  Epidemic spreading is well understood when a disease propagates around a
contact graph.
  In a stochastic susceptible-infected-susceptible setting, spectral conditions
characterise whether the disease vanishes. However, modelling human
interactions using a graph is a simplification which only considers pairwise
relationships.
  This does not fully represent the more realistic case where people meet in
groups. Hyperedges can be used to record such group interactions, yielding more
faithful and flexible models, allowing for the rate of infection of a node to
vary as a nonlinear function of the number of infectious neighbors. We discuss
different types of contagion models in this hypergraph setting, and derive
spectral conditions that characterize whether the disease vanishes.
  We study both the exact individual-level stochastic model and a deterministic
mean field ODE approximation.
  Numerical simulations are provided to illustrate the analysis. We also
interpret our results and show how the hypergraph model allows us to
distinguish between contributions to infectiousness that (a) are inherent in
the nature of the pathogen and (b) arise from behavioural choices (such as
social distancing, increased hygiene and use of masks).
  This raises the possibility of more accurately quantifying the effect of
interventions that are designed to contain the spread of a virus.
