Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate

Abstract

The article researches a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise. Firstly, we obtain a significant criterion $R_0^S$ which relies on environmental noises. By means of Lyapunov function approach, we show that there is a stationary distribution if $R_0^S>1$ . Its condition implies that when white noise is small, in the stochastic model, there exists a stochastic positive equilibrium state without changing the basic properties of its corresponding deterministic model. Secondly, we derive sufficient criteria for extinction of the disease. Finally, we propose a definition of the solution to an impulsive stochastic functional differential equation with Markovian switching (ISFDM).