Dynamics of a Within-Host Virus Infection Model with Multiple Pathways: Stability Switch and Global Stability

Abstract

In this paper, we consider an HIV infection model with virus-to-cell infection, cell-to-cell transmission, intracellular delay and mitosis of uninfected cells. The basic reproduction number is calculated by using the method of the next generation matrix. By comparison arguments, it is proved that when the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, the existence of Hopf bifurcation and stability switch at the chronic-infection equilibrium of the model with or without intracellular delay is established. Further, by constructing Lyapunov functionals, sufficient conditions are obtained for the global asymptotic stability of the chronic-infection equilibrium when the cell-to-cell transmission is negligible. Numerical simulations are carried out to illustrate the main theoretical results. The normal form is calculated to determine the bifurcation direction and stability, as well as amplitude and period of bifurcating periodic solutions when the intracellular delay is absent.