Locating the source of large-scale outbreaks of foodborne disease.

In today's globally interconnected food system, outbreaks of foodborne disease can spread widely and cause considerable impact on public health. We study the problem of identifying the source of emerging large-scale outbreaks of foodborne disease; a crucial step in mitigating their proliferation. To solve the source identification problem, we formulate a probabilistic model of the contamination diffusion process as a random walk on a network and derive the maximum-likelihood estimator for the source location. By modelling the transmission process as a random walk, we are able to develop a novel, computationally tractable solution that accounts for all possible paths of travel through the network. This is in contrast to existing approaches to network source identification, which assume that the contamination travels along either the shortest or highest probability paths. We demonstrate the benefits of the multiple-paths approach through application to different network topologies, including stylized models of food supply network structure and real data from the 2011 Shiga toxin-producing Escherichia coli outbreak in Germany. We show significant improvements in accuracy and reliability compared with the relevant state-of-the-art approach to source identification. Beyond foodborne disease, these methods should find application in identifying the source of spread in network-based diffusion processes more generally, including in networks not well approximated by tree-like structure.