Source detection in epidemic dynamics on hypergraphs using a dynamic message passing algorithm

Source detection is crucial for capturing the dynamics of real-world infectious diseases and informing effective containment strategies. Most existing approaches to source detection focus on conventional pairwise networks. However, emerging studies on the mathematical modeling and analysis of empirical contact data reveal that group-based interaction patterns, captured naturally by hypergraph representations, constitute a significant portion of infection events and are reshaping our understanding of epidemic propagation in real-world populations. In the present study, we propose a message passing algorithm, called the HDMPN, for source detection for a stochastic susceptible-infectious dynamics in which infection events within the hyperedge occur in a correlated manner. The HDMPN modifies the likelihood maximization with the use of the proportion of infectious neighbors, thus incorporating the information on hyperedges. We numerically show that, in most cases, the HDMPN outperforms benchmarks, including the likelihood maximization method without modification.