J4 ›› 2013, Vol. 48 ›› Issue (10): 68-77.

• Articles • Previous Articles     Next Articles

Persistence and extinction in stochastic SIS epidemic model with nonlinear incidence rate

ZHOU Yan-li1,2, ZHANG Wei-guo1   

  1. 1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
    2. Shanghai Medical Instrumentation College, Shanghai 200093, China
  • Received:2013-01-17 Published:2013-10-14

Abstract:

A stochastic SIS epidemic model with nonlinear incidence is investigated. First, the existence of global positive solution is obtained; Next, the asymptotic behaviors of the model are studied that is if R0≤1, the disease-free equilibrium is stochastically asymptotical stability, and if R0>1 the solution is oscillating around the endemic equilibrium of the deterministic model. Furthermore, the sufficient conditions of persistence in the mean and stochastic extinction are obtained. Finally, the theoretical results are illustrated by numerical simulations.

Key words: stochastic SIS epidemic model; Lyapunov function; extinction; Brownian motion; It formula

CLC Number: 

  • O175.1
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