  Many countries are currently gearing up to use smart-phone apps to perform
contact tracing as part of the effort to manage the COVID-19 pandemic and
prevent resurgences of the disease after the initial outbreak. With the
announcement of the Apple/Google partnership to introduce contact-tracing
functionality to iOS and Android, it seems likely that this will be adopted in
many countries. An important part of the functionality of the app will be to
decide whether a person should be advised to self-isolate, be tested or end
isolation. However, the privacy preserving nature of the Apple/Google contact
tracing algorithm means that centralised curation of these decisions is not
possible so each phone must use its own "risk model" to inform decisions.
Ideally, the risk model should use Bayesian inference to decide the best course
of action given the test results of the user and those of other users. Here we
present a decentralised algorithm that estimates the Bayesian posterior
probability of viral transmission events and evaluates when a user should be
notified, tested or released from isolation while preserving user privacy. The
algorithm also allows the disease models on the phones to learn from everyone's
contact-tracing data and will allow Epidemiologists to better understand the
dynamics of the disease. The algorithm is a message passing algorithm, based on
belief propagation, so each smart-phone can be used to execute a small part of
the algorithm without releasing any sensitive information. In this way, the
network of all participating smart-phones forms a distributed computation
device that performs Bayesian inference, informs each user when they should
start/end isolation or be tested and learns about the disease from user's data.
