Spreading models usually assume pairwise contacts, but many real-world transmissions occur in groups, motivating the use of hypernetworks (hypergraphs).

We study the stochastic SI model on networks and hypernetworks and derive exact expressions for the expected infection level as a function of time, without making any kind of approximation.

A key qualitative difference emerges: on connected networks, the epidemic spreads out to the entire network for any positive initial infection level, while on connected hypernetworks, it may remain contained.

We show analytically that the solution undergoes a phase transition at a positive threshold, and relate this result to percolation theory.

Abstract