Unveiling the impact of cross-order hyperdegree correlations in contagion processes on hypergraphs

TL;DR

This paper introduces an effective hyperdegree model for contagion on hypergraphs that accounts for correlations between different interaction orders, revealing their impact on epidemic thresholds and control strategies.

Contribution

It develops a novel model capturing cross-order degree correlations in hypergraphs, improving understanding of contagion dynamics beyond independent assumptions.

Findings

Positive correlation lowers epidemic threshold.

Anti-correlation desynchronizes infection pathways.

Optimal control strategies depend on correlation levels.

Abstract

Contagion processes in social systems often involve interactions that go beyond pairwise contacts. Higher-order networks, represented as hypergraphs, have been widely used to model multi-body interactions, and their presence can drastically alter contagion dynamics compared to traditional network models. However, existing analytical approaches typically assume independence between pairwise and higher-order degrees, and thus study their roles in isolation. In this paper, we develop an effective hyperdegree model (EHDM) to describe Susceptible-Infected-Susceptible (SIS) dynamics on hypergraphs that explicitly captures correlations between the distribution of groups with different sizes. Our effective hyperdegree model shows excellent agreement with stochastic simulations across different types of higher-order networks, including those with heterogeneous degree distributions. We explore the critical role of cross-order degree correlations, specifically, whether nodes that are hubs in pairwise interactions also serve as hubs in higher-order interactions. We show that positive correlation decreases the epidemic threshold and anti-correlation temporally desynchronizes infection pathways (pairwise and group interactions). Finally, we demonstrate that, depending on the level of correlation, the optimal control strategy shifts -- from one that is purely pairwise- or higher-order-focused to one in which a mixed strategy becomes optimal.