We present Epydemix, an open-source Python package for the development and calibration of stochastic compartmental epidemic models. The framework supports flexible model structures that incorporate demographic information, age-stratified contact matrices, and dynamic public health interventions. A key feature of Epydemix is its integration of Approximate Bayesian Computation (ABC) techniques to perform parameter inference and model calibration through comparison between observed and simulated data. The package offers a range of ABC methods such as simple rejection sampling, simulation-budget-constrained rejection, and Sequential Monte Carlo (ABC-SMC). Epydemix is modular, and supports ABC-based calibration both for models defined within the package and for those developed externally. To demonstrate the computational framework capabilities, we discuss usage examples that include (i) simulating an intervention-driven model with time-varying parameters, and (ii) benchmarking calibration performance using synthetic epidemic data. We further illustrate the use of the package in a retrospective case study that includes scenario projections under alternative intervention assumptions. By lowering the barrier for the implementation of computational and inference approaches, Epydemix makes epidemic modeling more accessible to a wider range of users, from academic researchers to public health professionals.

The initial rollout of COVID-19 vaccines has been challenged by logistical issues, limited availability of doses, scarce healthcare capacity, spotty acceptance, and the emergence of variants of concern. Non-pharmaceutical interventions (NPIs) have been critical to support these phases. However, vaccines may have prompted behavioural relaxation, potentially reducing NPIs adherence. Epidemic models have explored this phenomenon, but they have not been validated against data. Moreover, recent surveys provide conflicting results on the matter. The extent of behavioural relaxation induced by COVID-19 vaccines is still unclear. Here, we aim to study this phenomenon in four regions. We implement five realistic epidemic models which include age structure, multiple virus strains, NPIs, and vaccinations. One of the models acts as a baseline, while the others extend it including different behavioural relaxation mechanisms. First, we calibrate the baseline model and run counterfactual scenarios to quantify the impact of vaccinations and NPIs. Our results confirm the critical role of both in reducing infection and mortality rates. Second, using different metrics, we calibrate the behavioural models and compare them to each other and to the baseline. Including behavioural relaxation leads to a better fit of weekly deaths in three regions. However, the improvements are limited to a [Formula: see text] reduction in weighted mean absolute percentage errors and these gains are generally offset by models' increased complexity. Overall, we do not find clear signs of behavioural relaxation induced by COVID-19 vaccines on weekly deaths. Furthermore, our results suggest that if this phenomenon occurred, it generally involved only a minority of the population. Our work contributes to the retrospective validation of epidemic models developed amid the COVID-19 Pandemic and underscores the issue of non-identifiability of complex social mechanisms.

Vaccinations are fundamental public health interventions. Yet, inequalities in vaccine uptake across socioeconomic groups can significantly undermine their impact. Moreover, heterogeneities in vaccination coverage across socioeconomic strata are typically neglected by epidemic models and considered, if at all, only at posteriori. This limitation reduces their ability to predict and assess the effectiveness of vaccination campaigns. Here, we study the impact of socioeconomic inequalities in vaccination uptake on disease burden, measured as attack rate. We consider a modeling framework based on generalized contact matrices that extend traditional age-stratified approaches to incorporate socioeconomic status (SES) variables. We simulate epidemic dynamics under two scenarios. In the first, vaccination campaigns are concurrent with epidemics. In the second, instead, vaccinations are completed before the onset of infection waves. By using both synthetic and empirical generalized contact matrices, we find that inequalities in vaccine uptake can lead to non-linear effects on disease outcomes and exacerbate disease burden in disadvantaged groups of the population. We demonstrate that simpler models ignoring SES heterogeneity produce incomplete or biased predictions of attack rates. Additionally, we show how inequalities in vaccine coverage interact with non-pharmaceutical interventions (NPIs), compounding differences across subgroups. Overall, our findings highlight the importance of integrating SES dimensions, alongside age, into epidemic models to inform more equitable and effective public health interventions and vaccination strategies.

Understanding the feedback loop that links the spatiotemporal spread of infectious diseases and human behavior is an open problem. To study this problem, we develop a multiplex framework that couples epidemic spreading across subpopulations in a metapopulation network (i.e., physical layer) with the spreading of awareness about the epidemic in a communication network (i.e., virtual layer). We explicitly study the interactions between the mobility patterns across subpopulations and the awareness propagation among individuals. We analyze the coupled dynamics using microscopic Markov chains (MMCs) equations and validate the theoretical results via Monte Carlo (MC) simulations. We find that with the spreading of awareness, reducing human mobility becomes more effective in mitigating the large-scale epidemic. We also investigate the influence of varying topological features of the physical and virtual layers and the correlation between the connectivity and local population size per subpopulation. Overall the proposed modeling framework and findings contribute to the growing literature investigating the interplay between the spatiotemporal spread of epidemics and human behavior.

We analyze the effectiveness of the first six months of vaccination campaign against SARS-CoV-2 in Italy by using a computational epidemic model which takes into account demographic, mobility, vaccines data, as well as estimates of the introduction and spreading of the more transmissible Alpha variant. We consider six sub-national regions and study the effect of vaccines in terms of number of averted deaths, infections, and reduction in the Infection Fatality Rate (IFR) with respect to counterfactual scenarios with the actual non-pharmaceuticals interventions but no vaccine administration. Furthermore, we compare the effectiveness in counterfactual scenarios with different vaccines allocation strategies and vaccination rates. Our results show that, as of 2021/07/05, vaccines averted 29, 350 (IQR: [16, 454-42, 826]) deaths and 4, 256, 332 (IQR: [1, 675, 564-6, 980, 070]) infections and a new pandemic wave in the country. During the same period, they achieved a -22.2% (IQR: [-31.4%; -13.9%]) IFR reduction. We show that a campaign that would have strictly prioritized age groups at higher risk of dying from COVID-19, besides frontline workers and the fragile population, would have implied additional benefits both in terms of avoided fatalities and reduction in the IFR. Strategies targeting the most active age groups would have prevented a higher number of infections but would have been associated with more deaths. Finally, we study the effects of different vaccination intake scenarios by rescaling the number of available doses in the time period under study to those administered in other countries of reference. The modeling framework can be applied to other countries to provide a mechanistic characterization of vaccination campaigns worldwide.

