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Distinguishing Infections on Different Graph Topologies

机译：区分不同图拓扑上的感染

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摘要

The history of infections and epidemics holds famous examples where understanding, containing, and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV, and most computer viruses spread person to person, device to device, and through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper, we study two fundamental questions of detection. First, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a random illness operating independently of any contact network (e.g., seasonal allergies)? Second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread—the causative network—without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions that networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the -dimensional grid, and the Erdös-Renyi graphs.
机译：感染和流行病的历史举着著名的例子，其中了解，遏制并最终治疗爆发始于了解其传播方式。流感，HIV和大多数计算机病毒会在人与人之间，设备与设备之间以及通过联系网络传播；另一方面，霍乱，癌症和季节性过敏则没有。在本文中，我们研究了两个基本的检测问题。首先，给定快照的一部分（可能消失）的快照视图，在什么情况下是通过接触（例如流感）传播的流行病，可与独立于任何接触网络（例如季节性过敏）的随机疾病区分开来？其次，如果我们确实有流行病，那么在什么情况下可以确定是哪一个相互作用的网络是传播的主要原因（病因网络），而无需任何流行病知识，除了被感染的微小子样本的身份节点？因此，本文的核心是要了解网络信息的诊断能力。我们得出网络必须满足的足以识别这些问题的条件，并产生解决这些问题的高效，高度可扩展的算法。我们表明，我们给出的可识别性条件相当温和，尤其是通过两种常见的图拓扑得到了满足：-维网格和Erdös-Renyi图。

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