Jorge Xicoténcatl Velasco-Hernández

This brief work discusses potential superspreading events that may occur during the World Cup in México. The study is particularly focused on the city of Guadalajara due to a large recent outbreak in January and February and insufficient vaccine coverage previous to 2026.

Mathematical models have produced important insights into the relationships between disease transmission, risk perception, and human behaviour. However, the increase in scale and complexity of health and behavioural data accelerated by the COVID-19 pandemic demands a critical evaluation of the realism and readiness of mathematical models of infectious disease dynamics to inform preparation and response to (re)emerging public health threats. In this scoping review, we identify five thematic frontiers in extending coupled models of disease dynamics and human behaviour, spanning (1) information quality and scale, (2) data-driven versus perceived risk, (3) social influence, (4) barriers related to fatigue and access, and (5) disruptive events. For each frontier, we summarize key modelling approaches and results, identify knowledge gaps and provide recommendations on future directions with a focus on integrating big data into epidemiological models, incorporating social behavioural theory and accounting for heterogeneity within populations. In turn, each of these frontiers involves challenges that call for new analytical and technical developments. We close by providing general recommendations for modelers with a focus on interdisciplinary collaboration with social and behavioural scientists and establishing best practices for data collection and management to improve the public health relevance of infectious disease models.

In early 2025, a measles outbreak emerged in West Texas, USA, and spread into northern Mexico, with Chihuahua becoming the epicenter of Mexico's largest measles resurgence in decades. The outbreak affected Mennonite colonies, Indigenous Rarámuri (Tarahumara) communities in the Sierra Tarahumara, and highly mobile agricultural worker populations. We analyzed municipality-level confirmed case counts in Chihuahua using a generalized logistic growth model to estimate early epidemic growth rates and characterize deviations from exponential growth. Uncertainty was quantified by bootstrap resampling under a negative binomial observation model. We linked epidemic dynamics to structural deprivation using hierarchical clustering based on municipal-level social lag indicators. To conceptualize border regions coupling under heterogeneous immunization, we formulated a two-population vaccination model. Large urban municipalities showed rapid early growth with well-identified parameters, whereas remote Sierra Tarahumara municipalities exhibited sparse case reporting and wider uncertainty. Despite smaller absolute case counts, the mortality burden was disproportionately concentrated in high-deprivation municipalities. Poverty clustering separates municipalities into distinct socioeconomic groups, highlighting that conventional epidemic indicators may understate severity in structurally marginalized settings with delayed detection and socioeconomic barriers to overcome. Model results indicate that lower initial vaccination coverage leads to higher peak incidence, whereas higher inter-municipal mobility alone does not necessarily result in higher peak incidence. Outbreak assessment based solely on incidence-based indicators can underestimate impact in marginalized communities. Integrating epidemic growth models with structural deprivation metrics provides a more policy-relevant characterization of outbreak risk and severity. Sustained routine immunization and strengthened binational surveillance remain central to preventing sustained transmission in high-mobility border regions.

A bstract: We study an extension of an environmentally mediated epidemiological model that incorporates direct human-to-human transmission. While the original formulation accounted for environmental exposure, it did not include direct transmission between individuals. Allowing both transmission routes to interact leads to significant qualitative changes in the system dynamics. The analysis reveals multiple dynamical regimes governed by environmental and combined threshold quantities. The stability of the disease-free equilibrium is controlled by an environmental threshold, whereas a combined reproduction number determines the onset of multistability. For certain parameter ranges, endemic equilibria coexist with the disease-free equilibrium, giving rise to backward-type bifurcation behavior and sensitivity to initial conditions. Moreover, the direct transmission rate acts as an organizing parameter by inducing the emergence of an environmental-free equilibrium when exceeding its classical threshold. These results highlight how environmentally coupled transmission mechanisms can generate rich dynamics in low-dimensional models.

