  Complex networks with pairwise connections have been vastly used for the
modeling of interactions within systems. Although these type of models are
capable to capture rich structures and different phases within a great variety
of situations, their lack of explicit higher order interactions might result,
in some contexts, limited. In this work a stochastic epidemic model on a
simplicial complex is defined, generalizing the known Markovian SIR epidemic
process on networks. By direct simulations and mean field analysis is shown
that already by the introduction of third order interactions through a simplex,
the SIR model can display important differences in its dynamics and stationary
states with respect to the pairwise version of the model.
