复杂拓扑网络的传播动力学
Propagation dynamics on networks featuring complex topologies
摘要：
近年来，随机网络传播现象的解析描述蓬勃发展，然而更多的复杂系统主要通过数值方法进行研究。在本文中，一个平均场描述是用来相干耦合的网络元素（节点，顶点，个人…）的动态。一方面和他们的经常性拓扑模式（子图，群.）另一方面，在具有社团结构的社交网络上的SIS传染病传播模型中，该方法给出了系统时间演化的常微分方程组，以及传染病阈值和平衡点的解析解.所得结果与数值模拟结果非常一致，并在适当的范围内再现了随机网络行为，突出了拓扑结构对过程的影响。最后，它表明，我们的模型预测更高的流行病阈值的聚类结构比等价的随机拓扑结构的情况下，网络的零度相关性。
英文摘要：
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.
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