Second look at the spread of epidemics on networks
Second look at the spread of epidemics on networks
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DOI：
10.1103/physreve.76.036113
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发表时间：
2007-09-01
影响因子：
2.4
通讯作者：
Robins, James M.
中科院分区：
文献类型：
--
作者：
Kenah, Eben;Robins, James M.
在一篇重要的论文中，纽曼[Phys.Rev.E66,016128(2002年)]声称一般的基于网络的随机去除易感传染病(SIR)流行病模型与键渗流模型同构，其中键是接触网络的边缘，键占用概率等于从受感染节点传播到易感邻居的边际概率。在本文中，我们证明了这种同构是不正确的，并定义了一个半有向随机网络，我们称之为传染病渗流网络，它在任意有限种群中与SIR流行病模型完全同构。在大种群的极限中，(I)(自限)暴发大小的分布与(小)外分量的大小分布相同，(Ii)流行阈值对应于出现巨型强连通分量的相变，(Iii)大流行的概率等于初始感染发生在巨型内分量中的概率，以及(Iv)流行病的相对最终大小等于包含在巨型外分量中的网络的比例。对于Newman所考虑的SIR模型，我们证明了渗流网络预测的平均爆发规模低于流行阈值，相同的流行阈值，以及相同的最终流行病规模。然而，当存在非退化的感染期分布时，键渗流模型不能预测正确的暴发规模分布和发生流行病的概率。我们通过将渗流网络和键渗流模型的预测与模拟结果进行比较来证实我们的发现。在附录中，我们证明了对于任意时齐随机SIR模型，都可以定义一个与传染病渗流网络同构的模型。
In an important paper, Newman [Phys. Rev. E66, 016128 (2002)] claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In the Appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.