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Laurent Hebert-Dufresne, Department of Computer Science, University of Vermont

Approximate master equations forÌýcontagions on higher-order networks

Simple models of contagions tend to assume random mixing of elements (e.g.Ìýpeople), but real interactions are not random pairwise encounters: they occur within clearly defined higher-order structures (e.g. communities) which can be heterogeneous in size and nature.ÌýLikewise, not all groups are equivalent and important dynamical correlations can be missed by averaging over groups.ÌýTo accurately describe spreading processes on these higher-order networks and correctly account for the heterogeneity of the underlying structure, we leverage anÌýapproximate master equations framework. This mathematicalÌýmodelÌýallows us to unveil and characterize important properties of these systems. Here we focus on threeÌýof them: TheÌýlocalization of contagions within certain substructures, the bistability of the stationary state andÌýoptimal seeding strategies through influential groups.ÌýAltogether, these results highlight the complex behaviorÌýof contagions on higher-order networks, and the power of approximate master equations in capturingÌýthis complexityÌýinÌýa whole range of applications.