# A Note on the Extinction of a Stochastic Differential Equation SIS Epidemic Model

## TL;DR

This paper provides a simpler and more direct proof of the extinction conjecture for a stochastic differential equation SIS epidemic model, originally proposed by Gray et al. and proved by Xu.

## Contribution

It introduces a new, more straightforward proof of the extinction conjecture for the stochastic SIS model, improving understanding of the model's behavior.

## Key findings

- The proof confirms the extinction behavior of the stochastic SIS model.
- The new proof simplifies the mathematical approach to the conjecture.
- Supports the validity of the extinction conjecture in stochastic epidemic models.

## Abstract

The aim of this note is to give a new proof to the conjecture, proposed by Gray et al. (2011), on the extinction of a stochastic differential equation SIS epidemic model. The conjecture was proved by Xu (2017). Our proof is much more direct and simpler.