Threshold Dynamics of a Delayed HIV Model With Viral and Cellular Infections, Saturated CTL Immune Response, and Immune Impairment

ABSTRACT This paper proposes an innovative HIV infection model that simultaneously incorporates two modes of virus transmission, saturated infection rates and saturated CTL immune response, providing a more comprehensive representation of the viral dynamics than existing models. The model takes into account intracellular delay and immune response delay . Firstly, the nonnegativity and boundedness of the solutions are proved, and two key thresholds are defined, namely, the virus reproductive number and the immunity‐activated reproductive number . Secondly, by constructing Lyapunov functional and applying LaSalle's invariance principle, it is proven that and completely determine the stability of the infection‐free equilibrium and the immune‐inactivated equilibrium . Then, it is demonstrated that delay can destabilize the immune‐activated equilibrium , causing the system to occur Hopf bifurcation. Finally, sensitivity analysis is conducted to illustrate the impact of parameters on the thresholds, and numerical simulations are employed to verify the theoretical results.