Pastor-Satorras Romualdo, Vespignani Alessandro
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord, Mòdul B4, 08034 Barcelona, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):036104. doi: 10.1103/PhysRevE.65.036104. Epub 2002 Feb 8.
Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity provides an ideal environment for the spreading of infective agents. Here we show that the random uniform immunization of individuals does not lead to the eradication of infections in all complex networks. Namely, networks with scale-free properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals. The absence of any critical immunization threshold is due to the unbounded connectivity fluctuations of scale-free networks. Successful immunization strategies can be developed only by taking into account the inhomogeneous connectivity properties of scale-free networks. In particular, targeted immunization schemes, based on the nodes' connectivity hierarchy, sharply lower the network's vulnerability to epidemic attacks.
诸如性伙伴关系网络或互联网之类的复杂网络，其连接特性往往表现出高度的冗余性和异质性。这种特殊的连接性为传染源的传播提供了理想的环境。在此我们表明，对个体进行随机均匀免疫并不能根除所有复杂网络中的感染。也就是说，即使存在高得不符合实际的随机免疫个体密度，具有无标度特性的网络也无法从重大疫情爆发中获得全局免疫。不存在任何关键免疫阈值是由于无标度网络的连接波动无界。只有考虑到无标度网络的非均匀连接特性，才能制定出成功的免疫策略。特别是，基于节点连接层次的靶向免疫方案能大幅降低网络对疫情攻击的脆弱性。
