Topological data analysis model for the spread of the coronavirus

TL;DR

This paper demonstrates how topological data analysis, using the Mapper algorithm, can visualize and analyze the spread of COVID-19 across the U.S., capturing growth patterns and regional hot-spots.

Contribution

It introduces the application of Mapper to COVID-19 data, providing more comprehensive visualizations than traditional methods and highlighting its potential for prediction.

Findings

Mapper graphs reveal pandemic development across the U.S.

They encode geometric features of COVID-19 data.

Graphs facilitate comparison over time and regions.

Abstract

We apply topological data analysis, specifically the Mapper algorithm, to the U.S. COVID-19 data. The resulting Mapper graphs provide visualizations of the pandemic that are more complete than those supplied by other, more standard methods. They encode a variety of geometric features of the data cloud created from geographic information, time progression, and the number of COVID-19 cases. They reflect the development of the pandemic across all of the U.S. and capture the growth rates as well as the regional prominence of hot-spots. The Mapper graphs allow for easy comparisons across time and space and have the potential of becoming a useful predictive tool for the spread of the coronavirus.