The transmission of infectious diseases involves complex interactions across multiple biological scales, from within-host immunological processes to between-host transmission dynamics. While multiscale models have the potential to capture these interactions more accurately, they are often hindered by increased complexity and limited data availability. In this study, we develop a multiscale epidemic model linking host-vector population-level transmission dynamics to within-host and within-vector pathogen dynamics. Our model captures key features of within-vector viral progression and allows bidirectional coupling between within-host and between-host processes. The scales are linked under the assumption of dose-dependent transmission, with the functional form informed by empirical viremia–infectiousness data from arbovirus transmission. Focusing on Dengue, Zika, and West Nile viruses as case studies, we assess how different functional forms of the coupling affect the number of equilibria of the epidemic model. We find that when the transmission is modeled using linear coupling functions, the multiscale model yields the same bifurcation structure of the simpler, uncoupled model, indicating that the linking of scales does not alter the range of possible long-term epidemiological states in such cases. However, nonlinear coupling can induce complex behaviors such as multiple endemic equilibria and backward bifurcations, which the uncoupled model does not capture. These results underscore the importance of carefully selecting coupling functions and provide guidance on when multiscale modeling is essential for understanding and managing vector-borne diseases.

Vaccination is a cornerstone of infectious disease control, yet vaccines are not fully protective, leaving a fraction of the vaccinated population susceptible to infection. This partial protection can alter behavior, as individuals who perceive themselves as immune may reduce adherence to preventive measures. Motivated by this, we investigate how behavioral changes among non-immune vaccinated individuals influence the dynamics of a directly transmitted disease and the basic reproduction number. We propose a model that incorporates vaccine failure through three facets (take, degree, and duration) alongside a behavioral parameter that modifies contact rates according to compliance with mitigation measures. Our analysis highlights the critical role of the behavioral index in key phenomena, including backward bifurcation and overall disease dynamics. We identify two thresholds. The first specifies the values of the behavioral index for which backward bifurcation does not arise, thereby indicating the conditions under which the disease may persist. The second establishes a relationship between the behavioral index and vaccine efficacy, which allows us to compare the transmission dynamics of our model with those of the classical vaccination model.

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages, acute, severe and asymptomatic where severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates (as normally occur in directly-transmitted or vector-transmitted diseases) only occurs when a parameter R _* > 1. In this case, the forward transcritical bifurcation that exists for R _* < 1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R _* is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R _* describes the strength of the transmission to infectious classes other than the I -(acute) type infections. The epidemic outbreak conditions and the structure of R _* appearing in this model are both resposible for the existence of endemic states.

In this paper we develop a generalization of the Kermack-McKendrick SIR model where the time of infectiousness follows the Weibull distribution. We compute the equivalent classical results available for the classical SIR model, particularly a general expression for the basic reproduction number. We comment about the implications of this generalization in epidemic and metapopulation dynamics and illustrate our findings with some numerical simulations.

The high morbidity of acute respiratory infections constitutes a crucial global health burden. In particular, for SARS-CoV-2, non-pharmaceutical intervention geared to enforce social distancing policies, vaccination, and treatments will remain an essential part of public health policies to mitigate and control disease outbreaks. However, the implementation of mitigation measures directed to increase social distancing when the risk of contagion is a complex enterprise because of the impact of NPI on beliefs, political views, economic issues, and, in general, public perception. The way of implementing these mitigation policies studied in this work is the so-called traffic-light monitoring system that attempts to regulate the application of measures that include restrictions on mobility and the size of meetings, among other non-pharmaceutical strategies. Balanced enforcement and relaxation of measures guided through a traffic-light system that considers public risk perception and economic costs may improve the public health benefit of the policies while reducing their cost. We derive a model for the epidemiological traffic-light policies based on the best response for trigger measures driven by the risk perception of people, instant reproduction number, and the prevalence of a hypothetical acute respiratory infection. With numerical experiments, we evaluate and identify the role of appreciation from a hypothetical controller that could opt for protocols aligned with the cost due to the burden of the underlying disease and the economic cost of implementing measures. As the world faces new acute respiratory outbreaks, our results provide a methodology to evaluate and develop traffic light policies resulting from a delicate balance between health benefits and economic implications.