# Global stability of an SIS epidemic model with a finite infectious period

## TL;DR

This paper proves the global stability of the endemic equilibrium in a generalized SIS epidemic model with a finite infectious period, confirming a long-standing conjecture for nonfatal diseases.

## Contribution

It establishes the global asymptotic stability of the endemic equilibrium in an SIS model with a general infectious period distribution, solving a conjecture from 1995.

## Key findings

- Endemic equilibrium is globally asymptotically stable when it exists.
- The model uses a scalar integral equation with a general infectious period distribution.
- Confirms the conjecture for nonfatal diseases.

## Abstract

Assuming a general distribution for the sojourn time in the in- fectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically stable whenever it exists, solving the conjecture of Hethcote and van den Driessche (1995) for the case of nonfatal diseases.