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In this paper we introduce an approach to the management of infectiousdisease diffusion through the formulation of a controlled compartmental SVIR(Susceptible-Vaccinated-Infected-Recovered) model. We consider a costfunctional encompassing three distinct yet interconnected dimensions: thesocial cost, the disease cost, and the vaccination cost. The proposed modeladdresses the pressing need for optimized strategies in disease containment,incorporating both social control measures and vaccination campaigns. Throughthe utilization of advanced control theory, we identify optimal controlstrategies that mitigate disease proliferation while considering the inherenttrade-offs among social interventions and vaccination efforts. Finally,numerical implementation of the optimally controlled system through theForward-Backward Sweep algorithm is presented.

Optimal Social and Vaccination Control in the SVIR Epidemic Model