Mobility-driven synthetic contact matrices as a scalable solution for real-time pandemic response modeling

Domain: neuroscience
Published: 2026-01-27
Editorial outcome: minor_revision

Abstract
Accurately capturing time-varying human behavior remains a major challenge for real-time epidemic modeling and response. During the COVID-19 pandemic, synthetic contact matrices derived from mobility and behavioral data emerged as a scalable alternative to empirical contact surveys, yet their comparative performance remained unclear. Here, we systematically evaluate synthetic and empirical age-stratified contact matrices in France from March 2020 to May 2022, comparing contact patterns and their ability to reproduce observed epidemic dynamics. While both sources captured similar temporal trends in contacts, empirical matrices recorded 3.4 times more contacts for individuals under 19 than synthetic matrices during school-open periods. The model parameterized with synthetic matrices provided the best fit to hospital admissions and best captured hospitalization patterns for adolescents, adults, and seniors, whereas deviations remained for children across both models. Neither matrix allowed models to fully reproduce serological trends in children, highlighting the challenges both approaches face in capturing their disease-relevant contacts. The weekly update of synthetic matrices enabled smoother reconstructions of hospitalization trends during transitional phases, while empirical matrices required strong assumptions between survey waves. These findings support synthetic matrices as a reliable, flexible, cost-effective operational tool for real-time epidemic modeling, and highlight the need for routine collection of age-stratified mobility data to improve pandemic response.

Introduction
Mathematical models of infectious disease transmission represented a critical tool to guide real-time public health response during the COVID-19 pandemic1,2. However, one of the main challenges was accurately integrating changes in human behavior into transmission models3,4. The shifts in mobility and contact patterns produced by the unprecedented social distancing measures significantly impacted the spread of SARS-CoV-25–7. How to best characterize these shifts and integrate them in real-time modeling remains an open issue.

A key factor in the transmission of respiratory diseases is the pattern of social contacts between age groups8. This aspect can be incorporated into transmission models through a contact matrix, where each element represents the average number of daily contacts that individuals in one age group have with individuals in another age group. Starting from pioneering work in mid-2000s9, an increasing number of studies used population-based surveys10–12 to build static contact matrices describing age-stratified population-level mixing in European countries, as well as to generate synthetic contact matrices in other countries accounting for socio-demographical structures13–15. These pre-pandemic contact matrices were essential for early pandemic modeling16–18. But they became increasingly inadequate as the pandemic progressed and various interventions were implemented, such as school closures and remote working that affected age groups differently. Models relying on static matrices, or those assuming uniform rescaling of contacts19–22, struggled to accurately estimate the impact of these interventions across ages, e.g. in terms of hospitalizations and seroprevalence.

Ideally, time-varying contact matrices can be constructed from repeated social contact surveys, but such surveys are resource-intensive and often difficult to implement in real-time. During the COVID-19 pandemic, the CoMix project conducted successive waves of social contact surveys in representative samples of the populations of over 20 countries in Europe23. Yet, only the UK continuously collected data throughout the pandemic through weekly waves24, and only four countries (the UK25, Belgium26, the Netherlands27, and Norway28) covered also the first pandemic wave, the one reporting the largest shifts in behavior. In France, survey data throughout the pandemic were available through SocialCov29,30, a project collecting contact data from a convenience sample recruited online. While surveys with frequent waves, such as weekly data collection, can provide valuable information on social mixing patterns, they still present considerable challenges for real-time analysis. Processing raw survey data to construct accurate contact matrices in real-time is resource-intensive, requiring efficient data cleaning, aggregation, and interpretation to reflect dynamic behavioral shifts. When survey data were unavailable, transmission models had to rely on alternative proxies to estimate changes in social mixing.

Mobility data31–34 proved essential35, providing insights into movement flows and location-specific activity in response to restrictions and recommendations. Early in the pandemic, members of our team developed a novel framework to generate mobility-based synthetic contact matrices for France, capturing shifts in contact patterns driven by the epidemic and governmental measures. Initially introduced to assess the impact of the first lockdown18, this framework was later expanded to integrate various data sources throughout the pandemic36. The synthetic contact matrices were constructed by applying age-specific contact reductions to the pre-pandemic contact matrix12 based on contact setting and contact type. Google mobility data informed adjustments in workplace-related contacts, school attendance data shaped changes in contacts at school, and pandemic survey data on physical contact avoidance reduced skin-to-skin interactions. These data streams enabled us to produce weekly, real-time synthetic contact matrices throughout the pandemic18,36–40.

Although mobility-based synthetic contact matrices offer a promising alternative for real-time modeling, their comparative performance relative to empirical contact matrices remains unexplored. Meanwhile, traditional empirical contact matrices - though widely used - are limited by infrequent updates, which constrains their applicability for dynamic modeling. This study addresses two main objectives. First, we compared synthetic contact matrices informed from mobility and behavioral data37 and empirical matrices derived from social contact surveys29,30, focusing on age-specific contact numbers and matrix structure over time. Second, we assessed the capacity of each matrix type to reproduce age-specific hospitalization and seroprevalence data within a COVID-19 transmission model accounting for viral variants, vaccination, and immunity. This framework enables us to evaluate how well each matrix captures disease-relevant contacts over time. By using the COVID-19 pandemic in France as a case study, we provide insight into how different matrix sources can inform real-time transmission modeling for future outbreak response.

Results
Comparison of contact patterns over time
We derived weekly synthetic contact matrices from March 2020 to May 2022 using pre-pandemic empirical contact data (Fig. 1a) and behavioral data collected during the pandemic. These matrices incorporated age-specific contact reductions across different locations and contact types (physical or non-physical contacts) (Fig. 1b). Workplace contacts were adjusted using Google mobility data31 related to workplace presence (Fig. 1c), while reductions in physical contacts across all settings outside the household were informed by health protective behaviors from the French CoviPrev survey41 (Fig. 1d). Both indicators showed a sharp decline during the first lockdown, followed by a gradual upward trend throughout the pandemic. Although they approached pre-pandemic levels by May 2022, those levels were not yet fully recovered. Contacts in other settings (school, transport, leisure) were reduced in the matrix according to school attendance data, school closure schedules and non-essential businesses (Tables S5 and S6). These data sources captured changes in behavior in response to public health measures, spontaneous adaptation to rising case numbers, and seasonal variations. Detailed methodology for matrix construction is available in the Methods and Supplementary Information.

