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

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.