Expected Time to Extinction of SIS Epidemic Model Using Quasy Stationary Distribution

TL;DR

This paper analyzes the expected time to extinction in the SIS epidemic model using quasi-stationary distribution approximations, providing a method to estimate how long the epidemic persists before extinction occurs.

Contribution

It introduces a novel approach to approximate the mean time to extinction in the SIS model using CLT and quasi-stationary distributions, extending previous stochastic epidemic analyses.

Findings

Derived an asymptotic approximation for mean extinction time

Applied CLT to quasi-stationary distribution in SIS model

Provided insights into epidemic persistence duration

Abstract

We study that the breakdown of epidemic depends on some parameters, that is expressed in epidemic reproduction ratio number. It is noted that when $R_0 $ exceeds 1, the stochastic model have two different results. But, eventually the extinction will be reached even though the major epidemic occurs. The question is how long this process will reach extinction. In this paper, we will focus on the Markovian process of SIS model when major epidemic occurs. Using the approximation of quasi--stationary distribution, the expected mean time of extinction only occurs when the process is one step away from being extinct. Combining the theorm from Ethier and Kurtz, we use CLT to find the approximation of this quasi distribution and successfully determine the asymptotic mean time to extinction of SIS model without demography.