An age-structured virus model with two routes of infection in heterogeneous environments

On the basis of the complexity of the human body, we explore viral dynamics by using a two-compartment model incorporating the age since infection of infected cells and both virus-to-cell infection and cell-to-cell transmission routes. The basic reproduction number, R0, of the system is formulated from two mechanisms: one is the potential trigger from a single infection route in a compartment and the other is the synergistic effect of a viral infection in two compartments. Accordingly, we prove that the infection-free equilibrium is globally asymptotically stable (GAS) if R0<1, whereas virus persists uniformly with respect to the initial infection if R0>1. From the viewpoint of a predominant infection route incorporated with another mild infection route, we demonstrate global convergence to the infected equilibrium by applying a theory of perturbation on the globally stable steady state.