Dynamical behavior and optimal control of a stochastic SAIRS epidemic model with two saturated incidences

TL;DR

This paper extends a deterministic SAIRS epidemic model to a stochastic setting with capacity limits, analyzes its dynamics, and derives optimal control strategies using vaccination and isolation, supported by numerical simulations.

Contribution

It introduces a stochastic SAIRS model with capacity constraints and develops optimal control strategies via Pontryagin's principle, which is novel in this context.

Findings

Model exhibits persistence, extinction, and ergodic behavior under certain conditions.

Optimal vaccination and isolation strategies are derived.

Numerical simulations confirm theoretical results.

Abstract

Stochastic models are widely used to investigate the spread of epidemics in a complex environment. This paper extends a deterministic SAIRS epidemic model to a stochastic case with limited patient capacity and exposure. We first study the dynamical properties of the model under certain conditions, including persistence, extinction, and ergodic. Then, we introduce vaccination and isolation into the model as control variables. The optimal control strategies are obtained based on the Pontryagin minimum principle. Finally, numerical simulations are given to illustrate our theoretical results.