Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay

• We study the problem of global asymptotic stability for equilibria of a HIV-1 virus model.
• We broaden the construction method into the viral model with infinite distributed delay, and cell-to-cell transmission, respectively.
• Numerical examples are given to illustrate the effectiveness of the theoretical results for sharp threshold property.

The goal of this paper is to study the threshold dynamics of an HIV-1 viral infection model with cell-mediated immune responses and direct cell-to-cell transmission mechanism. The model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection ℜ0 and for CTL immune response ℜ1. The proofs of main results come from suitable uses of analyzing the characteristic equation and constructing Lyapunov functionals. Specifically, if ℜ0 < 1, the infection-free equilibrium E0 is locally and globally asymptotically stable, and the viruses are cleared. If ℜ1 < 1 < ℜ0, the CTL-inactivated equilibrium E1 is locally and globally asymptotically stable, and the infection becomes chronic but without persistent CTLs response. If ℜ1 > 1, the CTL-activated equilibrium E2 is locally and globally asymptotically stable, and the infection is chronic with persistent CTLs response. Numerical simulations are performed to support our results.