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

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}.