Free terminal Time Optimal Control Problem of an SIR Epidemic Model with Vaccination

This paper presents an approach that investigates a free terminal optimal time control of an SIR (Susceptible-Infected-Removed) epidemic model. In order to reduce the infected group and increase the removed individuals, we present a control simulating vaccination program considering also the minimum duration of a vaccination campaign. The optimal control and the optimal final time are found using Pontryagin's maximum principle and the additional transversality condition for the terminal time .We solved the optimality system by an iterative method, and then we confirm the performance of the optimization strategy by numerical simulations.