Source Detection in Hypergraph Epidemic Dynamics using a Higher-Order Dynamic Message Passing Algorithm

TL;DR

This paper introduces a higher-order dynamic message passing algorithm for detecting the source of epidemics in hypergraph models, improving accuracy over traditional pairwise network methods by accounting for group interactions.

Contribution

The study presents the HDMPN algorithm, a novel message-passing approach that incorporates higher-order interactions for more effective epidemic source detection.

Findings

HDMPN outperforms traditional likelihood maximization methods in most tested scenarios.

Incorporating higher-order structures improves source detection accuracy.

The algorithm effectively captures the influence of group interactions in epidemic spreading.

Abstract

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, whereas recent efforts on both mathematical modeling and analysis of contact data suggest that higher-order (e.g., group) interactions among individuals may both account for a large fraction of infection events and change our understanding of how epidemic spreading proceeds in empirical populations. In the present study, we propose a message-passing algorithm, called the HDMPN, for source detection for a stochastic susceptible-infectious dynamics on hypergraphs. By modulating the likelihood maximization method by the fraction of infectious neighbors, HDMPN aims to capture the influence of higher-order structures and do better than the conventional likelihood maximization. We numerically show that, in most cases, HDMPN outperforms benchmarks including the likelihood maximization method without modification.