Effective epidemic containment strategy in hypergraphs

TL;DR

This paper introduces a novel immunization strategy targeting hyperedges with high infection probability in hypergraphs, improving epidemic containment by identifying critical 'hotspot' hyperedges and outperforming existing methods.

Contribution

The paper proposes a new SIP-based immunization strategy for hypergraphs, generalizes existing edge importance methods, and demonstrates its effectiveness in epidemic containment.

Findings

SIP-based immunization outperforms EI-based methods in hypergraphs.

Immunizing high H-eigenscore hyperedges effectively contains epidemics.

SIP serves as a centrality measure for hyperedge influence.

Abstract

Recently, hypergraphs have attracted considerable interest from the research community as a generalization of networks capable of encoding higher-order interactions, which commonly appear in both natural and social systems. Epidemic dynamics in hypergraphs has been studied by using the simplicial susceptible-infected-susceptible ($s$-SIS) model; however, the efficient immunization strategy for epidemics in hypergraphs is not studied despite the importance of the topic in mathematical epidemiology. Here, we propose an immunization strategy that immunizes hyperedges with high simultaneous infection probability (SIP). This strategy can be implemented in general hypergraphs. We also generalize the edge epidemic importance (EI)-based immunization strategy, which is the state of the art in complex networks. However, it does not perform as well as the SIP-based method in hypergraphs despite its high computational cost. We also show that immunizing hyperedges with high H-eigenscore effectively contains the epidemics in uniform hypergraphs. A high SIP of a hyperedge suggests that the hyperedge is a "hotspot" of the epidemic process. Therefore, SIP can be used as a centrality measure to quantify a hyperedge's influence on higher-order dynamics in general hypergraphs. The effectiveness of the immunization strategies suggests the necessity of scientific, data-driven, systematic policy-making for epidemic containment.