Simulation of Adaptive Behavioral Feedback and Quarantine Incentives in an Evolutionary Game-Theoretic SIQRS Epidemic Model

This paper develops a coupled behavioral–epidemiological framework for infectious-disease dynamics by integrating an SIQRS compartmental model with an evolutionary game-theoretic representation of quarantine behavior. Unlike conventional epidemic models with exogenously specified behavioral rates, the proposed framework allows transmission and quarantine uptake to respond endogenously to payoff differences between behavioral strategies. This creates a feedback mechanism in which epidemic conditions influence individual incentives, while behavioral adaptation subsequently modifies disease transmission. The mathematical analysis establishes well-posedness and positive invariance of the coupled system, characterizes the disease-free equilibrium and the associated reproduction threshold, and investigates local stability. Sufficient small-gain conditions are also derived to characterize stability of the coupled behavioral–epidemiological dynamics. A discrete-time formulation based on the forward-Euler method is developed together with positivity and consistency conditions. Numerical experiments compare easy, moderate, and strict behavioral-response regimes under a common epidemiological and payoff parameterization. The results show that stronger behavioral responsiveness reduces the principal infectious peak and delays its occurrence. However, behavioral mitigation does not necessarily imply disease eradication, as waning immunity can replenish the susceptible population and generate recurrent epidemic activity over longer horizons. The discrete-time simulations closely reproduce the continuous-time trajectories for a sufficiently small time step, supporting the consistency of the numerical formulation. Overall, the proposed framework provides a mathematically tractable approach for studying the coevolution of strategic behavior and epidemic transmission and for evaluating how behavioral incentives can modify the magnitude, timing, and recurrence of epidemic outbreaks.