On SEIR Epidemic Dynamics with Pro- and Anti-Vaccination Strategies: An Evolutionary Game Theory Approach

We investigate a susceptible–exposed–infected–recovered ( S E I R ) epidemic model that distinguishes between two subpopulations: individuals favoring vaccination (pro-vaccination), represented by the compartments ( S P , E P , I P , R P ) , and those opposing vaccination (anti-vaccination), described by ( S A , E A , I A , R A ) . The two systems are interconnected through flows between the susceptible classes, capturing the possibility of individuals switching their vaccination strategy, as well as through transitions involving recovered individuals. This framework captures the behavioral interplay during an epidemic, where individuals may reconsider their strategies depending on infection prevalence and the perceived costs and benefits of vaccination versus infection. In the model, immunity may be acquired either through vaccination or after being infected, while waning immunity adds further complexity to individual decision-making. To study these dynamics, we embed the epidemiological system into an evolutionary game framework, where strategy adoption depends on infection levels and associated payoffs. Our analysis shows that, at Nash equilibrium, both pro- and anti-vaccination groups exhibit similar behavior. Numerical simulations further indicate that greater vaccination coverage mitigates the social dilemma, whereas higher rates of waning immunity intensify it.