Characteristic scales and adaptation in higher-order contagions

TL;DR

This paper introduces a new analytical method to model complex contagion processes on adaptive hypergraphs, accounting for group dynamics and correlations, revealing new regimes and strategies for contagion spread and adaptation.

Contribution

The paper develops generalized approximate master equations to accurately model higher-order contagions with adaptive group structures, addressing previous analytical limitations.

Findings

Nonlinear contagions differ when driven by group vs. individual dynamics

Characteristic group activity levels optimize contagion adaptation

Group structure enables new dynamical regimes and adaptation strategies

Abstract

People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to contagions. To address the lack of analytical models that account for dynamical correlations and adaptation in groups, we introduce the method of generalized approximate master equations. We first analyze how nonlinear contagions differ when driven by group-level or individual-level dynamics. We then study the characteristic levels of group activity that best describe the stochastic process and that optimize agents' ability to adapt to it. Naturally lending itself to study adaptive hypergraphs, our method reveals how group structure unlocks new dynamical regimes and enables distinct suitable adaptation strategies. Our approach offers a highly accurate model of binary-state dynamics on hypergraphs, advances our understanding of contagion processes, and opens the study of adaptive group-structured systems.