The stationary distribution of a stochastic heroin epidemic model with distributed delay

In view of the harm of heroin to human and society, the use and spread of heroin have been regarded as an epidemic, it is urgent for us to study and analyze the dynamical behavior of heroin epidemic model. Therefore, in this paper, we will investigate a stochastic heroin epidemic model with distributed delay. By constructing some suitable Lyapunov functions, we establish sufficient condition for the existence of a stationary distribution $\pi (\cdot )$ for the stochastic heroin epidemic model with distributed delay. Then, we analyze the theoretical results and give some suggestions to control the spread of heroin’s infectious diseases.