an:07177628
Zbl 1434.92035
Tuong, T. D.; Nguyen, Dang H.; Dieu, N. T.; Tran, Ky
Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate
EN
Nonlinear Anal., Hybrid Syst. 34, 121-130 (2019).
00447593
2019
j
92D30 34D23
SIRS; epidemic models; extinction; permanence
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 \textit{Y. Cai} et al. [J. Differ. Equations 259, No. 12, 7463--7502 (2015; Zbl 1330.35464)], \textit{Z. Han} and \textit{J. Zhao} [Nonlinear Anal., Real World Appl. 14, No. 1, 352--364 (2013; Zbl 1267.34079)], \textit{A. Lahrouz} et al. [Nonlinear Anal., Model. Control 16, No. 1, 59--76 (2011; Zbl 1271.93015)], \textit{A. Settati} et al. [J. Appl. Math. Comput. 52, No. 1--2, 101--123 (2016; Zbl 1366.60098)] and \textit{Y. Zhao} and \textit{D. Jiang} [Appl. Math. Lett. 34, 90--93 (2014; Zbl 1314.92174)].
Zbl 1330.35464; Zbl 1267.34079; Zbl 1271.93015; Zbl 1366.60098; Zbl 1314.92174