Global dynamics of an in-host viral model with intracellular delay

The dynamics of a general in-host model with intracellular delay is studied. The model can describe in vivo infections of HIV-I, HCV, and HBV. It can also be considered as a model for HTLV-I infection. We derive the basic reproduction number R0 for the viral infection, and establish that the global dynamics are completely determined by the values of R0. If R0 < or = 1, the infection-free equilibrium is globally asymptotically stable, and the virus are cleared. If R0 > 1, then the infection persists and the chronic-infection equilibrium is locally asymptotically stable. Furthermore, using the method of Lyapunov functional, we prove that the chronic-infection equilibrium is globally asymptotically stable when R0 > 1. Our results shows that for intercellular delays to generate sustained oscillations in in-host models it is necessary have a logistic mitosis term in target-cell compartments.