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

Abstract

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 $ - \mathcal{R}_{c1} $ (productive infection) and $ \mathcal{R}_{c2} $ (latent infection) -- and defines the stochastic control reproduction number as $ \mathcal{R}_c = \max\{\mathcal{R}_{c1}, \mathcal{R}_{c2}\} $. Our analysis reveals three distinct dynamical regimes: (1) viral extinction ($ \mathcal{R}_c < 1 $): the infection clears exponentially with probability one; (2) latent reservoir dominance ($ \mathcal{R}_c = \mathcal{R}_{c2} > 1 $): the system almost surely converges to a purely latent state, characterizing stable viral reservoir formation; (3) persistent productive infection ($ \mathcal{R}_c = \mathcal{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.