Epidemic outbreaks on random Voronoi–Delaunay triangulations.

Abstract

We study epidemic outbreaks on random Delaunay triangulations by applying the Asynchronous SIR (susceptible–infected–removed) dynamics coupled to two-dimensional Voronoi–Delaunay 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 observable related to percolation. 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.