The promise of efficacious vaccines against SARS-CoV-2 is fulfilled and vaccination campaigns have started worldwide. However, the fight against the pandemic is far from over. Here, we propose an age-structured compartmental model to study the interplay of disease transmission, vaccines rollout, and behavioural dynamics. We investigate, via in-silico simulations, individual and societal behavioural changes, possibly induced by the start of the vaccination campaigns, and manifested as a relaxation in the adoption of non-pharmaceutical interventions. We explore different vaccination rollout speeds, prioritization strategies, vaccine efficacy, as well as multiple behavioural responses. We apply our model to six countries worldwide (Egypt, Peru, Serbia, Ukraine, Canada, and Italy), selected to sample diverse socio-demographic and socio-economic contexts. To isolate the effects of age-structures and contacts patterns from the particular pandemic history of each location, we first study the model considering the same hypothetical initial epidemic scenario in all countries. We then calibrate the model using real epidemiological and mobility data for the different countries. Our findings suggest that early relaxation of safe behaviours can jeopardize the benefits brought by the vaccine in the short term: a fast vaccine distribution and policies aimed at keeping high compliance of individual safe behaviours are key to mitigate disease resurgence.

In this work, we aim to determine the main factors driving self-initiated behavioral changes during the seasonal flu.To this end, we designed and deployed a questionnaire via Influweb, a Web platform for participatory surveillance in Italy, during the 2017 -18 and 2018 -19 seasons.We collected 599 surveys completed by 434 users.The data provide socio-demographic information, level of concerns about the flu, past experience with illnesses, and the type of behavioral changes voluntarily implemented by each participant.We describe each response with a set of features and divide them in three target categories.These describe those that report i) no (26%), ii) only moderately (36%), iii) significant (38%) changes in behaviors.In these settings, we adopt machine learning algorithms to investigate the extent to which target variables can be predicted by looking only at the set of features.Notably, 66% of the samples in the category describing more significant changes in behaviors are correctly classified through Gradient Boosted Trees.Furthermore, we investigate the importance of each feature in the classification task and uncover complex relationships between individuals' characteristics and their attitude towards behavioral change.We find that intensity, recency of past illnesses, perceived susceptibility to and perceived severity of an infection are the most significant features in the classification task and are associated to significant changes in behaviors.Overall, the research contributes to the small set of empirical studies devoted to the data-driven characterization of behavioral changes induced by infectious diseases. Author summaryHuman behavior and infectious diseases are linked by a feedback loop.While individuals might change their behavior as a response to an epidemic, such changes might influence the spreading itself.So far, our understanding and characterization of behavioral changes induced by diseases has been strongly limited by the lack of empirical data.As result, the vast majority of research has been focused on theoretical, what if, scenarios.In this work, we collected a unique dataset comprised of 599 surveys submitted by 434 users to the participatory surveillance platform Influweb over the 2017 -18 and 2018 -19 flu seasons.

The availability of novel digital data streams that can be used as proxy for monitoring infectious disease incidence is ushering in a new era for real-time forecast approaches to disease spreading. Here, we propose the first seasonal influenza forecast framework based on a stochastic, spatially structured mechanistic model (individual level microsimulation) initialized with geo-localized microblogging data. The framework provides for more than 600 census areas in the United States, Italy and Spain, the initial conditions for a stochastic epidemic computational model that generates an ensemble of forecasts for the main indicators of the epidemic season: peak time and intensity. We evaluate the forecasts accuracy and reliability by comparing the results with the data from the official influenza surveillance systems in the US, Italy and Spain in the seasons 2014/15 and 2015/16. In all countries studied, the proposed framework provides reliable results with leads of up to 6 weeks that became more stable and accurate with progression of the season. The results for the United States have been generated in real-time in the context of the Centers for Disease Control and Prevention ``Forecasting the Influenza Season Challenge''. A characteristic feature of the mechanistic modeling approach is in the explicit estimate of key epidemiological parameters relevant for public health decision-making that cannot be achieved with statistical models that do not consider the disease dynamic. Furthermore, the presented framework allows the fusion of multiple data streams in the initialization stage and can be enriched with census, weather and socioeconomic data.

Every day millions of users are connected through online social networks, generating a rich trove of data that allows us to study the mechanisms behind human interactions. Triadic closure has been treated as the major mechanism for creating social links: if Alice follows Bob and Bob follows Charlie, Alice will follow Charlie. Here we present an analysis of longitudinal micro-blogging data, revealing a more nuanced view of the strategies employed by users when expanding their social circles. While the network structure affects the spread of information among users, the network is in turn shaped by this communication activity. This suggests a link creation mechanism whereby Alice is more likely to follow Charlie after seeing many messages by Charlie. We characterize users with a set of parameters associated with different link creation strategies, estimated by a Maximum-Likelihood approach. Triadic closure does have a strong effect on link formation, but shortcuts based on traffic are another key factor in interpreting network evolution. However, individual strategies for following other users are highly heterogeneous. Link creation behaviors can be summarized by classifying users in different categories with distinct structural and behavioral characteristics. Users who are popular, active, and influential tend to create traffic-based shortcuts, making the information diffusion process more efficient in the network.