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