Optimal Social and Vaccination Control in the SVIR Epidemic Model

In this paper, we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (susceptible-vaccinated-infected-recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the vaccination cost. The proposed model addresses the pressing need for optimized strategies in disease containment, incorporating both social control measures and vaccination campaigns. Through the utilization of advanced control theory, we identify optimal control strategies that mitigate disease proliferation while considering the inherent trade-offs among social interventions and vaccination efforts. Finally, we present the results from a simulation-based study employing a numerical implementation of the optimally controlled system through the forward-backward sweep algorithm. The baseline model considered incorporates parameters representative of typical values observed during the recent pandemic outbreak.