Topological data analysis of contagion maps for examining spreading processes on networks

Dane Taylor, Florian Klimm, Heather A. Harrington, Miroslav Kramár, Konstantin Mischaikow, Mason A. Porter, Peter J. Mucha

Research output: Contribution to journalArticlepeer-review

81 Scopus citations

Abstract

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges - for example, due to airline transportation or communication media - allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct 'contagion maps' that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.
Original languageEnglish (US)
JournalNature Communications
Volume6
Issue number1
DOIs
StatePublished - Jul 21 2015
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: D.T. and P.J.M. were partially supported by the Eunice Kennedy Shriver National Institute of Child Health & Human Development of the National Institutes of Health under Award Number R01HD075712. D.T. was also funded by the National Science Foundation under Grant DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute (SAMSI). D.T. also acknowledges an Institute of Mathematics and its Applications travel grant to attend the workshop Topology and Geometry of Networks and Discrete Metric Spaces. M.A.P. was supported by the European Commission FET-Proactive project PLEXMATH (Grant No. 317614) and also acknowledges a grant (EP/J001759/1) from the EPSRC. F.K.’s stay in Oxford was supported in part by the latter grant. H.A.H. gratefully acknowledges funding from EPSRC Fellowship EP/K041096/1, King Abdullah University of Science and Technology KUK-C1-013-04, a SAMSI Low-Dimensional Structure in High-Dimensional Data workshop travel grant and an AMS Simons travel grant. K.M. and M.K. were partially supported by NSF grants NSF-DMS-0915019, 1125174 and 1248071, and contracts from AFOSR and DARPA. We thank Yannis Kevrekidis and Barbara Mahler for discussions and numerous helpful comments on a version of this manuscript. We thank James Gleeson, Ezra Miller, Sayan Mukherjee and Hal Schenck for helpful discussions. The content is solely the responsibility of the authors and does not necessarily represent the official views of any of the funding agencies.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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