Network epidemic models with two levels of mixing
Network epidemic models with two levels of mixing
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DOI：
10.1016/j.mbs.2008.01.001
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发表时间：
2008-03-01
影响因子：
4.3
通讯作者：
Neal, Peter
中科院分区：
文献类型：
--
作者：
Ball, Frank;Neal, Peter
社交网络上的流行病研究最近引起了相当大的关注。在本文中，我们考虑了一个有限网络上流行病传播的随机SIR（易感->传染->消除）模型，该模型具有任意但指定的度分布，其中个体也进行偶然接触，即与从总体中均匀选择的人进行接触。研究了网络规模趋于无穷大时模型的行为。特别是，决定一种流行病在最初感染者很少的情况下是否能够确立的基本再生数R-0，以及流行病确立的概率和最终被这种流行病感染的人口比例。对于传染期为常数且网络中所有个体的度相同的情形，得到了传染病规模的渐近方差和中心极限定理.让个体进行偶然接触的速率降低到零，从理论上讲，对应于没有偶然接触的模型，即标准SIR网络流行病模型的结果。一个确定性的模型，近似的流行病，成为建立在一个大的人口的传播。数值研究表明，该理论的渐近近似工作良好，即使只有中等规模的网络，度分布和包含的偶然接触，每个都可以有一个重大影响的流行病的结果。(c)2008年爱思唯尔公司All rights reserved.
The study of epidemics on social networks has attracted considerable attention recently. In this paper, we consider a stochastic SIR (susceptible -> infective -> removed) model for the spread of an epidemic on a finite network, having an arbitrary but specified degree distribution, in which individuals also make casual contacts, i.e. with people chosen uniformly from the population. The behaviour of the model as the network size tends to infinity is investigated. In particular, the basic reproduction number R-0, that governs whether or not an epidemic with few initial infectives can become established is determined, as are the probability that an epidemic becomes established and the proportion of the population who are ultimately infected by such an epidemic. For the case when the infectious period is constant and all individuals in the network have the same degree, the asymptotic variance and a central limit theorem for the size of an epidemic that becomes established are obtained. Letting the rate at which individuals make casual contacts decrease to zero yields, heuristically, corresponding results for the model without casual contacts, i.e. for the standard SIR network epidemic model. A deterministic model that approximates the spread of an epidemic that becomes established in a large population is also derived. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations work well, even for only moderately sized networks, and that the degree distribution and the inclusion of casual contacts can each have a major impact on the outcome of an epidemic. (c) 2008 Elsevier Inc. All rights reserved.