A STOCHASTIC DIFFERENTIAL EQUATION SIS EPIDEMIC MODEL
A STOCHASTIC DIFFERENTIAL EQUATION SIS EPIDEMIC MODEL
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DOI：
10.1137/10081856x
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发表时间：
2011-01-01
影响因子：
1.9
通讯作者：
Pan, J.
中科院分区：
文献类型：
--
作者：
Gray, A.;Greenhalgh, D.;Pan, J.
本文将经典的传染病易感模型从确定性框架推广到随机框架，并将其表示为关于传染个体数I（t）的随机微分方程。然后证明了该方程存在唯一的全局正解I（t），并建立了I（t）的灭绝和持续生存的条件.我们讨论随机噪声扰动。在持久性的情况下，我们表明存在一个平稳分布，并推导出其平均值和方差的表达式。结果通过计算机模拟来说明，包括基于现实生活中的疾病的两个例子。
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.