Optimal Control of Epidemic Dynamics via Opinion Intervention in SIR Models

This paper proposes an SIR (susceptible-infected-recovered) epidemic model influenced by opinion dynamics and explore the effectiveness of opinion-based intervention strategies in controlling epidemic peaks. For a well-mixed population, we derive a theoretically optimal intervention strategy that minimizes the cumulative cost of opinion interventions while maintaining the infection proportion below a specified threshold. This strategy is shown to consist of three phases: no intervention, with intervention, and finally stop intervention, eliminating the need for full lockdowns. Extending our results to networked populations, we simulate the optimal intervention strategy on a dual-layer network comprising a physical transmission network (based on inter-prefecture migration data in Japan) and a small-world social network. The numerical simulations demonstrate the effectiveness of the strategy in large-scale networked systems.