A STOCHASTIC DIFFERENTIAL EQUATION SIS EPIDEMIC MODEL

被引：811

作者：

Gray, A. ^{[1
]}

Greenhalgh, D. ^{[1
]}

Hu, L. ^{[2
]}

Mao, X. ^{[1
]}

Pan, J. ^{[1
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[2] Donghua Univ, Dept Appl Math, Shanghai 201620, Peoples R China

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2011年 / 71卷 / 03期

关键词：

susceptible-infected-susceptible model; Brownian motion; stochastic differential equations; extinction; persistence; basic reproduction number; stationary distribution; gonorrhea; pneumococcus; STABILITY; TRANSMISSION; BEHAVIOR; AIDS;

D O I：

10.1137/10081856X

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). We then prove that this SDE has a unique global positive solution I(t) and establish conditions for extinction and persistence of I(t). We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.

引用

页码：876 / 902

页数：27

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