Stationary distribution and probability density function analysis of a stochastic HIV model with cell-to-cell infection

Abstract

In this paper, a stochastic HIV model with CD4+ T-cell proliferation, cell-free infection and cell-to-cell transmission is proposed. By constructing suitable Lyapunov function, we establish the existence of unique and ergodic stationary distribution of the model. Moreover, by using asymptotic analysis and employing the Fokker-Planck equation, we derive the probability density function around the quasi-steady state of the system. Through numerical simulations, the effects of the stochastic perturbation and cell-to-cell infection on model dynamic behavior are investigated, thus the probability density function of the system is also given under the realistic parameter values.