Sustainable Coexistence with Infectious Diseases: A Behavioral Feedback Model Driven by Resource Accessibility under Static-Dynamic Optimal Control.

This study develops a behavior-disease feedback model grounded in imitation dynamics to analyze optimal long-term epidemic coexistence strategies from both static and dynamic perspectives. Analytical findings reveal that the stability of the system depends on both the basic reproduction number and the behavioral threshold, with the latter and risk attention jointly determining optimal static intervention intensity. Data-driven analyses of influenza (Shanxi) and COVID-19 (Shanghai) show that adaptive public behavior can drive recurrent epidemic waves. In dynamic optimization simulations involving control of transmission rate alone or jointly with behavioral threshold, key insights include: seizing the critical rapid-growth window prevents both strategy oscillations and epidemic rebound resulting from delayed intervention; faster public response lowers both control costs and infection burden while accelerating attainment of control goals; stricter prevalence constraints require earlier and longer interventions, where proactive phased strategies outperform short, high-intensity measures in cost-effectiveness; achieving lower target prevalence necessitates earlier action and greater public caution, advancing the infection peak but substantially reducing its magnitude. These results offer a theoretical framework and practical insights for optimizing resource allocation and guiding policy in endemic disease management.