Stationary distribution of an HIV model with general nonlinear incidence rate and stochastic perturbations

We present a stochastic HIV infection model with logistic target cell growth, general nonlinear incidence rate, CTL immune response and parameter perturbations. Through a rigorous analysis of the model, we obtain that the solution of the model is positive and global. A critical condition R₀ ^s of the model is derived, which depends not only on the general incidence function but also on the noise intensities. Under certain assumptions, by constructing suitable Lyapunov functions, we find that the system has a unique ergodic stationary distribution when R₀ ^s>1. We further explore the effect of the noise intensity on model behavior. Our conclusion improves and generalizes the results of the existing HIV stochastic models.