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We study the problem of estimating the origin of an epidemic outbreak --given a contact network and a snapshot of epidemic spread at a certain time,determine the infection source. Finding the source is important in differentcontexts of computer or social networks. We assume that the epidemic spreadfollows the most commonly used susceptible-infected-recovered model. Weintroduce an inference algorithm based on dynamic message-passing equations,and we show that it leads to significant improvement of performance compared toexisting approaches. Importantly, this algorithm remains efficient in the casewhere one knows the state of only a fraction of nodes.

Inferring the origin of an epidemic with a dynamic message-passing algorithm