Nie et al., 2011; 226 Uz et al., 2022). The arrival rate, λ, decreases over time, with a maximum value equivalent 227 to 50% of the total patient volume within the first 24 hours. In the subsequent days, λtends 228 to zero, as shown in Figure 3. Besides, simulations were performed for two weeks after the 229 earthquake to capture the healthcare response during the second phase of the emergency ( <3 230 weeks). Finally, we assumed a random selection of patient types entering the ED to include the 231 variability of patient profiles according to the injury/illness distribution data presented in Table 232 3. 233 8 Figure 3: Assumed daily variation of patient arrival rates considered to perform simulations of injured/ill people demanding hospital services after the earthquake. λis presented in terms of the proportion of the total patients. 3.2 Processes 234 Healthcare processes were defined based on the medical resources needed to treat the arriving 235 patient types. In the proposed model, every process requires a list of resources that include 236 the physical area (or equipment, when corresponding) where the service is performed. Human 237 resources are assumed to be available if the service is available. Figure 4 shows the simulated 238 processes (dark boxes) and the corresponding resources (light boxes) associated with every pa- 239 tient type arriving to the hospital. Numbers define patient types according to Table 3, indicating 240 the different paths they go through. 241 Unlike existing models, the services considered herein cover specialized medical processes 242 at tertiary hospitals, including but not limited to the ED. Hospital services can be understood 243 in two components: ED-level treatment and hospital-level treatment. ED-level patients (mi- 244 nor injury, non-surgical injury) access medical services through the ED (triage, examination, 245 diagnosis support, minor trauma treatment). As they require minor treatment, they can be dis- 246 charged safely after receiving such treatment. In contrast, hospital-level patients (i.e., patient 247 types 3 to 7) are expected to undergo surgery, subsequent hospitalization, or intensive care for 248 recovery. This group of patients experiences longer waiting times for hospital-level services, 249 as bed and ICU occupation times are significantly higher than those at the ED. In past earth- 250 quakes, hospital-level services such as surgery and subsequent procedures represented a high 251 percentage of orthopedic treatment for trauma patients (Bortolin et al., 2017). 252 For the sake of completeness, we describe next the healthcare processes in our simulation 253 and the associated resources: 254 •Resuscitation refers to the process in which specialized medical staff assists critically 255 injured/ill patients under life-threatening conditions. It occurs in a resuscitation room, 256 RR (also known as a shock room), equipped with high-complexity medical resources 257 like those found within an operating room. Resuscitation procedures can be initiated as 258 a pre-hospital assistance process within an ambulance for severely injured patients that 259 9 Figure 4: Emergency healthcare flows for expected patient types. The processes in dark boxes are associated with the light boxes showing the corresponding required resources (AMB: am- bulance; RR: resuscitation room; TR: triage room; ER: examination room; IMG: imaging room [X-rays/CT/ultrasound(US)]; LAB: laboratory; OR: operating room; HEM: hemodynamics room/catheterization laboratory; ICU: intensive care unit; BED: general hospitalization bed; DM: dialysis machine).(1)This flow shows a non-surgical treatment approach for patients with ischemic conditions. However, surgical treatment is an alternative when the catheterization laboratory (HEM) is available for ischemic surgery can not reach the hospital autonomously. 260 •Triage refers to the initial examination of the patient’s vital signs performed by a nurse 261 or a physician (depending on the hospital protocols for disaster conditions) in the triage 262 room (TR). In a disaster setup, the triage process is intended to categorize the patient as 263 a function of the risk of death, the chance of survival, expected resource requirements, 264 and expected duration of treatment, among other variables (Merin et al., 2011). Hospital 265 triage can also occur after an initial triage performed as a part of a pre-hospital assistance 266 process within the ambulance for non autonomous patients. 267 •Examination refers to the initial patient assessment performed by a physician and sup- 268 ported by nursing staff in the examination room (ER) that requires basic equipment, so 269 human resources are imperative. 270 •Diagnosis support refers to the healthcare processes needed to deliver a diagnosis by 271 the physician when the initial assessment has not been enough to decide the necessary 272 treatment. Essential diagnosis support services generally include imaging (e.g., X-ray, 273 CT scan, US) and laboratory. They operate in imaging rooms (IMG) and laboratories 274 (LAB), respectively. For earthquake-related injuries, imaging services have been highly 275 demanded in past disasters to support decisions for treating trauma patients. Our model 276 considers that the imaging resource includes both X-ray and the CT scan. X-ray resource 277 can be a mobile machine or in a fixed room. They are expected to be used for ED-level 278 patients with minor injuries, and CT scan for those patients with more complex trauma 279 10 conditions. 280 •Non-surgical trauma treatment refers to the treatment for ED-level patients, for which 281 the required trauma equipment can be moved to any examination room to perform pro- 282 cedures for minor trauma injuries. 283 •Surgery refers to the medical process in which teams perform trauma treatment under 284 general anesthesia. Surgery is performed in operating rooms (OR). Several publications 285 have described the multiple emergency procedures developed for trauma patients in ORs 286 after great earthquakes (Gerdin et al., 2012; Herard & Boillot, 2016; Mohebbi et al., 287 2008). 288 •Intensive care refers to the process in which critical patients stay in the hospital under 289 specialized medical treatment and monitoring after surgery. The process requires an 290 intensive care unit (ICU) with high-complexity resources to support the patient’s life. 291