Self-similarity in pandemic spread and fractal containment policies
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915061023375360 |
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| author | Siegenfeld, Alexander F. Orioli, Asier Piñeiro Na, Robin Elias, Blake Bar-Yam, Yaneer |
| author_facet | Siegenfeld, Alexander F. Orioli, Asier Piñeiro Na, Robin Elias, Blake Bar-Yam, Yaneer |
| contents | 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 $R_0$ -- 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 $R_0$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similarity in pandemic spread and fractal containment policies Siegenfeld, Alexander F. Orioli, Asier Piñeiro Na, Robin Elias, Blake Bar-Yam, Yaneer Populations and Evolution Physics and Society Quantitative Methods 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 $R_0$ -- 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 $R_0$ 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. |
| title | Self-similarity in pandemic spread and fractal containment policies |
| topic | Populations and Evolution Physics and Society Quantitative Methods |
| url | https://arxiv.org/abs/2412.09021 |