Perturbation of a globally stable equilibrium: application on an age-structured model

TL;DR

This paper analyzes the stability of an age-structured epidemic model for Hepatitis B, demonstrating the global stability of the endemic equilibrium using perturbation methods under certain assumptions.

Contribution

It introduces a novel application of perturbation techniques to establish global stability in an age-structured epidemic model with multiple infected classes.

Findings

Proves global stability of endemic equilibrium

Shows asymptotic behavior of the epidemic system

Utilizes perturbation arguments for stability analysis

Abstract

In this manuscript we consider an age structured epidemic system modelling the dynamics of transmission of immunizing disease like Hepatitis B virus. Our model takes into account age as well as two classes of infected individuals (chronic carriers and acute infected human). Based on the low infectivity of chronic carriers, we study the asymptotic behavior of the system and, under some suitable assumptions, we prove the global stability of the endemic equilibrium point using perturbation arguments of semi-flow. The intuitive conservation of the global stability under perturbation, needs in fact very technical tools and complex results.