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arXiv · 1902.09307

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

T. D. Tuong·Dang H. Nguyen·N. T. Dieu·Ky Tran
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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}.

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T. D. Tuong, Dang H. Nguyen, N. T. Dieu, Ky Tran. 2019-02-25. Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate. https://arxiv.org/abs/1902.09307

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