多部网络中的流行病：涌现动力学
Epidemics in Multipartite Networks: Emergent Dynamics
摘要：
在文献中广泛探讨了完整网络上的单病毒流行病，因为在病毒感染的适当微观建模下，感染节点的分数是马尔可夫过程。在非完全网络中，这个宏观变量不再是马尔可夫的。本文研究了非完全随机网络上的病毒扩散问题，特别是多病毒传染病的扩散问题。我们专注于多方网络。在公司的工作http：//arxiv.org/abs/1306.6198，我们表明，对等的本地随机规则的病毒感染导致，在大型多部网络的限制，在宏观尺度上的结构化动力学的出现。被每个病毒株感染的跨岛节点的分数的精确流体极限演化服从一组非线性耦合微分方程，参见http://arxiv.org/abs/1306.6198。在本文中，我们开发的方法来分析这些限制动力学的定性行为，建立病毒的微观特征和网络结构的条件下，病毒持续存在或观察到的自然选择现象。
英文摘要：
Single virus epidemics over complete networks are widely explored in the literature as the fraction of infected nodes is, under appropriate microscopic modeling of the virus infection, a Markov process. With non-complete networks, this macroscopic variable is no longer Markov. In this paper, we study virus diffusion, in particular, multi-virus epidemics, over non-complete stochastic networks. We focus on multipartite networks. In companying work http://arxiv.org/abs/1306.6198, we show that the peer-to-peer local random rules of virus infection lead, in the limit of large multipartite networks, to the emergence of structured dynamics at the macroscale. The exact fluid limit evolution of the fraction of nodes infected by each virus strain across islands obeys a set of nonlinear coupled differential equations, see http://arxiv.org/abs/1306.6198. In this paper, we develop methods to analyze the qualitative behavior of these limiting dynamics, establishing conditions on the virus micro characteristics and network structure under which a virus persists or a natural selection phenomenon is observed.
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