Résumé
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 R-0(x) and R-0(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{R-0(x), R-0(y)} <= 1. With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R-0(x) not equal R-0(y) and max{R-0(x), R-0(y)} > 1, meaning that the strain with the largest R-0 persists and eliminates the other strain. In the limit case R-0(x) = R-y(0) > 1, an infinite number of endemic equilibria exists and constitute a globally attractive set.