Classification of Asymptotic Behavior in A Stochastic SIR Model

2015/12/23 by N. T. Dieu, Dang Nguyen, Dieu, N. T. +8
Mathematics · Medicine · #34C12 #60H10 #92D25 #COVID-19 epidemiological studies #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #math.DS #math.PR #msc:34C12 #msc:60H10 #msc:92D25

paper · pdf · doi:10.48550/arxiv.1512.07326

25 pages

arxiv created 2015/12/23 · openalex publication_date 2015/12/23 · arxiv updated 2015/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition, this paper develops ergodicity of the underlying system. It is proved that the transition probabilities converge in total variation norm to the invariant measure. Our result gives a precise characterization of the support of the invariant measure. Rates of convergence are also ascertained. It is shown that the rate is not too far from exponential in that the convergence speed is of the form of a polynomial of any degree.

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