Electron. J. Diff. Equ., Vol. 2014 (2014), No. 42, pp. 1-17.

Persistence and extinction in stochastic SIRS models with general nonlinear incidence rate

Yanli Zhou, Weiguo Zhang, Sanling Yuan, Hongxiao Hu

Abstract:
In this article, a SIRS epidemic model with general nonlinear incidence rate is proposed and investigated. We briefly discuss the global stability of the deterministic system by using Lyapunov function. For the stochastic version, the global existence and positivity of the solution are studied, and the global stability in probability and pth-moment of the system are proved under suitable assumptions on the white noise perturbations. Furthermore, the sufficient conditions for the persistence and extinction of the disease are obtained. Finally, the theoretical results are illustrated by numerical simulations.

Submitted December 21, 2012. Published February 10, 2014.
Math Subject Classifications: 34K15, 34K20, 92A15.
Key Words: General nonlinear incidence; stochastic; Ito formula; persistence; extinction.

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Yanli Zhou
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: zhouyanli_math@163.com
Weiguo Zhang
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: zwgzwm@126.com
Sanling Yuan
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: sanling@usst.edu.cn
Hongxiao Hu
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: hhxiao1@126.com

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