Global stability of an age-structured infection model in vivo with two compartments and two routes

In this paper, for an infection age model with two routes, virus-to-cell and cell-to-cell, and with two compartments, we show that the basic reproduction ratio $ R_0 $ gives the threshold of the stability. If $ R_0 > 1 $, the interior equilibrium is unique and globally stable, and if $ R_0 \le 1 $, the disease free equilibrium is globally stable. Some stability results are obtained in previous research, but, for example, a complete proof of the global stability of the disease equilibrium was not shown. We give the proof for all the cases, and show that we can use a type reproduction number for this model.