Stochastic Dynamics Between HIV-1 Latent Infection and cART Efficacy Within the Brain Microenvironment

We develop a stochastic human immunodeficiency virus type 1 (HIV-1) infection model to analyze combination antiretroviral therapy (cART) dynamics in the brain microenvironment, explicitly accounting for two infected cell states: (1) productively infected and (2) latently infected populations. The model introduces two key epidemiological thresholds - Rc1 (productive infection) and Rc2 (latent infection) -- and defines the stochastic control reproduction number as Rc = max1, Rc2\. Our analysis reveals three distinct dynamical regimes: (1) viral extinction (Rc < 1): the infection clears exponentially with probability one; (2) latent reservoir dominance (Rc = Rc2 > 1): the system almost surely converges to a purely latent state, characterizing stable viral reservoir formation; (3) persistent productive infection (Rc = Rc1 > 1): the infection persists indefinitely with a unique stationary distribution, for which we derive the exact probability density function. And numerical simulations validate these theoretical predictions, demonstrating how environmental noise critically modulates HIV-1 dynamics in neural reservoirs. Our results quantify the stochastic balance between productive infection, latency establishment, and cART efficacy, offering mechanistic insights into viral persistence in the brain.