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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 - R _c1 (productive infection) and R _c2 (latent infection) - and defines the stochastic control reproduction number as R _c = {R _c1, R _c2} . Our analysis reveals three distinct dynamical regimes: (1) viral extinction (R _c<1): the infection clears exponentially with probability one; (2) latent reservoir dominance ( R _c = R _c2 >1): the system almost surely converges to a purely latent state, characterizing stable viral reservoir formation; (3) persistent productive infection ( R _c = R _c1 > 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. , number=4, journal=CSIAM Transactions on Life Sciences, year=2025, month=Dec., pages=599–632