Supplementary material from "Homophily in a multi-group vaccination game and its impact on disease dynamics"

Metapopulation models are among the most frequently used approaches to address spatial heterogeneity in infectious disease modeling. While researchers typically consider the role of heterogeneity in disease transmission by dividing the population into subgroups according to levels of social activity, susceptibility, or perceived risk of infection, the role of heterogeneity in vaccination behavior has received less attention. The tendency to interact with others who share similar beliefs (homophily) can further reinforce such heterogeneity, leading to clustered vaccine sentiments in the population. In this paper, we develop a multi-group vaccination game model coupled with an SIRV epidemic model and examine how interactions among individuals in–and between–groups affect both vaccination behavior and disease dynamics. We find that in a three-group system with extremely pro- and anti-vaccine groups, each group can converge to a partially pro-vaccine equilibrium, causing population-level opinion polarization that can persist despite the severity of the disease. Our results highlight the dual role of homophily, offer insights on the design of effective public health interventions, and demonstrate the potential of a multi-group framework in real-world disease modeling.