Behavior-disease feedback and endogenous isolation under infection risk

Behavioral responses to infection risk can alter disease spread when isolation arises endogenously from epidemic conditions rather than from externally imposed rules. We study this mechanism in a behavior-coupled Susceptible-Exposed-Infected-Recovered (SEIR) model in which infectious individuals choose between isolation and non-isolation through an evolutionary game. The behavioral dynamics are governed by replicator equations derived from payoffs that depend on perceived infection risk, the social benefits of contact, and the cost of isolation, creating a two-way coupling between disease prevalence and behavioral change. We characterize the disease-free and endemic equilibria through the basic reproduction number and show that endogenous isolation qualitatively changes epidemic behavior relative to the classical SEIR system. In particular, prevalence-dependent behavioral adaptation generates time-varying adherence and recurrent infection waves even within an otherwise standard compartmental structure. Lower isolation cost or greater perceived risk shifts the evolutionary dynamics toward isolation, reducing transmission, lowering peak prevalence, and dampening later waves. We further study intervention in this coupled system by allowing time-dependent incentives to modify behavioral payoffs and promote isolation. The resulting optimal control problem is characterized using Pontryagin's Maximum Principle, showing that adaptive incentives can produce stronger and more sustained epidemic suppression than comparable static measures. Calibration to COVID-19 incidence data from Medan, Indonesia serves as an empirical illustration of the theoretical results. Overall, the analysis identifies behavior-disease coupling through endogenous isolation as a population-level mechanism that modifies both equilibrium structure and transient outbreak dynamics, while providing a general framework that links evolutionary behavioral adaptation and epidemic control.