Epidemics

Public health departments need evidence-backed scenario projections to support decision making in infectious disease outbreaks. However, traditional infectious disease models are often not readily deployable or responsive to the urgent questions and priorities of public health departments or health systems. Moreover, uncertainty in model outputs is not always adequately assessed or communicated, potentially undermining trust among public health practitioners and the public. To address these issues, we, the Insight Net Modeling Guidance for Public Health Working Group, used early COVID-19 data from Michigan to illustrate modeling approaches that can be used to answer urgent questions in three key phases of outbreak response: prior to local introduction, early exponential growth, and established transmission with potential interventions. In each phase, we integrate case, hospitalization, and death data and capture ranges of plausible future trajectories. These models, which produce status quo and scenario projections, are intended to inform planning and motivate action rather than forecast precise future outcomes. Importantly, this work offers guidance to focus modeling efforts and provides examples and code for how to fit and implement these models, ultimately serving as both a conceptual guide and practical toolkit to support more transparent, timely, and appropriate use of models in outbreak response.

The spread of viral respiratory infections is intricately linked to human interactions, and this relationship can be characterised and modelled using social contact data. However, many analyses tend to overlook the recurrent nature of these contacts. To bridge this gap, we undertake the task of describing individuals contact patterns over time, by characterising the interactions made with distinct individuals during a week. Moreover, we gauge the implications of this temporal reconstruction on disease transmission by juxtaposing it with the assumption of random mixing over time. This involves the development of an age-structured individual-based model, utilising social contact data from a pre-pandemic scenario (the POLYMOD study) and a pandemic setting (the Belgian CoMix study), respectively. We found that accounting for the frequency of contacts impacts the number of new, distinct, contacts, revealing a lower total count than a naive approach, where contact repetition is neglected. As a consequence, failing to account for the repetition of contacts can result in an underestimation of the transmission probability given a contact, potentially leading to inaccurate conclusions when using mathematical models for disease control. We therefore underscore the necessity of acknowledging the longitudinal nature of contacts when formulating effective public health strategies.

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 of routine collection of age-stratified mobility data to improve pandemic response.

This report considers three mechanisms that might underlie the course of the secondary peak of coronavirus infections in the United Kingdom. It considers: (i) fluctuations in transmission strength; (ii) seasonal fluctuations in contact rates and (iii) fluctuations in testing. Using dynamic causal modelling, we evaluated the contribution of all combinations of these three mechanisms using Bayesian model comparison. We found overwhelming evidence for the combination of all mechanisms, when explaining 16 types of data. Quantitatively, there was clear evidence for an increase in transmission strength of 57% over the past months (e.g., due to viral mutation), in the context of increased contact rates (e.g., rebound from national lockdowns) and increased test rates (e.g., due to the inclusion of lateral flow tests). Models with fluctuating transmission strength outperformed models with fluctuating contact rates. However, the best model included all three mechanisms suggesting that the resurgence during the second peak can be explained by an increase in effective contact rate that is the product of a rebound of contact rates following a national lockdown and increased transmission risk due to viral mutation.

Backfill is the process of revising case data, often by retrospectively assigning or reassigning newly reported cases to earlier symptom onset dates. Time- and spatial-varying delays in the backfill process may compromise real-time surveillance and forecasting efforts by obscuring the true underlying transmission patterns. Using Michigan COVID-19 case data, we developed a statistical mixture model to describe backfill and geographical and temporal variations. The model combined an exponential process (case reporting delay) and a gamma-distributed process (date reassignment). Parameters were estimated by maximum likelihood with lasso regularization, and the Akaike Information Criterion was used to determine the necessity of the reassignment component for each date. We estimated the exponential reporting speed over time and space and, if appropriate, the transient peak and time of case reassignment. We found that case reporting improved over the pandemic: reporting speed increased over time (with substantial day-to-day variation), and case reassignments were processed faster. We also identified potential regional disparities: rural regions with population densities below 50 people/km2 had slower backfill speeds. These findings provide critical insights about the evolution of case reporting and backfill dynamics that can be leveraged for "nowcasting" models to complete real-time surveillance data, ultimately improving outbreak preparedness and response.

