Effective Resistance Sampling

Network science has increasingly become central to the field of epidemiology and our ability to respond to infectious disease threats. However, many networks derived from modern datasets are very dense, such as mobility networks where each location has links to a large number of destinations. As a result, simulating large-scale epidemics using data-driven networks requires substantial computational resources and in many cases is practically infeasible. One way to reduce the computational cost of simulating epidemics on these networks is \emph{sparsification}, where a representative subset of edges is selected based on some measure of their importance. We test several sparsification strategies, ranging from naive thresholding to random sampling of edges, on mobility data from the U.S. Following recent work in computer science, we find that the most accurate approach uses the \emph{effective resistances} of edges, which prioritizes edges that are the only efficient way to travel between their endpoints. The resulting sparse network preserves many aspects of the behavior of an SIR model, including global quantities, like the epidemic size, and details of stochastic events at individual nodes, including the probability each node becomes infected and its distribution of arrival times. This holds even when the sparse network preserves fewer than 10% of the edges of the original network. In addition to its practical utility, this method helps illuminate which links of a weighted, undirected network are most important to disease spread.