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

In this paper, we propose an HIV model with latent reservoir, delayed CTL immune response and immune impairment in which both virus-to-cell infection and cell-to-cell viral transmission are considered. By using Lyapunov functionals and LaSalle’s invariance principle, it is verified that when time delay is equal to zero, the global threshold dynamics of the model is determined by the basic reproduction ratio. With the help of uniform persistence theory for infinite dimensional systems, we obtain the uniform persistence when the basic reproduction ratio is greater than unity. By choosing time delay as a bifurcation parameter and analyzing the corresponding characteristic equation of the system, we establish the existence of Hopf bifurcation at the chronic-infection equilibrium. Numerical simulations are carried out to illustrate the corresponding theoretical results.