We compared the weekly synthetic contact matrices with empirical contact matrices from seven waves of the SocialCov survey29,30 conducted during different phases of the pandemic in France (Fig. 2 and Fig. 3a). SocialCov recruited participants through the governmental app TousAntiCovid. Since the survey sample was not representative of the French population, it was adjusted using sampling with replacement in each wave to reproduce the age and gender distribution in France. While synthetic matrices were available weekly throughout the study period, empirical matrices were only available for the seven specific SocialCov survey waves. Therefore, direct comparison between the two sources was restricted to these time points (Fig. 2).

We first compared the two matrix sources in terms of average number of contacts (overall and by age group). In the first lockdown (spring 2020), synthetic matrices estimated 3.4 average daily contacts, closely matching survey-based estimates of 3.6 (Fig. 3b). This corresponded to a 76% reduction in contacts compared to pre-pandemic values. Over time, the number of synthetic contacts gradually increased, modulated by intermittent school closures and social distancing measures, reaching 10.4 contacts by May 2022 (age-stratified trends shown in Fig. 3e, f). To contextualize these dynamics, we examined correlations with the Normalcy Index, which captures behavioral adaptation, and with the Stringency Index, which quantifies the intensity of social distancing measures. The synthetic contacts time series was highly correlated with both indices (Normalcy Index: Pearson’s coefficient = 0.84, p-value < 10-199, Fig. 3c, S11b; Stringency Index: Pearson’s coefficient = 0.82, p-value < 10-196, Fig. S11b), supporting the plausibility of the behavioral signals integrated into the synthetic matrices. This correlation reflects concurrent behavioral shifts rather than overlap in data inputs. Empirical SocialCov matrices also showed an increasing trend in the average number of contacts (correlated with both the Normalcy and Stringency indexes, Fig. S11c), but contact numbers after the first lockdown were on average nearly twice as high as synthetic estimates across the remaining six survey waves. The empirical-to-synthetic contact ratio decreased from 2.1 in December 2020 to 1.5 in May 2022, with a dip to 1.2 during summer 2021 (Fig. 3d). These differences were primarily driven by children and adolescents, with contacts being 3-4 times higher in empirical matrices compared to synthetic matrices, except during school closures in April 2020 and August 2021 when they mostly aligned (Fig. 3d, f). In contrast, contact numbers for adults and seniors were largely consistent between the two sources, with empirical-to-synthetic contact ratios ranging between 0.9 and 1.4 (Fig. 3d, e).

We then compared contact matrices in terms of mixing patterns using a set of metrics accounting for matrix elements, structure, and contact distribution. Element-wise comparisons revealed that, when restricting to mixing among adults and seniors, the number of contacts engaged by adults and seniors (both within and across these two age groups) was similar in the two matrix types (Fig. 4a). In contrast, substantial discrepancies were observed for contacts involving younger individuals — especially in within-group contacts during school-open periods (Fig. 4b, Fig. 2b, c). Analysis of age assortativity showed that empirical matrices exhibited weaker within-group mixing compared to synthetic matrices, particularly for adolescents, adults, and seniors (Fig. 4c, d). In contrast, children had more assortative contacts in the empirical data (Fig. 4d). Moreover, in the empirical matrices, young individuals (i.e. children and adolescents) contributed to 50% of total connectivity, twice as in the synthetic contact matrices (Fig. S12b). Overall, these suggest that empirical matrices featured more intergenerational mixing and a stronger influence of younger age groups on overall contact patterns, compared to synthetic matrices.

Cosine similarity—a metric defined between 0 and 1 assessing the similarity in mixing structure, independent of overall contact volume—was higher during periods of school closure, indicating a larger agreement in age-specific mixing patterns between the two matrix sources (Fig. S10a). When schools were open, particularly in March 2021, similarity dropped, reflecting greater deviations in mixing among young age groups. Notably, cosine similarity between empirical and synthetic matrices was consistently higher than that between synthetic matrices and homogeneous mixing (Figure S10a), reinforcing that synthetic matrices retain meaningful age structure beyond proportional mixing.

We also compared synthetic and SocialCov matrices with empirical contact data from the CoMix study42, conducted in France between December 2020 and April 2021. Due to its limited temporal coverage and inclusion of minors in only two waves (Fig. S12), CoMix was not used in the transmission model; however, its matrices showed lower contact rates than SocialCov and age assortativity similar to synthetic matrices (Figs. S13, S14).

Transmission dynamics and model selection
To assess the impact on transmission dynamics of the differences measured between the two types of contact matrices, we used an age-stratified compartmental model for COVID-19 (Fig. S1), fitting it to daily age-stratified hospital admissions and age-stratified seroprevalence data, using either weekly synthetic contact matrices obtained from mobility data or pandemic survey-based matrices (Fig. 5a). We also considered a model using the static pre-pandemic contact matrix for comparison. For the model using pandemic survey-based matrices, we extended the seven empirical contact matrices to periods beyond the survey waves based on assumed similarity of mixing conditions. For example, we used the matrix estimated for August 2021 for all periods with school holidays, including periods prior to the data collection (i.e., this retrospective approach implies inputting matrices also before the actual survey date; see Methods and Fig. 5b). Our fitting approach estimated a baseline transmission rate per contact in the pre-lockdown phase and a time-varying correcting factor to adjust the transmission rate over time. This correcting factor acts as a global rescaling of the contact volumes of the matrices, accounting for latent drivers of transmission, without altering the internal structure of the contact matrices.

We evaluated each matrix type based on model fit quality. All models captured the observed trajectory of daily hospital admissions well (Fig. 5a, Fig. S3). This consistency reflects the use of short fitting windows (averaging three weeks), which allow flexible alignment with the hospitalization curve. However, the quality of fit varied across models. It was best in terms of both AIC (Table S9) and mean absolute error (Fig. 5c) for the model parameterized with synthetic contact matrices. Notably, this model captured smooth transitions in the epidemic trajectory during periods of gradual behavioral changes (e.g. curfews and school closures between the second wave and third wave), whereas the empirical and pre-pandemic matrix models showed abrupt and unrealistic shifts in epidemic trends (Figure S4).

