Triadic approximation for contagions on higher-order networks

Contagion processes relying on the exposure to multiple sources are prevalent in both social and biochemical systems, and are effectively represented by hypergraphs. In our study, we consider up to three-body interactions and derive a mean-field model that moves beyond standard node- and pair-based approximations. This approach reveals how the stability of the inactive state is influenced by both two- and three-body interactions, and relates it to the degree of overlap between these interactions. Our findings demonstrate the dual effect of an increased overlap: it leads to a lower invasion threshold, but results in smaller outbreaks. Corroborated by numerical simulations, our results emphasize the significance of the chosen representation in describing a higher-order process.