Papers › Self-similarity in pandemic spread and fractal containment policies
Self-similarity in pandemic spread and fractal containment policies
Alexander F. Siegenfeld, Asier Piñeiro Orioli, Robin Na, Blake Elias, Yaneer Bar-Yam
Although pandemics are often studied as if populations are well-mixed, disease transmission networks exhibit a multi-scale structure stretching from the individual all the way up to the entire globe. The COVID-19 pandemic has led to an intense debate about whether interventions should prioritize public health or the economy, leading to a surge of studies analyzing the health and economic costs of various response strategies. Here we show that describing disease transmission in a self-similar (fractal) manner across multiple geographic scales allows for the design of multi-scale containment measures that substantially reduce both these costs. We characterize response strategies using multi-scale reproduction numbers -- a generalization of the basic reproduction number R₀ -- that describe pandemic spread at multiple levels of scale and provide robust upper bounds on disease transmission. Stable elimination is guaranteed if there exists a scale such that the reproduction number among regions of that scale is less than 1, even if the basic reproduction number R₀ is greater than 1. We support our theoretical results using simulations of a heterogeneous SIS model for disease spread in the United States constructed using county-level commuting, air travel, and population data.
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