Threshold dynamics of SAIRS epidemic model with Semi-Markov switching

TL;DR

This paper analyzes a stochastic SAIRS epidemic model with vaccination and semi-Markov switching, providing conditions for disease extinction or persistence, and exploring long-term behavior through invariant measures.

Contribution

It introduces a semi-Markov switching mechanism into the SAIRS model and derives new conditions for epidemic extinction and persistence.

Findings

Conditions for almost sure epidemic extinction.

Criteria for disease persistence and invariant measures.

Analysis of long-term epidemic dynamics.

Abstract

We study the threshold dynamics of a stochastic SAIRS-type model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the epidemic dynamics. In the model, the values of the disease transmission rate may switch between different levels under the effect of a semi-Markov process. We provide sufficient conditions ensuring the almost surely epidemic extinction and persistence in time mean. In the case of disease persistence, we investigate the omega-limit set of the system and give sufficient conditions for the existence and uniqueness of an invariant probability measure.