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Phase transitions in contagion processes mediated by recurrent mobility patterns

Nature Physics volume 7, pages 581586 (2011) | Download Citation

Abstract

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumours, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modelled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyse contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous deterministic models because of the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behaviour by analysing diffusion processes mediated by real human commuting data.

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Acknowledgements

We would like to thank to C. Poletto and V. Colizza for interesting discussions during the preparation of this manuscript. This work was partially funded by the NIH R21-DA024259 award and the DTRA-1-0910039 award to A.V.; the work was also partly sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government.

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Affiliations

  1. Center for Complex Networks and Systems Research (CNetS), School of Informatics and Computing, Indiana University, Bloomington, Indiana 47408, USA

    • Duygu Balcan
    •  & Alessandro Vespignani
  2. Pervasive Technology Institute, Indiana University, Bloomington, Indiana 47406, USA

    • Duygu Balcan
    •  & Alessandro Vespignani
  3. Institute for Scientific Interchange (ISI), Torino 10133, Italy

    • Alessandro Vespignani

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Contributions

D.B. and A.V. conceived and executed the study, performed the analytical calculations and drafted the manuscript. D.B. performed the numerical simulations.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Alessandro Vespignani.

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DOI

https://doi.org/10.1038/nphys1944

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