(untitled) (CSIAM Transactions on Life Sciences, 2025)
During chronic viral infection, sustained antigen stimulation leads to exhaustion of virus-specific CD8^+ T cells, characterized by elevated expression of inhibitory receptors and progressive functional impairment, including loss of cytokine production, reduced cytotoxicity, and diminished proliferative capacity. In this paper, to investigate how T cell exhaustion influences viral persistence, we developed a within-host mathematical model integrating viral infection dynamics with adaptive immune responses. The model demonstrates three non-trivial equilibria: infection-free equilibrium (S_1), uncontrolled-infection state (S_2), and immune-controlled equilibrium (S_3). Through dynamical systems analysis, we established the local stability of all states (S_1-S_3) and prove global stability for both S_1 (complete viral clearance) and S_2 (chronic infection). Notably, the system exhibits Hopf bifurcations at S_2 and S_3, with distinct critical thresholds governing oscillatory dynamics. Numerical simulations reveal that successful immune-mediated control of viral load and infected cell levels requires maintenance of low CD8^+ T cell exhaustion rates.