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

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