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 λ that is used to classify the extinction and permanence of the disease. In particular, λ<0 implies that the disease-free (K,0,0) is globally asymptotic stable, i.e., the disease will eventually disappear. If λ>0 the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in Cai et al. (2015), Han and Zhao (2013), Lahrouz et al. (2011), Settati et al. (2016) and Zhao and Jiang (2014).