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

Abstract

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 <0 and immune-response reproduction number <1. When <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 <1 < 1 < <0, the immune-inactivated infection steady state exists and is globally asymptotically stable; and when <1 > 1, which implies that <0 > 1, the immune-activated infection steady state exists and is globally asymptotically stable. Numerical simulations are given to support our theoretical results.