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We study a competitive infection-age structured SI model between twodiseases. The well-posedness of the system is handled by using integratedsemigroups theory, while the existence and the stability of disease-free orendemic equilibria are ensured, depending on the basic reproduction number$R_0^x$ and $R_0^y$ of each strain. We then exhibit Lyapunov functionals toanalyse the global stability and we prove that the disease-free equilibrium isglobally asymptotically stable whenever $\max\{R_0^x, R_0^y\}\leq 1$. Withrespect to explicit basin of attraction, the competitive exclusion principleoccurs in the case where $R_0^x\neq R_0^y$ and $\max\{R_0^x,R_0^y\}>1$, meaningthat the strain with the largest $R_0$ persists and eliminates the otherstrain. In the limit case $R_0^x=R^0_y>1$, an infinite number of endemicequilibria exists and constitute a globally attractive set.

Global stability in a competitive infection-age structured model