Characteristic scales and adaptation in higher-order contagions

Area of Science:

• Complex Systems Science
• Network Science
• Mathematical Modeling

Background:

• Contagions spread through organized groups, but modeling these processes is complex due to dynamic correlations and group evolution.
• Existing analytical models often fail to account for both dynamical correlations and agent adaptation within groups.

Purpose of the Study:

• To develop an analytical model for contagion dynamics in adaptive group structures, considering correlations and agent adaptation.
• To analyze how group-level versus individual-level dynamics affect nonlinear contagions.
• To identify optimal group activity levels for agent adaptation.

Main Methods:

• Introduction of the generalized approximate master equations method.
• Analysis of nonlinear contagion dynamics driven by group-level and individual-level factors.
• Study of adaptive hypergraphs to model group structure evolution.

Main Results:

• The generalized approximate master equations provide a highly accurate model for binary-state dynamics on hypergraphs.
• New dynamical regimes and distinct adaptation strategies are unlocked by group structure.
• Understanding the characteristic levels of group activity is crucial for optimizing agent adaptation.

Conclusions:

• The developed method advances the understanding of contagion processes in complex, adaptive group systems.
• Group structure plays a critical role in shaping contagion spread and enabling specific adaptation strategies.
• This work opens new avenues for studying adaptive group-structured systems and their emergent behaviors.