Global dynamics of an age-structured within-host viral infection model with cell-to-cell transmission and general humoral immunity response

In this paper, an age-structured within-host viral infection model with cell-to-cell transmission and general humoral immune response is investigated. We give a rigorous mathematical analysis on some necessary technical materials, including the relative compactness and persistence of the solution semiflow, and existence of a global attractor. By subtle construction and estimates of a Lyapunov functional, we show that the global dynamics is determined by two sharp thresholds, namely, basic reproduction number $\Re_0$ and immune-response reproduction number $\Re_1$. When $\Re_0