The median correcting factor over time was estimated at 1.17 (0.59 [0.88, 1.34] 1.81, indicating Q2.5 [Q25, Q75] Q97.5 quantiles) for the model using synthetic matrices and 0.77 (0.45 [0.65, 1.07] 1.35) for the one using empirical matrices (Fig. 6a). In total, 66% and 53% of the correcting factors in the synthetic and empirical matrix models, respectively, fell within the range 0.75–1.25, indicating that modest adjustments were sufficient in most weeks across both cases. The correcting factors showed temporal correlation across the models informed with synthetic and empirical matrices (Fig. S6). For the model using synthetic matrices, the correcting factor was close to 1 during the Alpha, Delta, and Omicron BA.1 waves, while for the model using empirical matrices, it was around 1 in 2020 and during the Omicron BA.2 wave (Figure S5). The synthetic matrices showed the largest deviations from 1 during summer 2020 (Fig. 6b). By contrast, the model using a static pre-pandemic contact matrix required consistently larger adjustments (median 0.5, quantiles 0.26 [0.43, 0.66] 0.87), reflecting the need to substantially scale down contact volumes to match observed dynamics during the pandemic (Fig. 6a).

We then compared the three models in terms of their ability to reproduce observed age-stratified data, specifically hospitalizations and seroprevalence. Age-specific hospitalization patterns were more accurately reproduced by the model parameterized with synthetic contact matrices, particularly for adolescents, adults and seniors. In contrast, the model using empirical matrices showed larger deviations in these age groups (Fig. 5d, Fig. S8). The model based on the pre-pandemic contact matrix underestimated hospitalizations among seniors (Fig. 5d, Fig. S8), likely reflecting outdated contact patterns not representative of pandemic conditions. For children, all models showed notable deviations between predicted and observed hospitalizations. Regarding serological data, estimates for adults and seniors were broadly consistent across all three models and aligned well with observations (Fig. 6e, f). In contrast, model predictions diverged more substantially for younger age groups. The model informed by empirical contact matrices consistently overestimated seroprevalence in children and adolescents after summer 2020. This overestimation matched the observed seropositivity in adolescents in June 2021, but substantially exceeded the values reported in February 2021, where the synthetic model provided a closer match (Fig. 6d). For children, neither model successfully reproduced the observed temporal trend in 2021: the model parameterized with empirical matrices overestimated seropositivity, while the model with synthetic matrices underestimated it (Fig. 6c).

We tested alternative calibration strategies, fitting the model using (i) age-stratified hospitalizations only or (ii) total hospitalizations, while reserving age-stratified serological and hospitalization data for validation (Figs. S17–S21). In both cases, model performance, the distribution of the correcting factor and the outcomes of model comparisons remained robust to the choice of calibration targets. The model informed by the synthetic contact matrices reproduced the main age-stratified hospitalization and serological patterns—though systematic deviations persisted for children—even when age-stratified hospitalization and serological data were not used for fitting.

To disentangle the relative role of the correcting factor and the contact matrices in capturing observed transmission dynamics and age-specific trends, we carried out a series of sensitivity tests using modified versions of the synthetic matrices. These tests systematically altered who is most at risk (by changing age-specific contact volumes while preserving total contacts; Figs. S22–S24) and from whom the risk comes (by modifying mixing patterns while preserving both total and age-specific contact volumes; Figs. S25–S27). Across all tests, the correcting factor remained comparable to that of the model parameterized with the original synthetic contact matrices. However, substantial differences emerged in age-stratified outcomes—both for hospitalizations and seroprevalence—highlighting that the correcting factor alone cannot compensate for structural changes in contact patterns. Notably, none of the models integrating the test matrices improved model fit compared to the original synthetic matrix model (Tables S14, S15).

Additional sensitivity analyses supported the robustness of our findings across alternative model specifications and assumptions. We first examined the role of physical contact avoidance in shaping the synthetic matrices (Section 4.2.4 in the Supplementary Information). In the main analysis, we reduced total contacts based on self-reported avoidance of physical contact, as a proxy for reduced transmission risk. However, this assumes that avoided physical contacts were entirely suppressed, whereas some may have continued in a non-physical form (e.g., masked or distanced), likely leading to an overestimation of the contact reduction. To test the impact of this conservative assumption, we generated a set of weekly matrices without applying this reduction. As expected, the average number of contacts across age groups increased (Fig. S28). Both the AIC and the mean absolute error indicated that this model performed better than the empirical matrix model, but still worse than the original synthetic matrix model incorporating contact avoidance (Table S16, Fig. S29). While this change improved the agreement with serological data for adolescents, it simultaneously worsened predictions of senior hospitalizations and children seroprevalence, underscoring age-specific trade-offs (Fig. S30). Varying the specification of empirical contact matrices–by incorporating weekend contact patterns or using May 2022 as a proxy for pre-pandemic behavior–did not improve model fit compared to the synthetic matrix model (Fig. S15, Table S11). Finally, assuming a lower relative susceptibility for children and adolescents (70% with respect to adults for all variants) did not improve alignment with serological data (Fig. S16, Table S12).

Methods
Pre-pandemic baseline contact matrix
We used pre-pandemic contact data collected from a large-scale survey in France in 201212, distinguishing between contacts engaged during regular weekdays, weekends or school holidays. We derived a social contact matrix corrected by reciprocity, and broken down by location (home, school, work, transport, leisure, other) and type of contact (skin-to-skin or non-physical contact at short distance), using the Social Contact Rates (SOCRATES) Data Tool48 (Fig. 1a, b). The original survey collected Supplementary Professional Contacts (SPC), i.e. participants with more than 20 daily professional contacts were asked not to report them but rather to provide their total number and age distribution. We included SPC only in the elements of the work matrix involving adults and seniors. This baseline matrix was then adapted to the French population in 2020 using demography data, applying an appropriate density correction (following ref. 15). Through the density correction, the original matrix M ij (whose elements represent the average number of contacts an individual in age group i establishes with individuals in age group j) is projected to the demographic structure of 2020 by defining a new matrix M0 ij = M ij * N/N j * (N0 j /N0), where N, N j, refer to the total population and the population in age group j, respectively, in the year of the survey, while N0, N0 j refer to the population in 2020. This density correction preserves reciprocity, so that the projected matrix fulfills the condition M0 ij N0 i = M0 ji N0 j. We considered the contact matrix estimated for a regular weekday, defined as Monday-Friday excluding holidays. We did not model explicitly the weekday/weekend effect, which is absorbed in the calibration procedure of the transmission model (see section Inference Framework below). However, we accounted for the impact of school holidays. We used the pre-pandemic contact data collected during spring school holidays to model the synthetic pandemic contact matrix during spring, winter and Christmas holidays. We made some assumptions when modeling summer holidays in the lack of available pre-pandemic contact data. See the section below and the Supplementary Information (Section 4) for further details.

