Extinction time of stochastic SIRS models with small initial size of the infected population

TL;DR

This paper analyzes the extinction time of stochastic SIRS epidemic models with small initial infections, deriving a closed-form asymptotic distribution and validating it through simulations.

Contribution

It provides a new closed-form expression for the extinction time distribution in stochastic SIRS models with small initial infected populations.

Findings

Derived the asymptotic distribution of extinction time.

Validated theoretical results with Monte Carlo simulations.

Enhanced understanding of epidemic extinction dynamics.

Abstract

The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time of stochastic SIRS models as $N$ tends to infinity. When the initial size of infected population is small, we obtain the closed-form expression of the asymptotic distribution of this extinction time, and compare it with the data from Monte Carlo simulation.