Global stability in a competitive infection-age structured model

Université de Bordeaux, IMB, UMR CNRS 5251, 33400 Talence, France.

^* Corresponding author: quentin.richard@math.cnrs.fr

Received: 4 November 2019
Accepted: 13 March 2020

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 R₀^x and R₀^y 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{R₀^x, R₀^y} ≤ 1. With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R₀^x ≠ R₀^y and max{R₀^x, R₀^y} > 1, meaning that the strain with the largest R₀ persists and eliminates the other strain. In the limit case R₀^x = R_y⁰ > 1, an infinite number of endemic equilibria exists and constitute a globally attractive set.