Critical behavior of epidemics depending on the interplay between temporal scales and human behavior

The spatial spread of infectious diseases is ruled by two processes: the disease progression and human behavior, which comprises human contacts and human mobility. A standard modeling approach is to define an epidemiological model upon a metapopulation network under some restrictive assumptions, such as that all processes happen at the same time scale, dispersal is diffusive, and agents are indistinguishable with respect to age and behavioral features. Although several models relax at least one of those assumptions, providing new insights about an epidemic, rarely are they relaxed all at once. Here, we introduce a model whose equations explicitly contain two parameters that encode the ratios between the time scales of the recovery, contact, and mobility processes, while simultaneously accounting for the age structure of the agents, different mobility layers, and different social settings for contacts. Furthermore, to reflect more closely real-world scenarios, we consider two settings: a diffusion-based one in which agents disperse like particles to spread the epidemics, effectively changing the starting population size far from and at equilibrium, and a force-based one where spread happens without changing the population of patches far from equilibrium. For both spreading frameworks, we study the regimes under which they provide distinct results and the critical properties of the epidemic process, finding that the curve of the critical points, which separate increasing or decreasing trends in the number of infected individuals – as well as other macroscopic observables of interest such as the attack rate – in the space of the two scale parameters exhibits a critical point itself. Complementing spatially-oriented strategies, the proposed approaches can contribute to the design of effective non-pharmaceutical interventions by focusing on the mutual influence of temporal scales, dispersal dynamics, and human behavior. In particular, our study allows for an optimal tuning of mobility and contact restrictions based on the characteristics of the disease and its spatial distribution in the early phase of spreading.