  The hypergraph offers a platform to study structural properties emerging from
more complicated and higher-order than pairwise interactions among constituents
and dynamical behavior such as the spread of information or disease. Recently,
a simplicial contagion problem was introduced and considered using a simplicial
susceptible-infected-susceptible (SIS) model. Although recent studies have
investigated random hypergraphs with a Poisson-type facet degree distribution,
hypergraphs in the real world can have a power-law type of facet degree
distribution. Here, we consider the SIS contagion problem on scale-free uniform
hypergraphs and find that a continuous or hybrid epidemic transition occurs
when the hub effect is dominant or weak, respectively. We determine the
critical exponents analytically and numerically. We discuss the underlying
mechanism of the hybrid epidemic transition.
