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) in- fection model to analyze combination antiretroviral therapy (cART) dynamics in the brain microenvironment, explicitly accounting for two infected cell states: (1) produc- tively infected and (2) latently infected populations. The model introduces two key epidemiological thresholds $-\overline{\mathcal{R}}_{c 1}$ (productive infection) and $-\overline{\mathcal{R}}_{c 2}$ (latent infection) – and defines the stochastic control reproduction number as $\overline{\mathcal{R}}_{c}=\max \left\{\overline{\mathcal{R}}_{c 1}, \overline{\mathcal{R}}_{c 2}\right\}$. Our analysis reveals three distinct dynamical regimes: (1) viral extinction $\left(\overline{\mathcal{R}}_{c}<1\right)$: the in- fection clears exponentially with probability one; (2) latent reservoir dominance $\left(\overline{\mathcal{R}}_{c}=\overline{\mathcal{R}}_{c 2}>1\right)$: the system almost surely converges to a purely latent state, characterizing stable viral reservoir formation; (3) persistent productive infection $\left(\overline{\mathcal{R}}_{c}=\overline{\mathcal{R}}_{c 1}>1\right)$: the infection persists indefinitely with a unique stationary distribution, for which we de- rive 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 be- tween productive infection, latency establishment, and cART efficacy, offering mecha- nistic insights into viral persistence in the brain.

Keywords

Brain reservoirs / combination antiretroviral therapy / HIV-1 infection model / extinc-tion / probability density function