Which links matter most? Sparsifying epidemic models with effective resistance, Cristopher Moore:

https://youtu.be/Ln_CIhxV840

Network science has increasingly become central to the field of 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 a subset of edges is selected and reweighted based on some measure of their importance. Following recent work in computer science, we find that the most accurate approach uses the effective resistances of edges, which can be computed from the graph Laplacian. 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. Our work helps illuminate which links of a network are most important to disease spread. Defining edge importance using purely topological methods, or by thresholding edge weights, does not perform nearly as well.