Optimal control of an sir epidemic model based on dynamic programming approach

This paper investigates optimal control of a susceptible-infected-recovered (SIR) epidemic model using the dynamic programming approach. In fact, our study focuses on the modified model by incorporating it with a Bolza-type objective function. We use a certain refinement of Cauchy’s method of characteristics for stratified Hamilton-Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by a certain admissible control. The optimality is justified by using one of the well-known verification theorems, which provides an argument for sufficient optimality conditions. Through numerical tests, we demonstrate how adjustments to the infection and recovery rates, guided by the optimization framework provided by the guidance function, can significantly impact epidemic outcomes.