Sexual networks often have heavy-tails, where a small number of exceptional individuals in a population have many more sexual partners than the average (e.g., more than five standard deviations). Heavy-tails pose challenges when surveying this group, as these exceptional individuals are uncommon in the population (and so hard to detect), but have disproportionate impact on epidemiological questions, such as those related to the spread of sexually transmitted diseases. In essence, omitting these individuals is a severe error. In this modeling study, we use prior estimates of the distribution of sexual partners amongst men who have sex with men to explore the implication of different sample sizes on survey estimates. We find that even large surveys consistently fail to capture the variance of the sexual network. Surveys of heavy-tailed sexual networks should be designed with this high variance in mind so as not to underestimate the disease dynamics. The failure to adequately capture the variance within a heavy-tailed network has strong implications for infectious disease dynamics and modeling as disease dynamics are often driven by the heavy-tail.

Capturing the structure of a population and characterising contacts within the population are key to reliable projections of infectious disease. Two main elements of population structure - contact heterogeneity and age - have been repeatedly demonstrated to be key in infection dynamics, yet are rarely combined. Regarding individuals as nodes and contacts as edges within a network provides a powerful and intuitive method to fully realise this population structure. While there are a few key examples of contact networks being measured explicitly, in general we need to construct the appropriate networks from individual-level data. Here, using data from social contact surveys, we develop a generic and robust algorithm to generate an extrapolated network that preserves both age-structured mixing and heterogeneity in the number of contacts. We then use these networks to simulate the spread of infection through the population, constrained to have a given basic reproduction number (R0) and hence a given early growth rate. Given the over-dominant role that highly connected nodes ( superspreaders) would otherwise play in early dynamics, we scale transmission by the average duration of contacts, providing a better match to surveillance data for numbers of secondary cases. This network-based model shows that, for COVID-like parameters, including both heterogeneity and age-structure reduces both peak height and epidemic size compared to models that ignore heterogeneity. Our robust methodology therefore allows for the inclusion of the full wealth of data commonly collected by surveys but frequently overlooked to be incorporated into more realistic transmission models of infectious diseases.

Epidemic models often heavily simplify the dynamics of human-to-human contacts, but the resulting bias in outbreak dynamics - and hence requirements for control measures - remains unclear. Even if high-resolution temporal contact data were routinely used for modelling, the role of this temporal network structure towards outbreak control is not well characterised. We address this by assessing dynamic networks across varied social settings in three ways. Firstly, we characterised the distribution of retained contacts over consecutive timesteps by developing a novel metric, the "retention index", which accounts for the change in the number of contacts over consecutive timesteps on a normalised scale with the extremes representing fully static and fully dynamic networks. Secondly, we described the repetition of contacts over the days by estimating the frequency of contact pairs occurring over the study duration. Thirdly, we distinguish the difference between superspreader and infectious individuals driving superspreading events by estimating the connectivity of an individual (i.e. individual has high connectivity in a timestep if he accounts for 80% of the contacts in the timestep) and the frequency of exhibiting high connectivity. Using 11 networks from 5 settings studied over 3-10 days, we estimated that more than 80% of the individuals in most settings were highly connected for only short periods. This suggests a challenge to identify superspreaders, and more individuals would need to be targeted as part of outbreak interventions to achieve the same reduction in transmission as predicted from a static network. Taking into account repeated contacts over multiple days, we estimated simple resource planning models might overestimate the number of contacts made by an infector by 20%-70%. In workplaces and schools, contacts in the same department accounted for most of the retained contacts. Hence, outbreak control measures would be better off targeting specific sub-populations in these settings to reduce transmission. In contrast, no obvious type of contact dominated the retained contacts in hospitals, so reducing the risk of disease introduction is critical to avoid disrupting the interdependent work functions. This study identified key epidemiological properties of temporal networks that potentially shape outbreak dynamics and illustrated the need for incorporating such properties in outbreak simulations. SignificanceDirectly transmitted infectious diseases spread through social contacts that can change over time. Modelling studies have largely focused on simplifying these contact patterns to predict outbreaks but the assumptions on contact patterns may bias results and, in turn, conclusions on the effectiveness of control measures. An ongoing challenge is, therefore, how to measure key properties of complex and dynamic networks to facilitate the development of network disease simulation models, which ensures that outbreak analysis is transparent and interpretable in the real-world context. To address this challenge, we analysed 11 networks from 5 different settings and developed new metrics to capture crucial epidemiological features of these networks. We showed that there is an inherent difficulty in identifying individual superspreaders reliably in most networks. In addition, the key types of individuals driving transmission vary across settings, thus requiring different outbreak control measures to reduce disease transmission or the risk of introduction. Simple models to mimic disease transmission in temporal networks may not capture the repeated contacts over the days, and hence could incorrectly estimate the resources required for outbreak control. Our study characterised temporal network data in epidemiologically relevant ways and is a step towards developing simplified contact networks to capture real-world contact patterns for future outbreak simulation studies.

