Behavioral–epidemiological coevolution: An evolutionary game-theoretic framework for pandemic dynamics

This paper develops an evolutionary game-theoretic framework for epidemic dynamics that couples payoff-driven behavioral adaptation with disease transmission in an SVEIR compartmental model. The framework integrates imitation-based behavioral dynamics — governing vaccination and contact decisions — into the epidemiological process through endogenous feedback on transmission and vaccination rates. We derive the unified continuous-time system, prove equilibrium existence and stability results, and identify the critical threshold of the effective reproduction number R₀^eff. Mathematically, the system forms a coupled behavioral–epidemiological dynamical structure admitting bounded contraction under small-gain conditions. These theoretical properties are validated through discrete-time Monte Carlo simulations based on a forward-Euler finite-difference scheme preserving positivity and mass on the epidemiological simplex. Three policy regimes — easy , moderate , and strict — are defined by behavioral sensitivity (α) and subsidy intensity (σ). Numerical experiments show that increasing responsiveness systematically lowers R₀^eff, flattens epidemic peaks, and accelerates convergence toward the disease-free state. In quantitative terms, the infection peak declines from about I_max≈0.12 in the easy regime, to 0.06 in the moderate case, and 1.5×10⁻⁴ under strict control, with vaccination coverage rising from V(T)≈0.23 to 0.49. The strict regime achieves early subcriticality (R₀^eff<1 by day 25), effectively eradicating infections, while the moderate regime delays and flattens the peak relative to the easy case. Overall, the results confirm that behavioral feedback and economic incentives act as stabilizing control mechanisms that reshape epidemic equilibria. All parameter sweeps and replication data are fully reproducible, supporting the theoretical findings and potential applications to adaptive epidemic policy design.