Exploring the potential for persistent HIV infection through dynamical analysis of models incorporating homeostatic proliferation of CD8+ T cells

This study presents a comprehensive dynamical analysis of HIV models that incorporate homeostatic proliferation of CD8+ T cells. For the deterministic model, we classify the equilibria and derive the conditions under which a backward bifurcation occurs at the basic reproduction number R0=1, revealing that viral clearance depends not only on R0 < 1 but also on the initial conditions. Biologically, this shows that the homeostatic proliferation of CD4+ T cells and macrophages complicates control of HIV infection, whereas the homeostatic proliferation of CD8+ T cells promotes viral clearance. Furthermore, we establish the global stability of the infection-free equilibrium and prove the uniform persistence of the model when R0 > 1, indicating the existence of sustained infection. Our analyses of the long-term dynamical behavior enriches the current understanding of HIV infection dynamics. Considering the intrinsic noise in viral dissemination, we extend the deterministic model to a stochastic framework by introducing the logarithmic Ornstein-Uhlenbeck process. For the stochastic model, we demonstrate the existence of a stationary distribution, indicating that the virus undergoes sustained fluctuations around the infected equilibrium, and we also derive sufficient conditions for viral clearance. These results quantitatively delineate the regimes of viral persistence and clearance under stochastic influences. All theoretical findings are corroborated by numerical simulations, offering a nuanced understanding of HIV dynamics under uncertainty.