Abstract
This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.
•A stochastic HIV-I infection model with logistic growth is proposed and studied.•We establish sufficient conditions for the existence of ergodic stationary distribution.•We obtain sufficient conditions for extinction of the infection.•The stationary distribution shows that the infection can become persistent in vivo.