Stochastic threshold dynamics of an HIV model with latent cell activation under mean-reverting environmental noise.

Motivated by the impact of environmental variability on within-host HIV dynamics, we develop a stochastic HIV model incorporating latent cell activation. Infection and activation rates are modeled as logarithmic mean-reverting Ornstein-Uhlenbeck processes, ensuring positive parameters and biologically realistic fluctuations. We prove the existence and uniqueness of a global positive solution and derive stochastic thresholds characterizing persistence and extinction. If the persistence threshold exceeds one, the model admits a stationary distribution, indicating sustained viral presence; conversely, sufficiently strong environmental noise can drive latent cells, actively infected cells, and free virus to extinction almost surely, even when the deterministic model predicts persistence. Analysis of the associated Fokker-Planck equation provides explicit expressions for the covariance structure near quasi-equilibrium, quantifying stochastic fluctuations. Numerical simulations support the theoretical findings and illustrate how environmental noise reshapes HIV dynamics. Our results highlight the crucial role of stochastic variability in modulating viral persistence and latent reservoir dynamics.