Laurent Hebert-Dufresne, Department of Computer Science, University of Vermont
Approximate master equations for contagions on higher-order networks
Simple models of contagions tend to assume random mixing of elements (e.g. people), 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. Likewise, not all groups are equivalent and important dynamical correlations can be missed by averaging over groups. To accurately describe spreading processes on these higher-order networks and correctly account for the heterogeneity of the underlying structure, we leverage an approximate master equations framework. This mathematical model allows us to unveil and characterize important properties of these systems. Here we focus on three of them: The localization of contagions within certain substructures, the bistability of the stationary state and optimal seeding strategies through influential groups. Altogether, these results highlight the complex behavior of contagions on higher-order networks, and the power of approximate master equations in capturing this complexity in a whole range of applications.