Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity

Direct cell-to-cell transmission of HIV-1 is proved to be a more efficient means of virus infection than virus-to-cell transmission. In this paper, we incorporate both virus-to-cell and cell-to-cell transmissions into an HIV-1 virus model, which also contains intracellular delay and humoral immunity. By analyzing the characteristic equations, the local stability of feasible equilibria is established. By using Lyapunov functionals and LaSalle's invariance principle, it is verified that global threshold dynamics of the model can be explicitly described by immune-inactivated reproduction rate and immune-activated reproduction rate. Numerical simulations are carried out to illustrate the corresponding theoretical results.