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

2021/01/13 by Jingran Zhai, Zhai, Jingran
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2101.04857

openalex publication_date 2021/01/13 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

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.

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