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Volume 9, Number 6, 2019, Pages 2096-2110                                                                DOI:10.11948/20180041
Threshold dynamics in a stochastic SIRS epidemic model with nonlinear incidence rate
Yanan Zhao,Xiaoying Zhang,Donal O'Regan
Keywords:SIRS epidemic model, nonlinear incidence rate, extinction, persistence, threshold.
      We discuss the dynamic of a stochastic Susceptible-Infectious-Recovered-Susceptible (SIRS) epidemic model with nonlinear incidence rate.The crucial threshold $\tilde{R}_0$ is identified and this will determine the extinction and persistence of the epidemic when the noise is small. We also discuss the asymptotic behavior of the stochastic model around the endemic equilibrium of the corresponding deterministic system. When the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it dies out. Finally, these results are illustrated by computer simulations.
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