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Mathematics > Dynamical Systems

arXiv:1812.03333 (math)
[Submitted on 8 Dec 2018 (v1), last revised 23 Jul 2021 (this version, v2)]

Title:Permanence and Extinction for the Stochastic SIR Epidemic Model

Authors:N. H. Du, N. N. Nhu
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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 \begin{equation*} \begin{cases} dS(t)=\big[a_1-b_1S(t)-I(t)f(S(t),I(t))\big]dt + \sigma_1 S(t) dB_1(t) -I(t)g(S(t),I(t))dB_3(t),\\ dI(t)=\big[-b_2I(t) + I(t)f(S(t),I(t))\big]dt + \sigma_2I(t) dB_2(t) + I(t)g(S(t),I(t))dB_3(t). \end{cases} \end{equation*} Moreover, the rate of all convergences of the solution are also established. A number of numerical examples are given to illustrate our results
Subjects: Dynamical Systems (math.DS)
MSC classes: 34C12, 60H10, 92D25
Cite as: arXiv:1812.03333 [math.DS]
  (or arXiv:1812.03333v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1812.03333

Submission history

From: Nhu Nguyen [view email]
[v1] Sat, 8 Dec 2018 15:08:08 UTC (2,145 KB)
[v2] Fri, 23 Jul 2021 02:28:10 UTC (2,568 KB)
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