A concern in infectious disease modelling is how accurately population mixing is incorporated, as it shapes the type and frequency of contacts through which infection spreads, and consequently, estimated intervention effectiveness. Although synthesizing mixing patterns from diary-based surveys is an established framework, geographical information is poorly or sparsely captured. Here we propose a generalizable workflow to quantify geographical connectivity from job registry data covering over 8 million Dutch working population. The derived colleague connectedness shows heterogeneous spatial patterns, quantified from the number of connections per municipality triplet, two residential municipalities and one shared workplace municipality. We demonstrate the utility of this spatial connectivity in signalling regions with elevated outbreak risks. Using SARS-CoV-2 Omicron as an example: a ten-fold increase in within-province connections is associated with a 12-day earlier (95% CI: 2 to 22 days) Omicron onset, and between-province connections associated with an 8-day earlier (95% CI: - 4 to 21 days) onset. These results suggest that the impact of regional interventions shifting spatial connectivity patterns should be expected to vary by region and type of intervention. Together, our findings draw attention of using this highly fine-grained spatial connectivity to enable more regionally tailored and network-targeted policy measures.

Most countries have enacted some restrictions to reduce social contacts to slow down disease transmission during the COVID-19 pandemic. For nearly two years, individuals likely also adopted new behaviours to avoid pathogen exposure based on personal circumstances. We aimed to understand the way in which different factors affect social contacts - a critical step to improving future pandemic responses. The analysis was based on repeated cross-sectional contact survey data collected in 21 European countries between March 2020 and March 2022. We calculated the mean daily contacts reported using a clustered bootstrap by country and by settings (at home, at work, or in other settings). Where data were available, contact rates during the study period were compared with rates recorded prior to the pandemic. We fitted censored individual-level generalized additive mixed models to examine the effects of various factors on the number of social contacts. The survey recorded 463,336 observations from 96,456 participants. In all countries where comparison data were available, contact rates over the previous two years were substantially lower than those seen prior to the pandemic (approximately from over 10 to <5), predominantly due to fewer contacts outside the home. Government restrictions imposed immediate effect on contacts, and these effects lingered after the restrictions were lifted. Across countries, the relationships between national policy, individual perceptions, or personal circumstances determining contacts varied. Our study, coordinated at the regional level, provides important insights into the understanding of the factors associated with social contacts to support future infectious disease outbreak responses.

