[Paper Review] Visualising the Evolution of English Covid-19 Cases with Topological Data Analysis Ball Mapper

Pawel Dlotko, Simon Rudkin|arXiv (Cornell University)|Apr 7, 2020

Topological and Geometric Data Analysis12 references4 citations

TL;DR

This paper applies the Ball Mapper algorithm from Topological Data Analysis to visualize the evolution of Covid-19 cases across English NUTS3 regions using socio-economic indicators. It reveals non-linear, cluster-based spread patterns, showing that infection hotspots emerge in specific socio-economic groupings rather than uniformly, with London and Northern industrial regions showing distinct, accelerating case growth despite similar proximity.

ABSTRACT

Understanding disease spread through data visualisation has concentrated on trends and maps. Whilst these are helpful, they neglect important multi-dimensional interactions between characteristics of communities. Using the Topological Data Analysis Ball Mapper algorithm we construct an abstract representation of NUTS3 level economic data, overlaying onto it the confirmed cases of Covid-19 in England. In so doing we may understand how the disease spreads on different socio-economical dimensions. It is observed that some areas of the characteristic space have quickly raced to the highest levels of infection, while others close by in the characteristic space, do not show large infection growth. Likewise, we see patterns emerging in very different areas that command more monitoring. A strong contribution for Topological Data Analysis, and the Ball Mapper algorithm especially, in comprehending dynamic epidemic data is signposted.

Motivation & Objective

• To visualize the spatiotemporal evolution of Covid-19 cases in England beyond traditional maps and trends.
• To apply Topological Data Analysis, specifically the Ball Mapper algorithm, to uncover hidden patterns in multi-dimensional socio-economic data.
• To identify how specific combinations of economic and demographic characteristics correlate with rapid infection growth.
• To demonstrate the transparency and interpretability of Ball Mapper compared to black-box ML models in epidemic data analysis.
• To inspire policy-relevant insights by revealing non-linear, non-geographic dynamics in disease spread across socio-economic space.

Proposed method

• The Ball Mapper algorithm constructs a 2D abstract representation of high-dimensional NUTS3 region data by covering the data cloud with overlapping balls of radius ε.
• Landmarks are selected as centers of balls, with edges connecting overlapping balls to form a graph structure.
• The size of each ball in the graph reflects the number of data points it contains, indicating cluster density.
• Covid-19 case counts are overlaid on the Ball Mapper graph to visualize infection levels across socio-economic clusters.
• Dynamic evolution of case numbers is tracked per ball over time using time-series plots of average cases per ball.
• The method avoids full distance matrices (unlike t-SNE) and requires only one parameter (ε), ensuring stability and interpretability.

Experimental results

Research questions

• RQ1 How do socio-economic characteristics of English NUTS3 regions correlate with the rate and intensity of Covid-19 case growth?
• RQ2 Where in the multi-dimensional socio-economic space do infection clusters emerge, and how do they evolve over time?
• RQ3 To what extent do regions with similar geographic proximity but different socio-economic profiles exhibit divergent epidemic trajectories?
• RQ4 Can the Ball Mapper algorithm reveal non-linear, non-intuitive patterns in disease spread that are missed by standard visualizations?
• RQ5 How does the dynamic evolution of case numbers across Ball Mapper clusters inform public health monitoring and policy response?

Key findings

• Ball 20, originally the highest-case region (Hammersmith and Fulham & Kensington and Chelsea), saw a decline in case growth, while Ball 22 overtook it as the new hotspot.
• London boroughs and commuter areas (Ball 22) are now recording more cases than the original London hotspot, indicating a shift in transmission dynamics.
• Balls 9 and 14 in the North of England, particularly in Lancashire and Yorkshire, showed the fastest-growing case proportions, suggesting emerging regional hotspots.
• Ball 7, encompassing cities like Manchester, Liverpool, and Bristol, acted as a conduit to these northern clusters, with increasing case proportions over time.
• The dynamic case evolution plots show no flattening of curves in most clusters except Ball 20, indicating sustained or rising transmission in other regions.
• Regions with similar geographic proximity but different socio-economic profiles—such as London vs. its commuter towns—exhibited markedly different epidemic trajectories, highlighting the importance of socio-economic context.