Path-Based Epidemic Spreading in Networks
Path-Based Epidemic Spreading in Networks
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DOI：
10.1109/tnet.2016.2594382
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
W. Chai;G. Pavlou
中科院分区：
文献类型：
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作者：
W. Chai;G. Pavlou
传统的流行病模型假设全方位的接触为基础的感染。这将流行病传播过程与节点度紧密联系起来。感染传播媒介的作用往往被忽视。然而，在现实世界的网络中，作为物理传染媒介的传染媒介通常通过特定的有向路由（基于路径的感染）从一个节点流向另一个节点。在这里，我们使用连续时间马尔可夫链分析模型的传染性病原体和路由路径的传播行为的影响，考虑到每个节点的状态转换单独，而不是所有节点的平均聚合行为。通过应用平均场近似，基于路径的感染机制的分析复杂度从指数降低到多项式。我们发现，拓扑结构起着次要的作用，在确定的规模的流行病。相反，路由算法和流量强度决定了疫情的生存能力和稳定状态。我们定义了一个感染特征矩阵，编码路由和交通信息。在此基础上，我们推导出基于关键路径的流行病阈值，低于该阈值的流行病将死亡，以及网络运营商可以用来促进/抑制基于路径的传播在其网络中的这个阈值的条件界限。最后，除了人工生成的随机和无标度图，我们还使用真实世界的网络和流量，作为案例研究，以比较接触和路径为基础的流行病的行为。我们的研究结果进一步证实了最近的经验观察，传播网络中的流行病是高度持久的。
Conventional epidemic models assume omni-directional contact-based infection. This strongly associates the epidemic spreading process with node degrees. The role of the infection transmission medium is often neglected. In real-world networks, however, the infectious agent as the physical contagion medium usually flows from one node to another via specific directed routes (path-based infection). Here, we use continuous-time Markov chain analysis to model the influence of the infectious agent and routing paths on the spreading behavior by taking into account the state transitions of each node individually, rather than the mean aggregated behavior of all nodes. By applying a mean field approximation, the analysis complexity of the path-based infection mechanics is reduced from exponential to polynomial. We show that the structure of the topology plays a secondary role in determining the size of the epidemic. Instead, it is the routing algorithm and traffic intensity that determine the survivability and the steady-state of the epidemic. We define an infection characterization matrix that encodes both the routing and the traffic information. Based on this, we derive the critical path-based epidemic threshold below which the epidemic will die off, as well as conditional bounds of this threshold which network operators may use to promote/suppress path-based spreading in their networks. Finally, besides artificially generated random and scale-free graphs, we also use real-world networks and traffic, as case studies, in order to compare the behaviors of contact- and path-based epidemics. Our results further corroborate the recent empirical observations that epidemics in communication networks are highly persistent.