Locally Dependent Random Graphs and their use in the Study of Epidemic Models

Abstract

A locally dependeni random graph is a generalization of directed bond and site percolation processes, where the dependence structure of the bonds from any particular site being open is general. The marginal probabilities for different bonds being open need not be equal, so that it is possible that there are an infinite number of bonds from a site. This paper summarizes some results about locally dependent random graphs and shows how they have been used to investigate the threshold behaviour of a continuous time spatial general epidemic model.