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疾病传播与级联失效相互作用的研究：度不相关网络中疾病扩散条件的分析
Dynamic interplay b etween epidemics and cascades:Epidemic outbreaks in uncorrelated networks
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摘要: 在网络科学中，对疾病传播和级联失效的研究分属两个独立的领域，但在实际中存在许多两个过程相互耦合的情况。比如在通信网络中，病毒传播会对数据传输造成影响，导致网络中负载变化，进而可能引发级联失效。这个现象已被观察到。通过建立两个动态过程相互作用的模型及针对该模型的分析，本文给出了计入节点的负载和容量时疾病爆发的条件。这一条件是由描述疾病传播速率的传播概率与描述节点容量大小的冗余系数共同决定的。进一步探讨表明，当疾病传播速率一定而冗余系数变化时，疾病恰好开始传播的临界点附近未感染且未失效的节点的数量是最大的，即在此点上网络处于最佳工作状态。因此给出疾病爆发的临界条件具有重要意义。Abstract: Epidemics and cascades are independently studied topics in network science, but in practice, there are cases where they interact and neither of their effects can be ignored, e.g., when a digital virus spreads in a communication network that is transferring data. We have built a model to study their interplay in previous works. Here we present the epidemic threshold criteria of this model. When the infectivity is fixed, the tolerance parameter α, in capturing the capacity of nodes, must be larger than a critical value to fulfill the criteria, and at equilibrium the fraction of nodes both uninfected and un-failed is the largest at this critical point. So the the presentation of the epidemic threshold criteria is of significance.
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