Permanence and Extinction for the Stochastic SIR Epidemic Model

2018/12/08 by Nguyen Huu Du, Du, N. H., Nguyen Ngoc Nhu +1
Mathematics · Medicine · #34C12 #60H10 #92D25 #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1812.03333

openalex publication_date 2018/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost necessary condition for the extinction and permanence for an epidemic system with multi noises \begincases dS(t)=[a₁-b₁S(t)-I(t)f(S(t),I(t))]dt + σ₁ S(t) dB₁(t) -I(t)g(S(t),I(t))dB₃(t),
dI(t)=[-b₂I(t) + I(t)f(S(t),I(t))]dt + σ₂I(t) dB₂(t) + I(t)g(S(t),I(t))dB₃(t). \endcases Moreover, the rate of all convergences of the solution are also established. A number of numerical examples are given to illustrate our results

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