Complex Dynamics of a Delayed HIV Infection Model Involving Latently Infected Cells and Impaired Immunity

This paper explores the dynamics analysis of an HIV model with delayed effects, latently infected cells, and impaired immunity. The model incorporates two different delays: the intracellular delay and the CTL response delay. Firstly, the local stability of equilibria is studied through discussing two thresholds. Subsequently, we establish sufficient conditions for the global stability of equilibria based on Lyapunov function and LaSalle's invariance principle. Numerical simulations confirm the theoretical analysis and further reveal the complex dynamic behaviors of the immune infection equilibrium in the presence of two delays. Furthermore, sensitivity analysis on the model parameters is used to identify the highly influential factors affecting two reproduction numbers.