Stationary distribution and extinction of a stochastic HIV-1 model with Beddington-DeAngelis infection rate

In this paper, we consider a stochastic HIV-1 model with Beddington-DeAngelis infection rate. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution to the model. Then we obtain sufficient conditions for extinction of the disease. The existence of a stationary distribution implies stochastic weak stability.