# Lyapunov stability of an SIRS epidemic model with varying population

## TL;DR

This paper analyzes the stability of an SIRS epidemic model with density-dependent mortality, demonstrating global stability of disease-free and endemic states using Lyapunov functions.

## Contribution

It introduces a Lyapunov function approach to establish global stability for both disease-free and endemic equilibria in a generalized SIRS model.

## Key findings

- Global stability of disease-free equilibrium proven.
- Global stability of endemic state demonstrated.
- Lyapunov function constructed for broad conditions.

## Abstract

In this paper we consider an SIRS epidemic model under a general assumption of density-dependent mortality. We prove the global stability of the disease-free equilibrium and propose a Lyapunov function that allows to demonstrate the global stability of the (unique) endemic state under broad conditions.