Modeling Effects of T Cell Exhaustion on the Dynamics of Chronic Viral Infection

Abstract

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: infectionfree equilibrium (S₁ ), uncontrolled-infection state (S₂), and immune-controlled equilibrium (S₃). Through dynamical systems analysis, we established the local stability of all states (S₁-S₃) and prove global stability for both S₁ (complete viral clearance) and S₂ (chronic infection). Notably, the system exhibits Hopf bifurcations at S₂ and S₃, 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.

Keywords

Viral infection dynamics / T cell exhaustion / stability analysis / Hopf bifurcation