# Distance-amplified power-law distributions better characterize human long-distance travel

## TL;DR

This paper introduces a new model for human long-distance travel that improves upon traditional power-law assumptions, using real-world data and showing better accuracy for disease spread modeling.

## Contribution

The novel contribution is a distance-amplified power-law model that better captures long-distance trip distributions and improves disease spread predictions.

## Key findings

- Trip length distributions from real data deviate from traditional power-law assumptions.
- The new distance-amplified model outperforms conventional models in capturing mobility patterns.
- The model improves accuracy in simulating the spread of diseases like COVID-19.

## Abstract

Human mobility patterns have been the subject of research for many decades. Understanding long-distance trips is critical in our globalized world, for example, to model the spread of diseases. Traditional models generally assume that trip lengths follow a power-law distribution. We analyze over one million long-distance trips using three datasets: two survey-based (from Germany and the U.S.) and one from mobile network data in the U.K. We find that the observed trip length distributions deviate from typical power-law behavior, motivating a new approach. In addition, we examine COVID-19 spreading patterns in Germany and identify mobility dynamics that traditional power-law models fail to capture. To address these limitations, we introduce a model that extends the power-law framework by amplifying long-distance trips – based on the intuition that once a journey exceeds a certain length, the remaining distance is also likely to be substantial. Our experiments underscore the need for advanced models of long-distance travel and demonstrate that distance amplification can enhance the accuracy of conventional models.