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

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