Construction of synthetic contact matrices
We built time-varying synthetic contact matrices on a weekly basis (except for lockdown periods) from March 2020 to May 2022. We considered four age groups: children [0–10], adolescents [11–18], adults [19–64] and seniors (65+ years old). We chose a limited number of groups to parametrize the matrices using the available behavioral data (missing finer age-stratification) with minimal assumptions, while capturing epidemiologically relevant groups and ensuring interpretability and real-time feasibility of the framework. Matrices were obtained by applying reductions to the components of the pre-pandemic contact matrix (location and type of contact) to simulate the social mixing conditions experienced during the pandemic. In particular, we parametrized the matrices to account for (i) impact of adoption of remote working in reducing contacts at work and on transports, (ii) impact of full or partial school closure (or remote learning) and impact of school holidays on school-related contacts, (iii) impact of social-distancing measures on contacts associated to non-essential activities, (iv) impact of adoption of health preventive behaviors, such as avoiding physical contacts. We used proxy contact data collected during the pandemic to inform the parameterization of the synthetic contact matrices. In particular, we used Google mobility data31 related to workplaces to adjust the number of contacts in the work matrix over time (Fig. 1c). Google measures the change in the number of visitors to a specific location with respect to a pre-pandemic baseline; the mobility change related to workplaces can thus be interpreted as an effective reduction in attendance at work. We assumed that such reduction in attendance produces a non-linear reduction of contact rates (Section 4.2.1 in the Supplementary Information) that is in between the frequency-dependent and the density-dependent assumption65. We also used data on voluntary school attendance in the exit phase of the first lockdown, and the calendar of school holidays to adjust school-related contacts (Table S5). Finally, we used data from the CoviPrev survey41 on declared avoidance of physical contacts during the pandemic to reduce the proportion of skin-to-skin contacts (Fig. 1d). We assumed that physical contacts were removed rather than replaced with non-physical contacts, thus representing a lower-bound scenario; this assumption was tested in a sensitivity analysis (see section Sensitivity Analyses below). The framework for building the synthetic contact matrices is fully detailed in Section 4.2 of the Supplementary Information, and summarized in Table S6. The resulting average number of contacts over time was tested for correlation with the Normalcy Index and the Stringency Index (Fig. 3c and Fig. S13). The Normalcy Index66 is a measure of the impact of the pandemic on human behavior, integrating multiple daily indicators of human activities in a score from 0 to 100, with 100 representing the pre-pandemic level. It is important to note that the Normalcy Index and the indicators used for constructing synthetic matrices are not the same: the Normalcy Index aggregates eight broad measures of societal activity (e.g. retail, transport, leisure, office occupancy), while our synthetic matrices mainly relied on workplace mobility and physical contact avoidance. The latter indicator has no equivalent in the Normalcy Index. The Stringency Index67 is a composite measure of nine response metrics (e.g. as school closure, restrictions on public gatherings) to quantify the strictness of government policies for epidemic control, in a scale from 0 to 100, with 0 indicating absence of measures.

SocialCov contact surveys
Seven survey waves were conducted in France to collect data on contact behavior29,30. Survey participants were recruited online and contact matrices were adjusted to the French population for representativeness. SocialCov recruited participants through convenience sampling via the governmental app TousAntiCovid. In particular, the survey was promoted via the news channel of the app which invited individuals aged 18 and above to complete the questionnaire. If participants declared living with minors (i.e. individuals under the age of 18), they were invited to complete a second specific questionnaire for one of them, in his/her presence. Since the survey sample was not representative of the French population, synthetic populations were generated for each campaign to better reflect the age and gender distribution in France, using sampling with replacement from the SocialCov participant pool; the matrices were bootstrapped to account for sampling variance30. The first survey was conducted during the first lockdown (matrix LD1)29. The survey was then implemented in 6 additional waves30, in December 9–22, 2020 (M1), January 10–21, 2021 (M2), March 2–10, 2021 (M3), August 12–24, 2021 (M4), December 6–17, 2021 (M5), and May 20–29, 2022 (M6). Contacts were defined as either a physical contact (such as a kiss or a handshake) or a close contact (such as face-to-face conversation at less than 1m distance). Total contacts (physical and non-physical) for each individual were truncated at 50 to reduce the impact of outliers. We used contacts reported on Monday-Friday excluding holidays, to allow comparison with the synthetic contact matrices that were built based on a regular weekday pre-pandemic matrix. In a sensitivity analysis, we used matrices weighted by weekday and weekend. Participants in the survey reported contacts aggregated by age group, and were used to produce age-stratified 10×10 contact matrices. We aligned the age groups of the contact survey with the four age groups used for the synthetic matrices to allow comparison (see Section 4.3 of the Supplementary Information).

Comparison of contact patterns
From the set of weekly synthetic contact matrices, we extracted the ones with the closest matching period to the seven survey waves and made direct comparison between the two sets of matrices (Table S7). We summarized the information contained in each contact matrix through different metrics in order to make the comparisons. We computed (i) the average number of contacts, overall and by age class, (ii) a measure of matrix correlation based on the cosine similarity, (iii) the proportion of average connectivity due to young individuals (<19 y.o., i.e., including children and adolescents), (iv) an index for age-assortativity and (v) the age-specific proportion of within-group contacts. All these quantities are mathematically defined in the Supplementary Information (Section 5). Indicators (iv) and (v) are different measures of the degree assortativity, quantifying the extent to which contacts occur between individuals who share their same characteristics (in our case, the relevant characteristic is age). Contact matrices estimated from empirical data usually show some assortativity with age, i.e. they have a strong diagonal component, as individuals tend to mix with individuals with similar age9. More assortative contacts have implications on disease spread, increasing the epidemic risk and leading to lower herd immunity thresholds68,69.

We further compared the synthetic and SocialCov matrices with two empirical matrices from the CoMix study (Section 8.3 in the Supplementary Information), which was conducted in France between December 2020 and April 2021. CoMix provided complementary age-stratified data, but its limited temporal coverage and inclusion of minors in only two of seven waves restricted this comparison to two periods.

