SIS Epidemic Propagation Under Strategic Non-Myopic Protection: A Dynamic Population Game Approach

We consider a dynamic game setting in which a large population of strategic individuals decides whether to adopt protective measures to protect themselves against an infectious disease, specifically the susceptible-infected-susceptible (SIS) epidemic. Protection is costly and partially effective, and adopting protection reduces the probability of becoming infected for susceptible individuals and the probability of transmitting the infection for infected individuals. In a departure from most prior works that assume the decision-makers to be myopic, we model individuals who choose their actions to maximize the infinite horizon discounted expected reward. We define the notion of best response and stationary Nash equilibrium in this class of games, and completely characterize the equilibrium policy and stationary state distribution for different parameter regimes. Numerical results illustrate the evolution and convergence of the infected proportion and the policy of protection adoption to the equilibrium.