  We study epidemic outbreaks on random Delaunay triangulations by applying
Asynchronous SIR (susceptible-infected-removed) model kinetic Monte Carlo
dynamics coupled to lattices extracted from the triangulations. In order to
investigate the critical behavior of the model, we obtain the cluster size
distribution by using Newman-Ziff algorithm, allowing to simulate random
inhomogeneous lattices and measure any desired percolation observable. We
numerically calculate the order parameter, defined as the wrapping cluster
density, the mean cluster size, and Binder cumulant ratio defined for
percolation in order to estimate the epidemic threshold. Our findings suggest
that the system falls into two-dimensional dynamic percolation universality
class and the quenched random disorder is irrelevant, in agreement with results
for classical percolation.
