Buono Camila, Alvarez-Zuzek Lucila G, Macri Pablo A, Braunstein Lidia A
Instituto de Investigaciones Físicas de Mar del Plata, Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Mar del Plata, Argentina.
Instituto de Investigaciones Físicas de Mar del Plata, Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Mar del Plata, Argentina; Center for Polymer Studies, Boston University, Boston, Massachusetts, United States of America.
PLoS One. 2014 Mar 14;9(3):e92200. doi: 10.1371/journal.pone.0092200. eCollection 2014.
Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction [Formula: see text] of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted [Formula: see text]. We also theoretically determine the dependence of the epidemic threshold on the fraction [Formula: see text] of shared nodes in a system composed of two layers. We find that in the limit of [Formula: see text] the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.
许多真实网络呈现出分层结构，其中每一层中的链接反映了节点在不同环境中的功能。这些多种类型的链接通常由一个多层网络表示，其中每一层都有不同的拓扑结构。然而，在现实世界的网络中，并非所有节点都存在于每一层。为了生成更现实的场景，我们使用一个广义多层网络，并假设各层仅共享一部分（公式：见正文）节点。我们为一个分支过程开发了一个理论框架，以描述流行病在这些部分重叠的多层网络上的传播。这使我们能够得到感染个体的比例作为疾病传播有效概率（公式：见正文）的函数。我们还从理论上确定了在由两层组成的系统中，流行病阈值对共享节点比例（公式：见正文）的依赖性。我们发现，在（公式：见正文）的极限情况下，阈值由具有较小孤立阈值的层主导。尽管两个完全孤立的网络系统与仅共享少数节点的两个网络系统几乎无法区分，但我们发现，这些少数共享节点的存在会导致传播能力较低的孤立网络的流行病阈值发生不连续变化，并获得另一个网络的阈值。
