Finite horizon optimal control of reaction-diffusion SIV epidemic system with stochastic environment

2024/01/22 by Wang, Zong
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2401.11744

Abstract

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 stochastic reaction diffusion 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.

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