Dynamic behavior of a stochastic HIV model with latent infection and Ornstein–Uhlenbeck process

HIV spreads in the body through two infection patterns: virus-to-cell (VTC) infection and cell-to-cell (CTC) transmission. This study introduces an HIV dynamic model incorporating both transmission patterns, where CTC transmission occurs when healthy CD4+T cells come into contact with latently and actively infected cells. The research first analyzes the local asymptotic stability of the disease-free equilibrium and the global asymptotic stability of the endemic equilibrium in the deterministic model. Subsequently, a corresponding stochastic HIV model is developed by introducing log-normal Ornstein–Uhlenbeck (OU) process to perturb the infection rates. The study establishes the conditions for the extinction of HIV infection in the stochastic system and examines the existence of an ergodic stationary distribution by constructing a series of stochastic Lyapunov functions. Specifically, the paper proposes the explicit expression of the probability density function for the linearized stochastic system near the quasi-equilibrium when all infected cells transform into latently infected cells. Finally, the theoretical conclusions are validated through numerical simulations.