  The dynamics of network social contagion processes such as opinion formation
and epidemic spreading are often mediated by interactions between multiple
nodes. Previous results have shown that these higher-order interactions can
profoundly modify the dynamics of contagion processes, resulting in
bistability, hysteresis, and explosive transitions. In this paper, we present
and analyze a hyperdegree-based mean-field description of the dynamics of the
SIS model on hypergraphs, i.e. networks with higher-order interactions, and
illustrate its applicability with the example of a hypergraph where contagion
is mediated by both links (pairwise interactions) and triangles (three-way
interactions). We consider various models for the organization of link and
triangle structure, and different mechanisms of higher-order contagion and
healing. We find that explosive transitions can be suppressed by heterogeneity
in the link degree distribution, when links and triangles are chosen
independently, or when link and triangle connections are positively correlated
when compared to the uncorrelated case. We verify these results with
microscopic simulations of the contagion process and with analytic predictions
derived from the mean-field model. Our results show that the structure of
higher-order interactions can have important effects on contagion processes on
hypergraphs.
