Thresholds for Epidemic Spreading in Networks
Thresholds for Epidemic Spreading in Networks
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DOI：
10.1103/physrevlett.105.218701
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发表时间：
2010-11-17
影响因子：
8.6
通讯作者：
Pastor-Satorras, Romualdo
中科院分区：
文献类型：
--
作者：
Castellano, Claudio;Pastor-Satorras, Romualdo
研究了淬灭网络中流行病模型的阈值，该阈值的程度分布为幂律。对于易感-感染-易感模型，在任何最大度k（max）随系统大小发散的网络上，活动阈值lambda(c)在大尺寸极限中消失，这与异质平均场（HMF）理论不一致。阈值的消失与网络的无标度特性无关，而是源于系统中最大的集线器在任何传播速率（lambda > 1/root k(max)）下都处于活动状态，并扮演自我维持源的角色，将感染传播到系统的其余部分。相反，易受感染-去除模型与HMF理论一致，并且对于富尺度网络具有有限阈值。我们推测，在淬灭的富尺度网络上，一般流行病模型的阈值随稳态的存在或不存在而消失或有限。
We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold lambda(c) vanishes in the large size limit on any network whose maximum degree k(max) diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate lambda > 1/root k(max) and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.