Mathematical analysis of an HIV model with latent reservoir, delayed CTL immune response and immune impairment

In this paper, an in-host HIV infection model with latent reservoir, delayed CTL immune response and immune impairment is investigated. By using suitable Lyapunov functions and LaSalle's invariance principle, it is shown that when time delay is equal to zero, the immunity-inactivated reproduction ratio is a threshold determining the global dynamics of the model. By means of the persistence theory for infinite dimensional systems, it is proven that if the immunity-inactivated reproduction ratio is greater than unity, the model is permanent. Choosing time delay as the bifurcation parameter and analyzing the corresponding characteristic equation of the linearized system, the existence of a Hopf bifurcation at the immunity-activated equilibrium is established. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics.