Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence

Abstract

The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value (R0m) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If R0m1, the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If R0m>1, the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease.

Keywords

• stochastic SIRS epidemic model
• Logistic birth
• nonlinear incidence
• global stability
• stationary distribution