Global stability properties of a class of renewal epidemic models with variable susceptibility

TL;DR

This paper analyzes the global stability of a renewal epidemic model with variable susceptibility, demonstrating conditions under which the disease persists or dies out based on the basic reproduction number R0.

Contribution

It establishes the global stability of endemic and disease-free equilibria in a renewal epidemic model with variable susceptibility, extending previous models.

Findings

Endemic equilibrium exists and is globally stable when R0 > 1.

Infection-free equilibrium is globally stable when R0 ≤ 1.

The model provides a comprehensive understanding of epidemic persistence and eradication conditions.

Abstract

We investigate the global dynamics of a renewal-type epidemic model with variable susceptibility. We show that in this extended model there exists a unique endemic equilibrium and prove that it is globally asymptotically stable when $R_0 > 1$, i.e. when it exists. We also show that the infection-free equilibrium, which exists always, is globally asymptotically stable for $R_0 \leq 1$.