# Epidemic Outbreaks on Random Delaunay Triangulations

## TL;DR

This paper investigates epidemic spread on random Delaunay triangulations using a kinetic Monte Carlo SIR model, revealing that the system exhibits 2D dynamic percolation behavior with quenched disorder being irrelevant.

## Contribution

It introduces a novel application of the Newman-Ziff algorithm to study epidemic thresholds on inhomogeneous Delaunay triangulations, connecting epidemic dynamics with percolation theory.

## Key findings

- Epidemic thresholds align with 2D dynamic percolation universality class.
- Quenched random disorder does not affect the critical behavior.
- The model accurately estimates percolation observables on complex lattices.

## Abstract

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.