Global stability in a competitive infection-age structured model

Quentin Richard¹

¹ Université de Bordeaux, IMB, UMR CNRS 5251, 33400 Talence, France.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 54.

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 and 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 . With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where and , meaning that the strain with the largest R0 persists and eliminates the other strain. In the limit case , an infinite number of endemic equilibria exists and constitute a globally attractive set.

Détail

DOI : 10.1051/mmnp/2020007

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