Transmission model
We integrated the two sets of contact matrices (synthetic and empirical) into an age-stratified transmission model to simulate the unfolding of the COVID-19 pandemic in France from early 2020 to May 2022. The model has been presented in depth in previous works18,36,37. We used a stochastic age-structured two-strain transmission model with vaccination, parameterized using French data on demography70, age profile70, and vaccine uptake71. Transmission dynamics follows a compartmental scheme illustrated in Figure S1, which accounts for latency period, pre-symptomatic transmission, asymptomatic and symptomatic infections with different degrees of severity, and individuals affected by severe symptoms requiring hospitalization. Contact rates for each disease stage are adjusted to model the effect of spontaneous change of behavior due to severe illness and the impact of testing and self-isolation (Section 4.4 of Supplementary Information). We did not differentiate transmissibility by contact type or setting, assuming all contacts contribute equally to transmission. The model reproduces the co-circulation of two strains, and was applied to describe the Wuhan-Alpha period (February 2020 – May 2021), the Alpha-Delta period (June 2021 – August 2021), and the Delta-Omicron period (September 2021 – May 2022). Epidemiological parameter values and sources for the Wuhan strain are reported in Table S1. The model is parametrized with age-dependent susceptibility and disease severity. For the Wuhan strain, children and adolescents have a relative susceptibility of 70% with respect to adults. Variant-dependent parameters include the generation time, the transmission advantage, the infection-hospitalization ratio (Table S2). The model is further stratified by (i) vaccine dose, to build vaccine coverage in the population over time according to data on vaccine doses administered in France71, and (ii) time since vaccination, to model steps of waning in vaccine effectiveness (Fig. S2). The model accounts for possible re-infection with Omicron after a prior infection, with waning in protection against re-infection. We distinguished between different levels of protection conferred by vaccine-only, natural (infection-only) and hybrid immunity (Section 3 of the Supplementary Information). In parallel to disease stage progression, we also modeled seropositivity to compare model results with seroprevalence data from Santé publique France measuring the presence of IgG-type antibodies. Following the modeling approach adopted in ref. 21, we assumed that upon becoming infectious (i.e. while exiting the E compartment in Fig. S1), infected individuals also enter in a compartment AB pre (in parallel to I p) which represents the pre-seropositivity compartment. Then, individuals move to the seroposivity compartment AB+ after seroconversion, and finally they move to the seronegativity compartment AB- after seroreversion. We informed the average time spent in AB pre and AB+ based on estimates from the literature for IgG-type antibodies. We used 12 days for seroconversion72 for all age groups, and 200 days for seroreversion for adults73–76. Given the evidence of slower seroreversion for more severe infections, we used 400 days for seniors77. In the lack of estimates specific for children and adolescents, we assumed the same value as adults. We then compared the proportion of AB+ over time predicted by the model with French national seroprevalence estimates78 collected by Santé publique France, available by age group, and corrected by test sensitivity. Since the IgG test does not distinguish between antibodies from infection and vaccination, and no information on vaccination status was collected from serologically tested individuals, we restricted our analysis to seroprevalence data collected before the start of the vaccination campaign. This ensures comparability with model estimates of antibody-positive individuals, which reflect infection-derived immunity only.

Inference framework
The model was fitted to daily age-stratified hospital admission data79 and age-stratified seroprevalence data78 since the start of the pandemic (February 2020) up to May 22, 2022. We used a maximum likelihood approach to fit a step-wise transmission rate per contact (see Section 6 of the Supplementary Information for full details). More specifically, in the pre-lockdown phase (February–March 2020), we fitted the starting date of the epidemic and the baseline transmission per contact β pre-LD. Then, we fitted a correcting factor α phase of the transmission rate, calibrated sequentially in successive time-windows (Table S8), each one representing a different pandemic phase, based on epidemic activity, behavior and interventions implemented (e.g., pre-lockdown, lockdown, exit phase, summer, curfew). As changes in the variant’s transmissibility are explicitly modeled through the transmission advantage, the parameter α phase is meant to absorb other factors potentially affecting the transmission that are not captured by the time-varying contact matrices, e.g., mask usage or outdoor/indoor activity, or mis-specification of contacts. This correcting factor can be thus interpreted as a global correction of the contact matrices used in the model. The product of the fitted α phase at time t with the corresponding contact matrix represent the effective contacts needed to reproduce the observed epidemic dynamic. The closer the correcting factor to 1, the better the alignment between the time-varying contact matrices and the effective contact rates needed to reproduce the total epidemic dynamic. However, acting as a global rescaling of the contact matrix, the correcting factor cannot alter the underlying matrix structure and mixing, responsible for the age-stratified model outcomes.

Model comparison
We compared the outcomes of three transmission models. The first model is informed with weekly mobility-based synthetic contact matrices, as done in our previous works during the pandemic18,36–40. The second model is informed with empirical contact matrices estimated from survey data (SocialCov29,30) collected during the pandemic. The contact matrices available from 7 distinct surveys were extended beyond the survey period in order to cover the timespan of the model, as pictured in Fig. 5b. We used the matrix estimated for summer 2021 as a proxy for school holidays, as this was the only survey wave fully occurring in a period with schools closed (excluding the lockdown). Both models used the empirical pre-pandemic contact matrix in the period prior to the implementation of the lockdown. The two models with time-varying contact matrices (either synthetic or empirical) were compared to a third reference model integrating the same static pre-pandemic contact matrix throughout the whole pandemic period. To identify the model which better reproduced the change of behavior and the resulting epidemic dynamic, we compared the model outcomes in terms of (i) Akaike Information Criterion (AIC) as a measure of goodness of fit, (ii) mean absolute error of the model trajectory of daily hospital admissions with respect to the data, (iii) distribution of the correcting factor, (iv) age-specific model estimates of the proportion of antibody-positive individuals over time (accounting for seroconversion and seroreversion) in comparison with seroprevalence data, and (v) age-specific model estimates of hospital admissions compared to age-stratified data. While the correcting factor provides indication about the adjustment required to reproduce the total epidemic, the comparison of age-stratified model outcomes with observations is an indicator of the ability of the matrices to capture contact structure and mixing patterns.

