Epidemic Source Detection in Contact Tracing Networks: Epidemic Centrality in Graphs and Message-Passing Algorithms

TL;DR

This paper introduces a novel statistical centrality measure and message-passing algorithms for epidemic source detection in contact networks, demonstrating improved accuracy over existing methods on real-world pandemic data.

Contribution

It develops a new graph-based likelihood framework and efficient algorithms for epidemic source detection, especially in complex cyclic contact networks.

Findings

Algorithms outperform state-of-the-art heuristics on real pandemic data.

Effective identification of superspreaders in large infection clusters.

Mathematical equivalence established between acyclic and cyclic graph cases.

Abstract

We study the epidemic source detection problem in contact tracing networks modeled as a graph-constrained maximum likelihood estimation problem using the susceptible-infected model in epidemiology. Based on a snapshot observation of the infection subgraph, we first study finite degree regular graphs and regular graphs with cycles separately, thereby establishing a mathematical equivalence in maximal likelihood ratio between the case of finite acyclic graphs and that of cyclic graphs. In particular, we show that the optimal solution of the maximum likelihood estimator can be refined to distances on graphs based on a novel statistical distance centrality that captures the optimality of the nonconvex problem. An efficient contact tracing algorithm is then proposed to solve the general case of finite degree-regular graphs with multiple cycles. Our performance evaluation on a variety of graphs shows that our algorithms outperform the existing state-of-the-art heuristics using contact tracing data from the SARS-CoV 2003 and COVID-19 pandemics by correctly identifying the superspreaders on some of the largest superspreading infection clusters in Singapore and Taiwan.