Contact-tracing is an essential tool in order to mitigate the impact of pandemic such as the COVID-19. 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 in order 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 lock-down 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 compatible with privacy preserving standards. We conclude that probabilistic risk estimation is capable to enhance performance of digital contact tracing and should be considered in the currently developed mobile applications.
We developed SIB, a message-passing algorithm for individual-level inference in epidemics. SIB assumes that the epidemic process is generated by a compartmental model (currently a generalized semi-continuous time SIR model is implemented). Among other things, SIB computes the probability of each individual to be susceptible, infected or recovered at a given time from a list of contacts and partial observations. The method is based on Belief Propagation equations for partial trajectories. See notes or go directly to results for more details.
The code by the Sibyl Team can be found here.
See a gentle introduction to the topic (in italian) at , an older article where the method was developed  or a preprint  for the application to COVID-19 with comparisons and more results. See also this other page.