Stochastic stability and long-term dynamics of an HIV infection model with CD4+ T-cell homeostasis and CTL immune response

Abstract

We examine a stochastic HIV infection model that includes CD4+ T-cell homeostasis and CTL-mediated immune response, represented by four compartments: uninfected CD4+ T cells, infected CD4+ T cells, free HIV virions, and CTL response. The model accounts for environmental fluctuations using multiplicative Itô noise. We establish the existence and uniqueness of the stochastic solution and derive Lyapunov estimates to show stochastic boundedness and long-term infection behavior. The impact of environmental noise on viral persistence and extinction thresholds is emphasized. Numerical simulations illustrate these theoretical findings, highlighting how stochastic perturbations affect CD4+ T-cell depletion, viral load, and CTL control, providing a robust framework for understanding HIV–immune system dynamics amidst environmental variability.