Finite horizon optimal control of reaction-diffusion SIV epidemic system with stochastic environment
Optimization and Control
2024-01-23 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2401.11744,
title = {Finite horizon optimal control of reaction-diffusion SIV epidemic system with stochastic environment},
author = {Zong Wang},
journal= {arXiv preprint arXiv:2401.11744},
year = {2024}
}