Travel distance, frequency of return and the spread of disease

TL;DR

This paper investigates how the invariant product of travel distance and return frequency influences the spread of disease, providing insights for modeling epidemics and informing travel policies.

Contribution

It reveals a simple relation between travel distance and return frequency that impacts disease spread, offering a unifying variable for epidemic modeling.

Findings

The product r·f is invariant across space.

r·f correlates with speed of disease spread.

The relation informs travel policy design.

Abstract

In 2020 and 2021, the spread of COVID-19 was globally addressed by imposing restrictions on the distance of individual travel. Recent literature has uncovered a clear pattern in human mobility that underlies the complexity of urban mobility: $r \cdot f$, the product of distance traveled $r$ and frequency of return $f$ per user to a given location, is invariant across space. This paper asks whether the invariant $r\cdot f$ also serves as a driver for epidemic spread, so that the risk associated with human movement can be modeled by a unifying variable $r\cdot f$. We use two large-scale datasets of individual human mobility to show that there is in fact a simple relation between $r$ and $f$ and both speed and spatial dispersion of disease spread. This discovery could assist in modeling spread of disease and inform travel policies in future epidemics -- based not only on travel distance $r$ but also on frequency of return $f$.