  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 different
contexts of computer or social networks. We assume that the epidemic spread
follows the most commonly used susceptible-infected-recovered model. We
introduce an inference algorithm based on dynamic message-passing equations,
and we show that it leads to significant improvement of performance compared to
existing approaches. Importantly, this algorithm remains efficient in the case
where one knows the state of only a fraction of nodes.
