Stability and bifurcation of HIV-1 infection model with latent reservoir, cell-to-cell transmission and immune impairment

In this paper, HIV-1 model with latent reservoir, cell-to-cell transmission mechanism, immune impairment, and time delay for immune response is investigated. The basic reproduction number R-0 and the cytotoxic T-lymphocyte (CTL) immune response reproductive number R-1 are derived by calculation. The local stability of each equilibrium is studied by analyzing corresponding characteristic equations. By choosing time delay for immune response as bifurcation parameter, the existence of Hopf bifurcation at the immune-activated equilibrium is established. By means of Lyapunov functionals and LaSalle's invariance principle, it is obtained that the infection-free equilibrium is globally asymptotically stable as R-0 < 1. When R-1 < 1 <R-0, the immune-inactivated equilibrium is globally asymptotically stable. When R-1 > 1 and the time delay equals to zero, the immune-activated equilibrium is globally asymptotically stable. Numerical simulations are performed to illustrate the analytical results.