Sensitivity analyses
We carried out sensitivity analyses on (i) the susceptibility of young individuals with SARS-CoV-2 variants; (ii) the integration of the empirical contact matrices into the transmission model, including the effect of weekend or using the empirical matrix of May 2022 as a pre-pandemic matrix; (iii) alternative specifications of the likelihood using other calibration targets, i.e., age-stratified hospitalizations only (without accounting for seroprevalence data) and total hospitalizations (without accounting for age-stratified data). To demonstrate that matrix structure (encoding which group is most at-risk for infection and from whom) plays a critical role in shaping epidemic outcomes, we also carried out multiple tests by systematically varying the structure of the synthetic matrices, introducing modifications in (iv) age-specific contact volumes or (v) mixing patterns. Finally, we tested an alternative parameterization of the synthetic matrices without assuming contact removal due to avoidance of physical contacts. All sensitivity analyses are reported in Section 9 of the Supplementary Information.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "# Summary\nThe authors present a comparison of two methods to generate dynamic contact matrices among 4 age groups for France between 2020 March and 2022 May: 1) synthetic matrices made by adjusting pre-pandemic contact matrices using mobility data and assumptions; and 2) empirical matrices, estimated from 7 serial surveys in France over a similar period, adjusted for non-representative sampling. As a control case 3), a static pre-pandemic matrix was also compared. The aims explored are interesting and important: i) how do these matrices compare to each other, and ii) which method performs better for transmission modelling (of covid-19), especially given that (1) can likely provide more timely and inexpensive estimates than (2).\nThe model design for aim (ii) includes numerous important features for covid-19 dynamics, such as age-stratified susceptibility & hospitalization, different viral strains, empiric vaccine uptake over time, natural/vaccine/hybrid & waning immunity, which all appear to be diligently parameterized. The discussion is also overall excellent, except some overstated conclusions. However, the inference framework for aim (ii) does not allow for the necessary evidence to address aim (ii) and aim (i) remains insufficiently explored. My overall recommendation is to split these aims into two papers to address each more thoroughly. Do to the above, I do not find the current results particularly useful.\n# Major Issues\n+ Model-based inference framework for aim (ii): Conclusions such as \"Our study demonstrates that mobility-based synthetic matrices performed well in capturing the dynamic changes in contact behavior across age groups throughout the pandemic\" are not well supported by the results, and are in some ways unfalsifiable in the current analysis framework, due to the unconstrained correcting factor alpha and lack of age-specific calibration targets. In other words, what results would cause the authors to draw a different conclusion?\n- Calibration targets: The only data used to fit the model were total hospitalizations per week. However, age-stratified hospitalization data appeared to be available (Suppl 7.3 & Figure S5), as well as age-stratified seropositivity prevalence over time (Figures 5 & S9). It's not clear why these age-stratified data weren't also used for fitting, as they could, crucially, help inform relative incidence / hospitalization across age groups. The two main roles of contact matrices in a model are indeed to inform: 1) who is most at-risk (via mean total contacts per group) and 2) from whom (via non-random mixing patterns). Neither of these aspects is directly tested in the current experiments, so we cannot draw strong conclusions about how well the contact matrices capture transmission dynamics. This point is underscored by the comparable performance of the pre-pandemic matrix (mean error & Figure S5).\n- Correcting factor (alpha): Variations in alpha over time for all three contact matrix cases (Figure 5b) were of a similar magnitude as variations in the mean numbers of contacts over time (Figure 2e-f), about 3-fold over time. We could crudely interpret this as: alpha explained about the same proportion of epidemic dynamics as the contact matrices themselves. While I commend the authors for explicitly modelling so many determinants of epidemic dynamics, the gap filled by alpha (~ 0.6--1.8 x reproduction number) is still large enough to almost completely absorb the influence of contact matrices on overall incidence / hospitalizations. While the magnitude of alpha varied across matrix approaches, time trends were highly correlated across approaches (Figure 5b), suggesting that all matrices were failing to capture some key driver(s) of epidemic dynamics. The model is essentially overparameterized by alpha, which might allow reconstruction of hospitalizations using almost any contact matrices.\n- One suggestion would be to incorporate specific correcting factors for age and/or contact-types, which could then be be used to examine age/type-specific discrepancies between estimated matrix contacts versus effective contacts.\n+ Comparing contact matrices for aim (i):\n- The level of detail in the contact matrices is quite limited for a paper focused on comparing contact matrices (e.g. only 4 age groups). Perhaps this is a limitation of the available data, but it doesn't appear so (for either SocialCov or COMES-F). Also, it's well known that epidemic dynamics are fundamentally different with vs without risk heterogeneity (e.g. increasing R0 and differences in herd effects). I would have hoped to see more age groups and/or further stratification of age groups into high/low risk groups. Adding even two risk groups may help fit the data better, and thereby reduce the range of alpha in aim (ii).\n- The comparison of empirical and synthetic contact matrices focuses almost entirely on total numbers of contacts per age group (rather than who contacts whom). This aspect is well done (e.g. time trends in discrepancies, and discrepancies by age group). However, differences in mixing *patterns* by both age and contact type should be explored to address this aim fully. It seems that contacts can be stratified by type in both data sources. For example, ages [0-10] and [11-18] had the largest discrepancies between empirical and synthetic matrices. While this was acknowledged, were differences driven by within or between age-group contacts, and for which types/locations of contacts? The four comparison metrics (Suppl 5) are useful, but these are discussed too briefly in the results and they remain rather abstract (e.g. what is a \"low\" measure of cosine similarity? Maybe a random mixing matrix can serve as a reference.)\n- Relatedly, only Figure 1a (in main text or supplement) depicts a complete mixing matrix (all 4 x 4 age group combinations), but this reflects the pre-pandemic matrix. Give the aims of comparing contact matrices, I was expecting to see more illustrations of complete mixing matrices, so that changes to mixing *patterns* can be examined (not just total contacts as in Figure 2e-f).\n## Medium issues\n- Overall, I found the methods-last structure of the paper (imposed by the journal I think) inefficient and confusing. The results section provides only a trickle of methods information, which distracted me from the results themselves with questions I had about the methods. However, reading the methods before the results section, ideas like the correcting factor were assumed to be already introduced. Still more methods are relegated to the supplement, so I am never quite sure where to look for a particular methods detail. An outline of the experiments is needed.\n- A related issue is that the research questions / aims are not stated explicitly anywhere. Also, the last paragraph of the introduction includes: \"Although mobility-based synthetic contact matrices ... their accuracy relative to empirical contact matrices remains unexplored\" which suggests that the empirical matrices will be taken as a \"gold standard\" in comparisons, but this is not really how the results are framed. Similarly: \"evaluating the effectiveness of these two approaches in modeling the pandemic dynamics\" should define \"effectiveness\" and \"pandemic dynamics\" more concretely.