  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.

Populations and Evolution;Statistical Mechanics;Artificial Intelligence;Machine Learning