Optimal Control and Numerical Methods for Hybrid Stochastic SIS Models

TL;DR

This paper develops optimal control strategies for hybrid stochastic SIS epidemic models with regime switching, incorporating vaccination, and demonstrates convergence of numerical schemes to the optimal solution.

Contribution

It introduces a Markov chain approximation method for solving optimal control problems in hybrid stochastic epidemic models with vaccination.

Findings

Numerical schemes converge to the optimal control as mesh size decreases.

The model effectively incorporates vaccination strategies.

Simulations illustrate the impact of control measures on epidemic dynamics.

Abstract

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can either influence the infectivity period or isolate infected individuals, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.