Effective resistance against pandemics: Mobility network sparsification for high-fidelity epidemic simulations

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 not just large, but dense, with a high ratio of edges to nodes. This includes human mobility networks where most locations have a large number of links to many other locations. Simulating large-scale epidemics 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 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 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 both global quantities, like the epidemic size, and local details of stochastic events, 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. Author summary Epidemiologists increasingly use social networks to understand how geography, demographics, and human mobility affect disease spread and the effectiveness of intervention strategies. While highly detailed data on human social networks are now available, the size and density of these modern networks makes them computationally intensive to study. To address this challenge, we study methods for reducing a network to its most important links. Following recent work in computer science, we use the effective resistance, which takes both local and global connectivity into account. We test this method in simulations on a U.S.-wide mobility network and find that it preserves epidemic dynamics with high fidelity. Combined with efficient epidemic simulation algorithms, our approach can facilitate a more effective response to epidemics.