Global analysis of an infection age SEI model with a large class of nonlinear incidence rates

TL;DR

This paper analyzes a nonlinear age-structured SEI infection model, establishing conditions for the global stability of disease-free and endemic states using Lyapunov functionals.

Contribution

It introduces a general nonlinear incidence rate in an age-structured SEI model and provides comprehensive stability criteria for equilibria.

Findings

Necessary and sufficient condition for global stability of disease-free equilibrium.

Global stability of endemic equilibrium under certain conditions.

Applicability to a broad class of nonlinear incidence functions.

Abstract

We propose and investigate an SEI infection's age model with a general class of nonlinear incidence rates. We give a necessary and sufficient condition for global asymptotic stability of the free-equilibrium related to the basic reproduction number. By using Lyapunov functionals, we show the global asymptotic stability of the endemic equilibrium whenever it exists.