Topological data analysis model for the spread of the coronavirus

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.

[1]  Pawel Dlotko,et al.  Visualising the Evolution of English Covid-19 Cases with Topological Data Analysis Ball Mapper , 2020, ArXiv.

[2]  Herbert Edelsbrunner,et al.  Computational Topology - an Introduction , 2009 .

[3]  Konstantin Mischaikow,et al.  Topological data analysis of contagion maps for examining spreading processes on networks , 2015, Nature communications.

[4]  Derek Lo,et al.  Modeling the spread of the Zika virus using topological data analysis , 2016, PloS one.

[5]  Gunnar E. Carlsson,et al.  Topology and data , 2009 .

[6]  G. Carlsson,et al.  Topology of viral evolution , 2013, Proceedings of the National Academy of Sciences.

[7]  A TOPOLOGICAL DATA ANALYSIS APPROACH TO THE EPIDEMIOLOGY OF INFLUENZA , 2015 .

[8]  Mason A. Porter,et al.  A roadmap for the computation of persistent homology , 2015, EPJ Data Science.

[9]  Facundo Mémoli,et al.  Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition , 2007, PBG@Eurographics.

[10]  Emerson G. Escolar,et al.  Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics , 2019, ArXiv.

[11]  Paul Rosen,et al.  The Shape of an Image - A Study of Mapper on Images , 2017, VISIGRAPP.

[12]  G. Carlsson.  Persistent homology and applied homotopy theory , 2020, 2004.00738.

[13]  G. Carlsson,et al.  Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival , 2011, Proceedings of the National Academy of Sciences.

[14]  Paul T. Pearson,et al.  Analyze High-Dimensional Data Using Discrete Morse Theory , 2015 .