The Impact of CD8$^+$ T Cell Exhaustion on HIV Infection Dynamics

Abstract

This study develops a time-varying model to investigate the impact of CD8$^+$ T cell exhaustion on human immunodeficiency virus infection dynamics. For the corresponding autonomous model, the existence and local stability of equilibria are established. Bifurcation analysis reveals complex dynamics, including bistability involving multiple attractors and periodic solutions. Numerical simulations of the time-varying model demonstrate that the progression of CD8$^+$ T cell exhaustion drives an increase in viral load and triggers a bifurcation-induced tipping (B-tipping) point. This leads to a rapid viral surge, which is characteristic of the transition from the asymptomatic stage to AIDS. The non-autonomous system robustly exhibits B-tipping regardless of the CD8$^+$ T cell exhaustion rate ($r$), which primarily governs the speed of this transition. These findings highlight CD8$^+$ T cell exhaustion as a key driver of post-infection disease progression and elucidate the mechanistic basis for rapid viral surges, thereby providing critical insights into human immunodeficiency virus pathogenesis and the development of therapeutic strategies.