Self-similarity in pandemic spread and fractal containment policies

TL;DR

This paper introduces a fractal-based approach to modeling pandemic spread across multiple geographic scales, enabling the design of effective multi-scale containment policies that balance health and economic considerations.

Contribution

It develops a multi-scale reproduction number framework and demonstrates how fractal transmission models can inform containment strategies across different geographic levels.

Findings

Multi-scale reproduction numbers predict disease spread at various levels.

Containment is possible if a scale exists with reproduction number below 1.

Simulations support the effectiveness of multi-scale strategies.

Abstract

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.