Global stability in a competitive infection-age structured model

Abstract

We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number R0x and R0y of each strain. We then exhibit Lyapunov functionals to analyse the global stability and we prove that the disease-free equilibrium is globally asymptotically stable whenever max{R0x, R0y} ≤ 1. With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R0x ≠ R0y and max{R0x, R0y} > 1, meaning that the strain with the largest R0 persists and eliminates the other strain. In the limit case R0x = Ry0 > 1, an infinite number of endemic equilibria exists and constitute a globally attractive set.