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Topological Data Analysis of Mortality Patterns During the COVID-19 Pandemic

Megan Fairchild, Matthew Lemoine

TL;DR

This work applies Topological Data Analysis to CDC weekly mortality data across the US during 2020–2023, employing persistent homology via Vietoris-Rips streams and the Mapper algorithm to reveal the data's shape at national and regional scales. By comparing analyses with and without date information, and by projecting data through PCA before Mapper and DBSCAN clustering, the study demonstrates that the national topology is heavily influenced by temporal structure, while regional topologies reflect geography and policy (e.g., lockdowns) differences. The combined barcode and Mapper insights identify distinct outliers (e.g., California in the West; New York/New York City in the Northeast; Texas and Florida in the South) and show how dates amplify or attenuate clustering, offering a topological perspective on pandemic mortality dynamics. The findings highlight the potential of TDA as a tool for epidemiological data interpretation and regional policy assessment, with implications for analyzing similar time-varying public health datasets.

Abstract

Topological Data Analysis is a relatively new field of study that uses topological invariants to study the shape of data. We analyze a dataset provided by the Centers for Disease Control and Prevention (CDC) using persistent homology and MAPPER. This dataset tracks mortality week-to-week from January 2020 to September 2023 in the United States during the COVID-19 pandemic. We examine the dataset as a whole and break the United States into geographic regions to analyze the overall shape of the data. Then, to explain this shape, we discuss events around the time of the pandemic and how they contribute to the observed patterns.

Topological Data Analysis of Mortality Patterns During the COVID-19 Pandemic

TL;DR

This work applies Topological Data Analysis to CDC weekly mortality data across the US during 2020–2023, employing persistent homology via Vietoris-Rips streams and the Mapper algorithm to reveal the data's shape at national and regional scales. By comparing analyses with and without date information, and by projecting data through PCA before Mapper and DBSCAN clustering, the study demonstrates that the national topology is heavily influenced by temporal structure, while regional topologies reflect geography and policy (e.g., lockdowns) differences. The combined barcode and Mapper insights identify distinct outliers (e.g., California in the West; New York/New York City in the Northeast; Texas and Florida in the South) and show how dates amplify or attenuate clustering, offering a topological perspective on pandemic mortality dynamics. The findings highlight the potential of TDA as a tool for epidemiological data interpretation and regional policy assessment, with implications for analyzing similar time-varying public health datasets.

Abstract

Topological Data Analysis is a relatively new field of study that uses topological invariants to study the shape of data. We analyze a dataset provided by the Centers for Disease Control and Prevention (CDC) using persistent homology and MAPPER. This dataset tracks mortality week-to-week from January 2020 to September 2023 in the United States during the COVID-19 pandemic. We examine the dataset as a whole and break the United States into geographic regions to analyze the overall shape of the data. Then, to explain this shape, we discuss events around the time of the pandemic and how they contribute to the observed patterns.
Paper Structure (22 sections, 19 figures, 3 tables)

This paper contains 22 sections, 19 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Vietoris-Rips Streams
  4. Methods and Data
  5. Code details and parameters
  6. Barcode Analysis
  7. Overarching Notes
  8. Whole US
  9. West
  10. Midwest
  11. Northeast
  12. South
  13. Non-Contiguous US
  14. Mapper Analysis
  15. Whole US
  16. ...and 7 more sections

Figures (19)

  • Figure 4.1: The Whole US barcodes, where the $x$-axis is our time.
  • Figure 4.2: The West barcodes, where the $x$-axis is our time.
  • Figure 4.3: The Midwest barcodes, where the $x$-axis is our time.
  • Figure 4.4: The Northeast barcodes, where the $x$-axis is our time.
  • Figure 4.5: The South barcodes, where the $x$-axis is our time.
  • ...and 14 more figures

Theorems & Definitions (1)

  • Definition 2.1: Vietoris-Rips Stream javaplex