Inferring the source of a diffusion in a large network of agents is a difficult but feasible task, if a few agents act as sensors revealing the time at which they got hit by the diffusion. One of the main limitations of current source identification algorithms is that they assume full knowledge of the contact network, which is rarely the case, especially for epidemics, where the source is called patient zero. Inspired by recent implementations of contact tracing algorithms, we propose a new framework, which we call Source Identification via Contact Tracing Framework (SICTF). In the SICTF, the source identification task starts at the time of the first hospitalization, and initially we have no knowledge about the contact network other than the identity of the first hospitalized agent. We may then explore the network by contact queries, and obtain symptom onset times by test queries in an adaptive way, i.e., both contact and test queries can depend on the outcome of previous queries. We also assume that some of the agents may be asymptomatic, and therefore cannot reveal their symptom onset time. Our goal is to find patient zero with as few contact and test queries as possible. We implement two local search algorithms for the SICTF: the LS algorithm, which has recently been proposed by Waniek et al. in a similar framework, is more data-efficient, but can fail to find the true source if many asymptomatic agents are present, whereas the LS+ algorithm is more robust to asymptomatic agents. By simulations we show that both LS and LS+ outperform previously proposed adaptive and non-adaptive source identification algorithms adapted to the SICTF, even though these baseline algorithms have full access to the contact network. Extending the theory of random exponential trees, we analytically approximate the source identification probability of the LS/ LS+ algorithms, and we show that our analytic results match the simulations. Finally, we benchmark our algorithms on the Data-driven COVID-19 Simulator (DCS) developed by Lorch et al., which is the first time source identification algorithms are tested on such a complex dataset.

如果一些智能体充当传感器，揭示它们受到扩散影响的时间，那么在大型智能体网络中推断扩散源是一项困难但可行的任务。当前源识别算法的主要局限性之一是它们假设完全了解接触网络，但这种情况很少见，特别是对于流行病来说，源被称为零号病人。受最近实施的接触者追踪算法的启发，我们提出了一个新的框架，我们将其称为通过接触者追踪框架进行源识别（SICTF）。在SICTF中，源识别任务从第一次住院时开始，最初除了第一个住院代理人的身份之外，我们对联系网络一无所知。然后，我们可以通过接触查询来探索网络，并以自适应方式通过测试查询来获得症状发作时间，即，接触查询和测试查询都可以取决于先前查询的结果。我们还假设某些感染者可能没有症状，因此无法透露他们的症状发作时间。我们的目标是通过尽可能少的接触和测试查询找到零号病人。我们为 SICTF 实现了两种本地搜索算法：LS 算法，该算法最近由 Waniek 等人提出。在类似的框架中，数据效率更高，但如果存在许多无症状感染者，则可能无法找到真正的来源，而 LS+ 算法对无症状感染者更稳健。通过模拟，我们表明 LS 和 LS+ 均优于先前提出的适应 SICTF 的自适应和非自适应源识别算法，即使这些基线算法可以完全访问接触网络。扩展随机指数树的理论，我们分析地近似了 LS/LS+ 算法的源识别概率，并且我们表明我们的分析结果与模拟相匹配。最后，我们在 Lorch 等人开发的数据驱动的 COVID-19 模拟器 (DCS) 上对我们的算法进行基准测试，这是首次在如此复杂的数据集上测试源识别算法。