Adaptive hypergraphs and the characteristic scale of higher-order contagions using generalized approximate master equations

TL;DR

This paper develops master equations for adaptive hypergraphs to model higher-order contagion dynamics, revealing regimes of beneficial and detrimental adaptation, and advancing understanding of complex group-based spreading processes.

Contribution

It introduces a novel framework of adaptive hypergraphs with master equations, capturing higher-order interactions and adaptive rewiring in contagion models.

Findings

Identification of bistability in contagion dynamics.

Discovery of regimes with beneficial, detrimental, and optimal rewiring.

Insights into higher-order adaptation and self-organized hypergraphs.

Abstract

People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To study the characteristic levels of group activity required to best model dynamics and for agents to adapt, we develop master equations for adaptive hypergraphs, finding bistability and regimes of detrimental, beneficial, and optimal rewiring, at odds with adaptation on networks. Our study paves the way for higher-order adaptation and self-organized hypergraphs.