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

• A stochastic HIV model with cell-free and cell-to-cell infections is formulated. • The positive and global solution of the model is rigorously verified. • Existence of the unique ergodic stationary distribution of the system is studied. • Probability density function is derived by applying asymptotic analysis. • The effects of noise and cell-to-cell infection on model behavior are investigated. In this paper, a stochastic HIV model with CD 4 + 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. [ABSTRACT FROM AUTHOR]