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 everyones 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 users data.
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