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 Cai et al. (2015), Han and Zhao (2013), Lahrouz et al. (2011), Settati et al. (2016) and Zhao and Jiang (2014). (C) 2019 Elsevier Ltd. All rights reserved.