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 $\Re_0 < 1$, the virus-free steady state is globally asymptotically stable, which means that the viruses are cleared and immune-response is not active; when $\Re_1 < 1 < \Re_0$, the immune-inactivated infection steady state exists and is globally asymptotically stable; and when $\Re_1>1$, which implies that $\Re_0>1$, the immune-activated infection steady state exists and is globally asymptotically stable. Numerical simulations are given to support our theoretical results