Contact tracing is an essential tool to mitigate the impact of a pandemic, such as the COVID-19 pandemic. In order to achieve efficient and scalable contact tracing in real time, digital devices can play an important role. While a lot of attention has been paid to analyzing the privacy and ethical risks of the associated mobile applications, so far much less research has been devoted to optimizing their performance and assessing their impact on the mitigation of the epidemic. We develop Bayesian inference methods to estimate the risk that an individual is infected. This inference is based on the list of his recent contacts and their own risk levels, as well as personal information such as results of tests or presence of syndromes. We propose to use probabilistic risk estimation to optimize testing and quarantining strategies for the control of an epidemic. Our results show that in some range of epidemic spreading (typically when the manual tracing of all contacts of infected people becomes practically impossible but before the fraction of infected people reaches the scale where a lockdown becomes unavoidable), this inference of individuals at risk could be an efficient way to mitigate the epidemic. Our approaches translate into fully distributed algorithms that only require communication between individuals who have recently been in contact. Such communication may be encrypted and anonymized, and thus, it is compatible with privacy-preserving standards. We conclude that probabilistic risk estimation is capable of enhancing the performance of digital contact tracing and should be considered in the mobile applications.

接触者追踪是减轻大流行（例如 COVID-19 大流行）影响的重要工具。为了实时实现高效且可扩展的联系人跟踪，数字设备可以发挥重要作用。尽管分析相关移动应用程序的隐私和道德风险受到了很多关注，但迄今为止，致力于优化其性能和评估其对缓解流行病影响的研究却很少。我们开发了贝叶斯推理方法来估计个人被感染的风险。这一推论是基于他最近接触过的人名单和他们自己的风险水平，以及个人信息，例如测试结果或是否患有综合症。我们建议使用概率风险估计来优化控制流行病的测试和隔离策略。我们的结果表明，在一定范围的流行病传播中（通常当手动追踪感染者的所有接触者变得几乎不可能，但在感染者的比例达到无法避免封锁的规模之前），这种对处于危险中的个体的推断可能是减轻流行病的有效方法。我们的方法转化为完全分布式的算法，只需要最近接触过的个人之间进行通信。这种通信可以被加密和匿名化，因此，它与隐私保护标准兼容。