\n- It should be clarified in the methods how contacts were reported by individuals < 18 in waves 2-7 of SocialCov. In Suppl 4.3 [310], this is indirectly suggested, but only the discussion acknowledges that parents might have reported for children. This is notable since ages [0-10] had the largest discrepancies between synthetic and empiric matrices.\n- Although acknowledged in the limitations, the *removal* of physical contacts (rather than replacing them with non-physical contacts) does not seem plausible. Since most covid-19 models make no distinction between these types, I think it is better to either ignore the level of avoidance (q at [273] in the Supplement) and treat all contacts equally, or use distinct rates of transmission (beta) for physical vs non-physical contacts in order to use q.\n- Figure S1 is very helpful, but analogous diagrams for the other strata (especially vaccination, prior infection, waning, and VoC) are needed too. These can be 1-2 separate subfigures (not drawing all compartments / joint strata in one diagram).\n## Minor Issues\n### Main\n- [41] Somewhere in this paragraph, a more precise definition of \"contact matrices\" should be given, e.g. \"in which matrix elements reflect the average number of contacts per day formed by individuals in one group with another.\"\n- [58] I think \"convenient\" should be \"convenience\" here?\n- [72] The term \"contact layer\" here and throughout might be confusing. Why not simply \"contact types\"?\n- [73] \"These data streams enabled to produce weekly ...\" is not grammatically correct - add \"enabled *us* to\"?\n- [101] \"to reproduce age and gender distribution in France\" same - add \"reproduce *the* age\"?\n- [102] Consider adding \"*average* daily contacts\" for precision.\n- [117] The meaning of \"normalized contact matrices, which disregard contact intensity\" is not clear - is this normalization redundant with the definition of cosine similarity?\n- [138] A suggested above, another comparator could be pure random (so-called proportionate) mixing matrix -- which could be used in both aims (i) and (ii).\n- [145] Why is the IQR reported, rather than 95% range? I would think the latter is more useful, but maybe both could be given like: median (Q2.5 [Q25, Q75] Q97.5)\n- [147] \"suggesting that small adjustments were needed\" as noted above, I do not agree these are small, especially those alpha outside IQR ...\n- [163] \"confirmed overall these findings\" grammar - maybe \"*generally* confirmed these findings\"\n- [173] \"strongly valuable\" grammar - maybe \"*highly* valuable\"\n- [197] \"survey frequency of surveys\" typo?\n- [233] I would not fully agree that \"However, these limitations critically depend on the mobility metrics chosen\" since masking can erode the correlation with effectively no impact on mobility metrics.\n- [245] It's not clear what is meant by \"optimal methods for extending empirical contact matrices\".\n- [262] The subject of \"underestimate transmission risks\" is not clear here: isn't transmission risk overestimated by ignoring repeat contacts?\n- [274] The word \"robust\" here is too strong.\n- [333] The overall value of these correlations with Normalcy Index and Stringency Index with respect to the aims are not clear to me.\n- [340] As far as I can tell, the only citation for the 7 SocialCov surveys is #25 in Eurosurveillance, which only comments on the first survey. This is notable since later surveys included all ages, while the first was restricted to 18+. I noticed when looking for information about how responses for young children/babies were obtained.\n- [365-372] The implications of assortativity for reproduction number & herd effects might be stated briefly somewhere here.\n- [375-408] I just want to reiterate that the level of model complexity is impressive.\n- [414] Perhaps Table S7 could be explicitly mentioned here regarding time windows.\n- [436] It would help to explain the rationale / strengths for each performance metric. For example, AIC would \"punish\" 20% error in predicting 50 or 500 hospitalizations more equally, whereas absolute error would \"punish\" 20% error on 500 hospitalizations ~10 times more than on 50.\n- [437] Relatedly, is there any benefit to using AIC over simple (log-)likelihood? I think k is the same across approaches, but this is never stated explicitly.\n- [462] I commend the authors on making their code available via GitHub.\n- [Figure 1] Ideally, the matrix figure (a) could use a perceptually uniform colormap, and the proportion figure (b) use a different, qualitative map. The hashing for non/physical is very nice. Perhaps (d) could extend the range from 30-100 to 0-100% to minimize misinterpretation.\n- [Figure 2] Overall these subfigures are excellent, and nicely communicate a lot of information.\n- [Figure 3] (a-b) Instead of these subfigures, which omit between-group mixing and have indistinguishable data points, perhaps an image like 1a can show the difference matrix (M1_ij - M2_ij) so readers can visually see where differences are largest; I think that is the goal here? Also, perhaps (d) can use the same x-axis as (c), as I'm not sure what the current axis (% contacts < 19) is communicating?\n- [Figure 4] Is excellent.\n- [Figure 5] (and S4, S9): Perhaps alpha should be plotted in log2 y-scale, since it is a multiplicative factor? Also, is it possible to scale densities so their maximum width is consistent, to improve clarity (especially Figure S4)?\n### Supplement\n- [65] Perhaps \"dimensions\" is a better term than \"layers\" to describe independent population stratifications?\n- [76] Table S1 should clarify that the relative infectiousness with mild and severe symptoms (I_ms, I_ss) are the same.\n- [78-105] To improve ease of use, this section (Suppl 2) could have the information added to Table S1 or summarized in a new Table S2?\n- [86] I cannot find the base probability of transmission (beta_pre-LD) anywhere. I understand this is fitted, but can the posterior mean (95%) be reported?\n- [178] The elements in matrix C_ij are described as \"per-capita rates of contact between age-group i and j\". This key definition is not very precise, especially to distinguish C_ij from M_ij. My understanding is that C_ij is equivalent to the \"intrinsic connectivity matrix\" in Arregui et al (2018) - perhaps this terminology can be used or added in parentheses for readers already familiar? Though, it does not add much precision. Another definition of C_ij is the expected number of contacts formed by a group-i individual with group-j individuals, if 100% of the population was in group-j, or equivalently, C_ij / N is the expected number of contacts formed by a group-i individual with group-j individuals per individual in group-j.\n- [204-221] While I appreciate the authors' consideration that not all declared work contacts will be symmetrically reported (e.g. a bus driver and passenger may report one another as \"work\" and \"travel\" contacts, respectively), I would think that most public-facing occupations would be infeasible for remote-work, and that occupations where remote-work is feasible would include mainly \"symmetrically reported\" (work-work) contacts. So, I don't agree that the two situations described here are equally likely, hence the average: (1-a) + (1-a)^2 / 2; and I would suggest using the (1-a)^2 approach throughout, unless the authors can provide some examples of public-facing occupations where remote-work is feasible?\n- [322-340] Suppl 4.4: The direct removal of contacts among those isolating essentially implies a density-dependent effect, since the isolating contacts are not \"replaced\" among everyone else. A frequency-dependent approach would add a lot of complexity to calculations with probably negligible difference in transmission because infection prevalence is never very high, so the current approach is fine, but it may be worth spelling out the implied assumption.