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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