Spread of transmissible diseases is dependent on contact patterns in a population (i.e. who contacts whom). Therefore, many epidemic models incorporate contact patterns within a population through contact matrices. Social contact survey data are commonly used to generate contact matrices; however, the resulting matrices are often imbalanced, such that the total number of contacts reported by group A with group B do not match those reported by group B with group A. While the importance of balancing contact matrices has been acknowledged, how these imbalances affect modelled projections (e.g., peak infection incidence, impact of public health measures) has yet to be quantified. Here, we explored how imbalanced contact matrices from age-stratified populations (<15, 15+) may bias transmission dynamics of infectious diseases. First, we compared the basic reproduction number of an infectious disease when using imbalanced versus balanced contact matrices from 177 demographic settings. Then, we constructed a susceptible exposed infected recovered transmission model of SARS-CoV-2 and compared the influence of imbalanced matrices on infection dynamics in three demographic settings. Finally, we compared the impact of age-specific vaccination strategies when modelled with imbalanced versus balanced matrices. Models with imbalanced matrices consistently underestimated the basic reproduction number, had delayed timing of peak infection incidence, and underestimated the magnitude of peak infection incidence. Imbalanced matrices also influenced cumulative infections observed per age group, and the projected impact of age-specific vaccination strategies. For example, when vaccine was prioritized to individuals <15 in a context where individuals 15+ underestimated their contacts with <15, imbalanced models underestimated cumulative infections averted among 15+ by 24.4%. We conclude stratified transmission models that do not consider reciprocity of contacts can generate biased projections of epidemic trajectory and impact of targeted public health interventions. Therefore, modellers should ensure and report on balancing of their contact matrices for stratified transmission models. AUTHOR SUMMARYTransmissible diseases such as COVID-19 spread according to who contacts whom. Therefore, mathematical transmission models - used to project epidemics of infectious diseases and assess the impact of public health interventions - require estimates of who contacts whom (also referred to as a contact matrix). Contact matrices are commonly generated using contact surveys, but this data is often imbalanced, where the total number of contacts reported by group A with group B does not match those reported by group B with group A. Although these imbalances have been acknowledged as an issue, the influence of imbalanced matrices on modelled projections (e.g. peak incidence, impact of public health interventions) has not been explored. Using a theoretical model of COVID-19 with two age groups (<15 and 15+), we show models with imbalanced matrices had biased epidemic projections. Models with imbalanced matrices underestimated the initial spread of COVID-19 (i.e. the basic reproduction number), had later time to peak COVID-19 incidence and smaller peak COVID-19 incidence. Imbalanced matrices also influenced cumulative infections observed per age group, and the estimated impact of an age-specific vaccination strategy. Given imbalanced contact matrices can reshape transmission dynamics and model projections, modellers should ensure and report on balancing of contact matrices.

Infection control requires integrating behavioural dynamics into epidemic models. However, models often overlook behavioural complexity due to limited empirical data. We adopted an interdisciplinary approach to develop a modelling-oriented behavioural dataset. We applied the Capability, Opportunity, Motivation-Behaviour (COM-B) framework to assess COVID-19 vaccination behaviour from 22,228 survey responses across six European countries (March-July 2024). We examined how willingness to vaccinate aligned with uptake and timeliness, and traced country-specific temporal changes in perceived COVID-19 severity and willingness. To capture peer-driven opinion formation, we introduced a novel indicator - discussion contacts - measuring interactions on relevant topics. Willingness correlated with both uptake and timeliness, yet 6-18% of initially unwilling respondents ultimately received [&ge;]2 doses. Lower willingness was associated with a 2.0-month vaccination delay. Perceived severity and willingness to vaccinate declined throughout the pandemic. Behavioural indicators systematically varied by vaccination status, particularly in the Motivation domain. Daily discussion contacts followed the patterns of in-person contacts, ranging from 1.4-2.9 for adults <60 years to 0.5-1.2 for those [&ge;]60 years. This dataset offers theory-informed and time-sensitive inputs to support the development of more realistic and policy-relevant behavioural-epidemic models.

