<p>HIV continues to pose a major clinical challenge within infectious diseases, with substantial implications for global public health. In this work, we develop a stochastic HIV infection model that integrates cytokine-enhanced transmission, CTL-mediated immune response, and the Black–Karasinski process to represent random fluctuations in infection rates. In contrast to linear white noise or the Ornstein–Uhlenbeck approach, the Black–Karasinski formulation ensures that infection rates remain strictly positive and that their variance stays bounded over arbitrarily short time scales—features that render it both mathematically tractable and biologically plausible for HIV dynamics. We establish the existence and uniqueness of global positive solution to the stochastic system. Through the construction of a novel Lyapunov function, we prove that the system admits at least one stationary distribution whenever the stationary basic reproduction number exceeds unity, whereas the virus is driven to exponential extinction if the stochastic extinction threshold falls below unity. Furthermore, we derive an explicit approximation of the probability density function in the neighborhood of the quasi-chronic-infection equilibrium. Numerical simulations indicate that increasing the mean-reversion speed or reducing the noise intensity can markedly attenuate viral replication, thereby offering theoretical guidance for HIV treatment strategies. Finally, it is validated the model predictions against experimental data from humanized mouse models of natural killer (NK) cell therapy, confirming that the proposed stochastic extinction threshold is biologically meaningful.</p>