  Mathematical modeling of epidemic propagation on networks is extended to
hypergraphs in order to account for both the community structure and the
nonlinear dependence of the infection pressure on the number of infected
neighbours. The exact master equations of the propagation process are derived
for an arbitrary hypergraph given by its incidence matrix. Based on these,
moment closure approximation and mean-field models are introduced and compared
to individual-based stochastic simulations. The simulation algorithm, developed
for networks, is extended to hypergraphs. The effects of hypergraph structure
and the model parameters are investigated via individual-based simulation
results.
