Stability analysis of a SIR epidemic model with random parametric perturbations

This paper is concerned with a SIR model for the spread of an epidemic amongst a population of individuals with random additive perturbations of the transmission rate. Recently, many papers are devoted to the case of the Gaussian white noise perturbation. However, this model violates the condition of positivity of the transmission rate. In the paper we consider three models of the random perturbation which do not change this condition. The two of them are the telegraphic noise, trichotomous noise and the third is the bounded noise. Explicit conditions of the amost sure asymptotic stability of disease-free equilibrium state are obtained in the case of the first two models. An efficient numerical procedure is proposed for the construction of stability charts in the case of bounded noise. The effect of random perturbations on the stability behavior of disease-free equilibrium is discussed. Some transient mean-square properties of the SIR stochastic epidemic model are also presented.