Triadic approximation for contagions on higher-order networks

Based on mechanisms of social reinforcement, complex contagion processes where transmission depends on the simultaneous exposure to multiple sources are a peculiar feature of human social systems. Such processes rely on many-body interactions and hypergraphs provide a suitable representation for them. Considering up to three-body interactions, we derive a mean-field model going beyond limiting node- and pair-based approximations. We reveal in this way how the stability of the contagion-free state is affected by both the two- and the three-body infection rates, and relate it to the degree of overlap between three- and two-body interactions. We show the double-edged effect of an increased overlap, yielding a lower critical point but at the expense of a smaller outbreak. Our results, corroborated by numerical simulations on hypergraphs which are either synthetic or constructed from real-world proximity data, underline the importance of the chosen representation to describe a higher-order process.