Short-term forecasts can provide predictions of how an epidemic will change in the near future and form a central part of outbreak mitigation and control. Renewal-equation based models are increasingly popular. They infer key epidemiological parameters from historical epidemiological data and forecast future epidemic dynamics without requiring complex mechanistic assumptions. However, these models typically ignore interaction between age-groups, partly due to challenges in parameterising a time varying interaction matrix. Social contact data collected regularly by the CoMix survey during the COVID-19 epidemic in England, provide a means to inform interaction between age-groups in real-time. We developed an age-specific forecasting framework and applied it to two age-stratified time-series: incidence of SARS-CoV-2 infection, estimated from a national infection and antibody prevalence survey; and, reported cases according to the UK national COVID-19 dashboard. Jointly fitting our model to social contact data from the CoMix study, we inferred a time-varying next generation matrix which we used to project infections and cases in the four weeks following each of 29 forecast dates between October 2021 and November 2022. We evaluated the forecasts using proper scoring rules and compared performance with three other models with alternative data and specifications alongside two naive baseline models. Overall, incorporating age-interaction improved forecasts of infections and the CoMix-data-informed model was the best performing model at time horizons between two and four weeks. However, this was not true when forecasting cases. We found that age-group-interaction was most important for predicting cases in children and older adults. The contact-data-informed models performed best during the winter months of 2020 - 2021, but performed comparatively poorly in other periods. We highlight challenges regarding the incorporation of contact data in forecasting and offer proposals as to how to extend and adapt our approach, which may lead to more successful forecasts in future.

This paper presents a smoothing method to estimate age-specific human contact patterns and their variations over different periods. Specifically, it examines how age-specific contact patterns shift under varying conditions, such as holiday periods and levels of public health intervention. The method uses Bayesian P-splines to smooth age-specific contact rates and leverages Laplace approximations for fast Bayesian inference, significantly reducing computational complexity. The proposed methodology is applied to the CoMix data from Belgium, a social contact survey collected during the COVID-19 pandemic. Results indicate significantly reduced contacts during periods in which strict social policies were in place, particularly among adults, and notable reductions among young individuals during holidays. This research advances our understanding of how human contact adapts in response to varying social and policy conditions, which can guide more realistic and adaptive infectious disease transmission models.

Wastewater-based epidemiology provides a low-cost, scalable view of community infection dynamics, but converting these signals into actionable epidemiological insights remains difficult. Mechanistic models offer interpretability, yet, assumptions such as a constant transmission rate limit realism over long simulation horizons and heterogeneous settings. We present a susceptible-exposed-infectious-recovered (SEIR) universal differential equation (UDE) that links wastewater viral loads to case counts and embeds neural networks to represent time-varying parameters. Parameter and prediction uncertainties are quantified using an ensemble method. We assessed the method using newly collected data for Bonn, Germany, as well as published data for five cities in Rhineland-Palatinate, Germany. The proposed approach produces realistic out-of-sample projections of case counts over an up to 50-week test horizon, and it learns city-specific mappings to prevalence that generalise within each location. Compared to SEIR models with fixed transmission rates, the UDE captures non-stationary drivers (policy, behaviour, seasonality) without sacrificing epidemiological structure, while propagating observation and model uncertainty into the projections. Accordingly, the approach facilitates a scalable interpretation and exploitation of wastewater data for the monitoring of infectious diseases.

The basic reproduction number of an infectious disease is known to depend on the structure of contacts between individuals in a population. This relationship has been explored mathematically through two well-known models: one which depends on a matrix of contact rates between different demographic groups, and another which depends on the variability of contact rates over the population. Here we introduce a model that combines and generalises these two approaches. We derive a formula for the basic reproduction number and validate it through comparisons to simulated outbreaks. Applying this method to contact survey data collected in Belgium between 2020 and 2022, we find that our model produces higher estimates of the basic reproduction number and larger relative changes over periods when social contact behaviour was changing during the COVID-19 pandemic. Our analysis suggests some practical considerations when using contact data in models of infectious disease transmission.

