Existence, multiplicity and stability of endemic states for an age-structured S-I epidemic model

TL;DR

This paper analyzes an age-structured S-I epidemic model, identifying conditions for the existence, uniqueness, and stability of endemic states, and explores how demographic factors influence disease persistence.

Contribution

It introduces a threshold criterion for endemic equilibrium stability and demonstrates conditions for uniqueness, including examples with multiple endemic states.

Findings

A threshold quantity determines stability of disease-free state.

Conditions for uniqueness of endemic equilibrium are established.

Numerical analysis shows demographic factors affect endemic stability.

Abstract

We study an S--I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic equilibrium. We obtain conditions on the age-dependence of the susceptibility to infection that imply the uniqueness of the endemic equilibrium. An example with two endemic equilibria is shown. Finally, we analyse numerically how the stability of the endemic equilibrium is affected by extra-mortality and by the possible periodicities induced by the demographic age-structure.