SIS Epidemic Containment under Game-theoretic Rational Learning

Abstract

We consider a susceptible-infected-susceptible (SIS) epidemiological model in which individuals dynamically decide whether to follow social distancing or not. Driven by game-theoretic payoffs, their actions influence the spread of infection. Much of the existing work in this area considers individuals that are imitative learners, leading to the well-studied replicator equation. In this paper, we investigate how the dynamical outcomes may fundamentally shift when individuals are instead equipped with logit learning rules, i.e., when individuals possess bounded rationality. We analyze the local asymptotic stability of equilibria that exist in different parameter regimes of the coupled dynamical system. We show that in regimes where the disease-free equilibrium is unstable under imitative learning and sufficiently high-rationality logit learning, sufficiently low rationality can avoid such an undesirable outcome by stabilizing the disease-free equilibrium. We also identify parameter regimes in which an unstable endemic equilibrium stabilizes when rationality falls below a threshold. We numerically illustrate the convergence of infection state and response trajectories to a stable disease-free equilibrium at a lower degree of rationality, whereas the same trajectories otherwise converge to a stable endemic equilibrium as the rationality level rises. We also compare a specific case in which trajectories under replicator dynamics fail to converge, and illustrate convergence when rationality is below an analytically derived threshold.