On the global asymptotic stability of an infection-age structured competitive model

TL;DR

This paper analyzes the long-term behavior of a complex infection-age structured model with multiple strains, extending classical results to more general cases using advanced mathematical tools.

Contribution

It provides a complete characterization of the asymptotic dynamics for multiple strains without assuming a unique maximal reproduction number, using integrated semigroups and Lyapunov functionals.

Findings

Established global asymptotic stability of equilibria.

Extended previous ODE model results to structured models.

Overcame technical challenges in Lyapunov functional analysis.

Abstract

We investigate an infection-age structured competitive epidemiological model involving multiple strains. While classical results establish competitive exclusion when a unique maximal basic reproduction number exists, we provide here a complete characterization of the asymptotic behavior for an arbitrary number of populations without assuming uniqueness of the maximal reproduction number. By means of integrated semigroups theory, persistence results, and Lyapunov functionals, we establish global asymptotic stability of equilibria and extend previous results obtained for simpler (ODE) models. A key contribution lies in overcoming technical difficulties related to the definition and differentiation of Lyapunov functionals, as well as in refining arguments based on the LaSalle invariance principle.