Human behavior plays a critical role in shaping epidemic trajectories. During health crises, people respond in diverse ways in terms of self-protection and adherence to recommended measures, largely reflecting differences in how individuals assess risk. This behavioral variability induces effective heterogeneity into key epidemic parameters, such as infectivity and susceptibility. We introduce a minimal extension of the susceptible-infected-removed (SIR) model, denoted HeSIR, that captures these effects through a simple bimodal scheme, where individuals may have higher- or lower-transmission-related traits. We derive a closed-form expression for the epidemic threshold in terms of the model parameters, and the network's degree distribution and homophily, defined as the tendency of like-risk individuals to preferentially interact. We identify a resurgence regime just beyond the classical threshold, where the number of infected individuals may initially decline before surging into large-scale transmission. Through simulations on homogeneous and heterogeneous network topologies we corroborate the analytical results and highlight how variations in susceptibility and infectivity influence the epidemic dynamics. We further show that, under suitable assumptions, the HeSIR model maps onto a standard SIR process on an appropriately modified contact network, providing a unified interpretation in terms of structural connectivity. Our findings quantify the effect of heterogeneous behavioral responses, especially in the presence of homophily, and caution against underestimating epidemic potential in fragmented populations, which may undermine timely containment efforts. The results also extend to heterogeneity arising from biological or other nonbehavioral sources.

Most vaccines require multiple doses, the first to induce recognition and antibody production and subsequent doses to boost the primary response and achieve optimal protection. We show that properly prioritizing the administration of first and second doses can shift the epidemic threshold, separating the disease-free from the endemic state and potentially preventing widespread outbreaks. Assuming homogeneous mixing, we prove that at a low vaccination rate, the best strategy is to give absolute priority to first doses. In contrast, for high vaccination rates, we propose a scheduling that outperforms a first-come first-served approach. We identify the threshold that separates these two scenarios and derive the optimal prioritization scheme and interdose interval. Agent-based simulations on real and synthetic contact networks validate our findings. We provide specific guidelines for effective resource allocation, showing that adjusting the timing between the primer and booster significantly impacts epidemic outcomes and can determine whether the disease persists or disappears.

The geographic distribution of the population on a region is a significant ingredient in shaping the spatial and temporal evolution of an epidemic outbreak. Heterogeneity in the population density directly impacts the local relative risk: the chances that a specific area is reached by the contagion depend on its local density and connectedness to the rest of the region. We consider an SIR epidemic spreading in an urban territory subdivided into tiles (i.e., census blocks) of given population and demographic profile. We use the relative attack rate and the first infection time of a tile to quantify local severity and timing: how much and how fast the outbreak will impact any given area. Assuming that the contact rate of any two individuals depends on their household distance, we identify a suitably defined geographical centrality that measures the average connectedness of an area as an efficient indicator for local riskiness. We simulate the epidemic under different assumptions regarding the socio-demographic factors that influence interaction patterns, providing empirical evidence of the effectiveness and soundness of the proposed centrality measure.

Network-based epidemic models that account for heterogeneous contact patterns are extensively used to predict and control the diffusion of infectious diseases. We use census and survey data to reconstruct a geo-referenced and age-stratified synthetic urban population connected by stable social relations. We consider two kinds of interactions, distinguishing daily (household) contacts from other frequent contacts. Moreover, we allow any couple of individuals to have rare fortuitous interactions. We simulate the epidemic diffusion on a synthetic urban network for a typical medium-sized Italian city and characterize the outbreak speed, pervasiveness, and predictability in terms of the socio-demographic and geographic features of the host population. Introducing age-structured contact patterns results in faster and more pervasive outbreaks, while assuming that the interaction frequency decays with distance has only negligible effects. Preliminary evidence shows the existence of patterns of hierarchical spatial diffusion in urban areas, with two regimes for epidemic spread in low- and high-density regions.