Department of Informatics, University of Zurich, 8050, Zurich, Switzerland.
School of Business, University of Applied Sciences and Arts FHNW, 4600, Olten, Switzerland.
Sci Rep. 2023 Jul 13;13(1):11363. doi: 10.1038/s41598-023-38282-8.
The problem of identifying the source of an epidemic (also called patient zero) given a network of contacts and a set of infected individuals has attracted interest from a broad range of research communities. The successful and timely identification of the source can prevent a lot of harm as the number of possible infection routes can be narrowed down and potentially infected individuals can be isolated. Previous research on this topic often assumes that it is possible to observe the state of a substantial fraction of individuals in the network before attempting to identify the source. We, on the contrary, assume that observing the state of individuals in the network is costly or difficult and, hence, only the state of one or few individuals is initially observed. Moreover, we presume that not only the source is unknown, but also the duration for which the epidemic has evolved. From this more general problem setting a need to query the state of other (so far unobserved) individuals arises. In analogy with active learning, this leads us to formulate the active querying problem. In the active querying problem, we alternate between a source inference step and a querying step. For the source inference step, we rely on existing work but take a Bayesian perspective by putting a prior on the duration of the epidemic. In the querying step, we aim to query the states of individuals that provide the most information about the source of the epidemic, and to this end, we propose strategies inspired by the active learning literature. Our results are strongly in favor of a querying strategy that selects individuals for whom the disagreement between individual predictions, made by all possible sources separately, and a consensus prediction is maximal. Our approach is flexible and, in particular, can be applied to static as well as temporal networks. To demonstrate our approach's practical importance, we experiment with three empirical (temporal) contact networks: a network of pig movements, a network of sexual contacts, and a network of face-to-face contacts between residents of a village in Malawi. The results show that active querying strategies can lead to substantially improved source inference results as compared to baseline heuristics. In fact, querying only a small fraction of nodes in a network is often enough to achieve a source inference performance comparable to a situation where the infection states of all nodes are known.
在给定接触网络和一组感染者的情况下，识别疫情源头（也称为零号病人）的问题引起了广泛的研究兴趣。成功及时地确定源头可以防止许多危害，因为可以缩小可能的感染途径数量，并隔离潜在的感染者。这一主题的先前研究通常假设，在尝试确定源头之前，有可能观察到网络中大量个体的状态。相反，我们假设观察网络中个体的状态是昂贵或困难的，因此最初只观察到一个或几个个体的状态。此外，我们假设不仅源头未知，而且疫情的持续时间也未知。从这个更一般的问题设置中，需要查询其他（迄今为止未观察到的）个体的状态。与主动学习类似，这导致我们提出了主动查询问题。在主动查询问题中，我们在源推断步骤和查询步骤之间交替进行。对于源推断步骤，我们依赖于现有工作，但采用贝叶斯方法，对疫情持续时间进行先验分布。在查询步骤中，我们的目标是查询那些提供有关疫情源头的信息最多的个体的状态，为此，我们提出了受主动学习文献启发的策略。我们的结果强烈支持一种查询策略，该策略选择那些个体，这些个体的个体预测之间的分歧最大，这些预测是由所有可能的源头分别做出的，而共识预测是最小的。我们的方法具有灵活性，特别是可以应用于静态和时间网络。为了展示我们方法的实际重要性，我们用三个经验（时间）接触网络进行了实验：一个猪的移动网络、一个性接触网络和一个马拉维一个村庄居民之间的面对面接触网络。结果表明，与基线启发式方法相比，主动查询策略可以显著提高源头推断结果。实际上，在网络中查询一小部分节点通常足以达到与所有节点的感染状态都已知的情况相当的源头推断性能。
