Effective Resistance for Pandemics: Mobility Network Sparsification for High-Fidelity Epidemic Simulation

TL;DR

This paper introduces a network sparsification method based on effective resistance to accurately simulate epidemics on large, dense mobility networks while significantly reducing computational costs.

Contribution

It demonstrates that effective resistance-based sparsification preserves epidemic dynamics and highlights key transmission links, outperforming simpler methods.

Findings

Sparse networks with less than 10% of edges retain epidemic behavior

Effective resistance prioritizes critical transmission pathways

Method reduces computational resources needed for epidemic simulations

Abstract

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.