Effective Resistance Against Pandemics: Which Links Matter in Mobility Network Sparsification?

Abstract: Network science has increasingly become central to the field of infectious disease epidemiology. However, many networks derived from modern datasets are not just large, but dense, with a high average degree. One way to reduce the computational cost of simulating epidemics on these networks is sparsification, where an edge subset is selected based on some measure of their importance. Looking at recent work in computer science, we find that the most accurate approach uses the effective resistance of edges, which prioritizes edges that are the most efficient way to travel between their endpoints. The resulting sparse network preserves both the local and global behavior of the SIR model, including the probability each node becomes infected and its distribution of arrival times. This holds even when the sparse network preserves less than 10% of the edges of a mobility network from the United States. Thresholding the number of edges by edge weight or similar purely topological methods do not perform nearly as well. In addition to the practical utility, sparsifying using effective resistances helps illuminate which links of a network are most important to disease spread.