Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Dynamics of a Stochastic SIRS Epidemic Model with Nonlinear and Saturated Incidence Rate

Download PDF (2250.2 KB) PP. 78 - 90 Pub. Date: April 2, 2020

DOI: 10.22606/jaam.2020.52004

Author(s)

  • Jiying Ma*
    College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, PR China
  • Qing Yi
    College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, PR China

Abstract

The article is dedicated to the dynamics of a stochastic SIRS epidemic model, which is obtained by introducing Gaussian white noise to the transmission coefficient of a deterministic epidemic model with non-monotone and saturated incidence rate. The existence and uniqueness of positive global solution is proved for the stochastic model. The threshold parameter Rs0 is established, and under some acceptable conditions the disease will go to extinction if Rs0 < 1. However, the stochastic system has a unique ergodic stationary distribution and the disease is persistent if Rs0 > 1. We also analyze the asymptotic behavior of the stochastic model near the disease-free equilibrium of the corresponding deterministic system. Numerical simulation is provided to support our theoretical results.

Keywords

stochastic epidemic model, extinction, asymptotic behavior, stationary distribution.

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