# Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate

## TL;DR

This paper analyzes a stochastic SIRS epidemic model with a general incidence rate under regime-switching, establishing conditions for disease extinction or permanence based on a threshold parameter.

## Contribution

It introduces a comprehensive stochastic SIRS model with general incidence and regime-switching, extending previous results by providing new criteria for disease extinction and permanence.

## Key findings

- Threshold $7$ determines disease extinction or permanence
- Disease-free state is globally stable if $7<0$
- Epidemic persists if $7>0$

## Abstract

In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $\lambda$ that is used to classify the extinction and permanence of the disease. In particular, $\lambda<0$ implies that the disease-free $(K, 0, 0)$ is globally asymptotic stable, i.e., the disease will eventually disappear. If $\lambda>0$ the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in \cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}.