A Universal Measure for Network Traceability

In today’s increasingly interconnected world, outbreaks of disease or contamination can spread widely and cause considerable impact on public health. Proactively assessing the ability to identify the source of an outbreak in a networked system is a critical step in aiding emergency and operational preparedness management prior to a crisis situation. While many methods have been developed to identify the source of an outbreak once it has occurred, limited research has been devoted to developing measures to assess the overall ability of a network structure to support accurate source identification, which we call traceability. Furthermore, while significant work has focused on understanding the role of network structure on propagation dynamics, its impact on traceability has yet remained unstudied. Here, we introduce a novel, comprehensive measure of network traceability, which calculates the information-theoretic entropy of the posterior probability distribution over feasible sources resulting from inferring the source location. By capturing information about the full posterior probability distribution, this measure presents an improvement over the binary logical outcome of the prediction accuracy metric generally applied to assess source identification method performance. Using food supply chain networks as an example, we use this measure to provide the first study systematically evaluating the role of network structural parameters on traceability, comparing both synthetic networks generated to exhibit a range of structural features known to be relevant to contamination propagation and real networks representing the Chinese pork supply chain across various cities. This analysis yields insights about the relationship between traceability and network structure, some counter-intuitive, and more generally, illustrates how this measure can be used in emergency and operational preparedness to proactively assess network traceability and recommend strategies for its improvement.