  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.