\n- [365-394] Supple 5.4: It may be more clear to simply omit the continuous domain functions and integrals, and focus on the discrete implementation via sums.\n- [398] The force of infection equation shown here is extremely simplified compared to the modifiers described (and the GitHub code), such as infectiousness, susceptibility, etc. The true equation spelling out the various factors involved would be much clearer. Also, since the denominator \"N\" differs from the usual \"N_j\", it may be worth reminding readers how this derives from the definition of \"C_ij\".\n- [492] Figure S5d should likely log-transform the y-axis to improve the visualization of differences, and because I think 50% relative difference is \"equally bad\" as 200% ?\n(Remarks on code availability)\nI have only briefly examined the code on GitHub to verify questions I had. It seems reproducible but would need to be fully tested.", "reviewer_2": "Mobility-Driven synthetic contact matrices: a scalable solution for real-time pandemic response modelling\nOverall, this is an interesting and well-written manuscript based on a thorough analysis, comparing the use of weekly synthetic transmission matrices, building on an elaborate method for exploring mobility data with matrices from online social survey waves to model the evolution of the pandemic in France. The study adds novelty and deserves publication. However, some clarification on the methods is warranted.\nAs pointed out by the authors, during a crisis where situational awareness are needed for policy recommendations, their method is easily automatized and can readily be used, compared to social survey studies that require data washing and more elaborate measurement.\nMain comments:\nThe “empirical matrices” are based on data from the SocialCov survey, with a reference to Bosetti et al. Eurosurveillance 26 (2021). However, this reference only addresses the primary wave exclusively conducted among adults 18+ years. Hence, it is unclear how data was collected among children and adolescents in the later waves. Do they involve parents reporting on behalf of their children? Are adolescents included in the survey? This is important information and should be properly documented. A sentence in the discussion hints that parents were answering on behalf of their children.\nThe methods for calculation of a typical weekday is not specified. Presumably, the SocialCov survey includes information collected on different weekdays. How is a “typical” weekday calculated? There are likely differences between contacts on Mondays vs. mid-week.\nIt is not clear to this reader what specific contacts were used to construct the “empirical matrices”. It is stated that both physical and non-physical contacts were collected –if the total number of contacts were used, it should be stated.\nThe imputation process (for the first wave of data collection) is not specified, and there are no specifics on the sampling procedure when reweighing the data. Were the matrices bootstrapped to account for sampling variance?\nThe paper does not consider the French CoMix data because the survey was conducted over only 5 months (late 2020 to spring 2021). However, the CoMix survey design allows for a more detailed description of contacts in children. I believe it would be informative and of general interest to include this data and compare average connectivity, cosine similarity and the proportion of young connectivity, even if the time period is restricted.\nHow was the serological status calculated for vaccinated individuals?\nMinor comments:\nLine 55: It is stated that (in the CoMix survey) only UK, Belgium and the Netherlands covered the first pandemic wave (also expressed in the reference that it cited). However, Norway was part of the CoMix survey and conducted six waves between April and September 2020, https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-024-18853-8\nLine 76 “accuracy” relative to empirical contact matrices. I would rephrase as both the synthetic and empirical matrices are estimates.\nSuppl. L 316. The matrix obtained from the first wave of data collection is named LD, while the national lockdowns are named LD1-LD3. Does this imply that this matrix was also used for later national lockdowns?\n(Remarks on code availability)", "reviewer_3": "This manuscript addresses an important question about whether it is sufficient to use ‘synthetic’ contact matrices, constructed using mobility and other publicly available data, or if it is essential to undertake resource-intensive efforts to collect empirical contact data to capture changing behaviors. The authors address this question in the context of the COVID-19 pandemic, though their findings are likely generalizable to other circumstances in which behavior may be changing substantially over the course of an epidemic. The authors undertake a detailed assessment of this question, by descriptively comparing contact matrices generated by each approach, evaluating the extent to which different contact assumptions align with hospitalization data and seroprevalence estimates from 2020-22. This is a thorough, clear, and important paper.\nI have a few minor comments for the authors to consider.\n1. Some discussion of the range and distribution of contacts reported, and if / how this was taken into account in the modeling, should be included. The matrices are nicely shown in Fig 1, but all that is shown is the averages (and averages by age group). Were the full distributions of contact accounted for in the modeling, or were only the average rates by age used? I think the latter is defensible, but for an airborne infection such as SARS-CoV-2 where contact heterogeneity (‘superspreading’) may play an important role in transmission dynamics, the distributional assumptions should be noted.\n2. Were there any important differences (contact definition, mode of survey, survey structure, etc.) in the data collection for the empirical contact studies during the pandemic and the study from which the pre-pandemic baseline was drawn for the synthetic matrices (2012 survey)? In the author’s opinion, would these design differences contribute to the differences in fit under the synthetic vs. empirical data?\n3. Please provide an explanation of ‘cosine similarity’. I am unfamiliar with this method and a brief explanation would help a reader to understand how to best interpret this analysis.\n4. I have not heard of the Normalcy Index (only the Stringency Index), but it is the only one shown in Fig 2c as a comparison to the synthetic contact rates. Can the Stringency index be shown as well? I understand this to be the more commonly used measure. If the authors would like to show the Normalcy Index, some additional explanation of how the indicator is constructed would be useful. Are the ‘indicators’ being used to construct the Normalcy Index similar to those being used to generate the synthetic contact patterns? If so, we would already expect them to be correlated.\n5. Lovely figures, but I think Figure 3 is largely redundant with Figure 2. Would recommend placing Figure 3 in the Supplement.\n6. I do not understand Figure 3D; more explanation may be required.\n7. A comment - the authors note this in their Discussion, but I feel that setting this up as a comparison of the empirical and synthetic contact data is somewhat unfair, since the empirical studies were conducted so sparsely across the pandemic. In fact, the empirical studies seem to do surprisingly well given the low frequency sampling.\n8. From Figure 4a, it appears that all of the contact assumptions allow for a reasonably good fit to hospitalization data. How do the authors reconcile this with the quite large discrepancies between the synthetic and empirical contact rates? Can this be attributed to the low rate of hospitalization among kids, among whom the discrepancy between synthetic and empirical rates was highest?\nOverall, an important contribution to the literature on this topic.\n(Remarks on code availability)"}, "author_response": "POINT-BY-POINT REPLY TO REVIEWERS’ COMMENTS\nMobility-driven synthetic contact matrices: a scalable solution for real-time pandemic\nresponse modeling\nLaura Di Domenico"}]

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