Finite horizon optimal control for a stochastic SIV epidemic model

This contribution mainly focuses on the finite horizon optimal control problems of a Susceptible-Infected-Vaccinated (SIV) epidemic system governed by reaction-diffusion equations and Markov switching. Stochastic dynamic programming is employed to find the optimal vaccination effort and economic return for a reaction diffusion stochastic SIV epidemic model. To achieve this, a key step is to show the existence and uniqueness of invariant measure for the model. Then, we obtained the necessary and sufficient conditions for the near-optimal control. Furthermore, we give an algorithm to approximate the Hamilton–Jacobi–Bellman (HJB) equation. Finally, some numerical simulations are presented to confirm our analytic results.