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Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate. (English) Zbl 1434.92035
Summary: 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 Y. Cai et al. [J. Differ. Equations 259, No. 12, 7463–7502 (2015; Zbl 1330.35464)], Z. Han and J. Zhao [Nonlinear Anal., Real World Appl. 14, No. 1, 352–364 (2013; Zbl 1267.34079)], A. Lahrouz et al. [Nonlinear Anal., Model. Control 16, No. 1, 59–76 (2011; Zbl 1271.93015)], A. Settati et al. [J. Appl. Math. Comput. 52, No. 1–2, 101–123 (2016; Zbl 1366.60098)] and Y. Zhao and D. Jiang [Appl. Math. Lett. 34, 90–93 (2014; Zbl 1314.92174)].
MSC:
92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
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