SARS-CoV-2 is primarily transmitted through person-to-person contacts. It is important to collect information on age-specific contact patterns because SARS-CoV-2 susceptibility, transmission, and morbidity vary by age. To reduce risk of infection, social distancing measures have been implemented. Social contact data, which identify who has contact with whom especially by age and place are needed to identify high-risk groups and serve to inform the design of non-pharmaceutical interventions. We estimated and used negative binomial regression to compare the number of daily contacts during the first wave (April-May 2020) of the Minnesota Social Contact Study, based on respondents age, gender, race/ethnicity, region, and other demographic characteristics. We used information on age and location of contacts to generate age-structured contact matrices. Finally, we compared the age-structured contact matrices during the stay-at-home order to pre-pandemic matrices. During the state-wide stay-home order, the mean daily number of contacts was 5.6. We found significant variation in contacts by age, gender, race, and region. Adults between 40 and 50 years had the highest number of contacts. Respondents in Black households had 2.1 more contacts than respondent in White households, while respondents in Asian or Pacific Islander households had approximately the same number of contacts as respondent in White households. Respondents in Hispanic households had approximately two fewer contacts compared to White households. Most contacts were with other individuals in the same age group. Compared to the pre-pandemic period, the biggest declines occurred in contacts between children, and contacts between those over 60 with those below 60.

Contact tracing is an important public health measure used to reduce transmission of infectious diseases. Contact tracers typically conduct telephone interviews with cases to identify contacts and direct them to quarantine, with the aim of preventing onward transmission. However, in situations where caseloads exceed the capacity of the public health system, timely interviews may not be feasible for all cases. Here we present a modelling framework for assessing the impact of different case interview prioritisation strategies on disease transmission. Our model is based on Australian contact tracing procedures and informed by contact tracing data on COVID-19 cases notified in Australia from 2020-21. Our results demonstrate that last-in-first-out strategies are more effective at reducing transmission than first-in-first-out strategies or strategies with no explicit prioritisation. To maximise the public health benefit from a given case interview capacity, public health practitioners should consider our findings when designing case interview prioritisation protocols for outbreak response.

Close-contact and respiratory infectious diseases are spread through social interactions, which were affected by the COVID-19 pandemic and wider demographic and cultural changes. To estimate post-pandemic social contact patterns in the United Kingdom, we conducted a cross-sectional survey of 13,238 participants from November 2024 to March 2025. We calculated the mean number of daily contacts and contact matrices stratified by age, ethnicity, and socioeconomic status (SES). The mean number of daily contacts was 9.11 (95% confidence interval (CI): 8.73 - 9.50). Age-assortativity was high, while assortativity between ethnic groups was strongest in the home, and between SES groups in the workplace. In a novel respiratory pathogen outbreak, we found 2.29 times higher infection risk for Black people compared to White (95% CI: 2.08-2.55). This study provides crucial data to inform post-pandemic models of infectious disease transmission, and incorporate ethnicity and SES into such models.

Using a Bayesian approach to epidemiological compartmental modeling, we demonstrate the "bomb-like" behavior of exponential growth in COVID-19 cases can be explained by transmission of asymptomatic and mild cases that are typically unreported at the beginning of pandemic events due to lower prevalence of testing. We studied the exponential phase of the pandemic in Italy, Spain, and South Korea, and found the R0 to be 2.56 (95% CrI, 2.41-2.71), 3.23 (95% CrI, 3.06-3.4), and 2.36 (95% CrI, 2.22-2.5) if we use Bayesian priors that assume a large portion of cases are not detected. Weaker priors regarding the detection rate resulted in R0 values of 9.22 (95% CrI, 9.01-9.43), 9.14 (95% CrI, 8.99-9.29), and 8.06 (95% CrI, 7.82-8.3) and assumes nearly 90% of infected patients are identified. Given the mounting evidence that potentially large fractions of the population are asymptomatic, the weaker priors that generate the high R0 values to fit the data required assumptions about the epidemiology of COVID-19 that do not fit with the biology, particularly regarding the timeframe that people remain infectious. Our results suggest that models of transmission assuming a relatively lower R0 value that do not consider a large number of asymptomatic cases can result in misunderstanding of the underlying dynamics, leading to poor policy decisions and outcomes.