- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Message-passing approach to epidemic tracing and mitigation with apps

Ginestra Bianconi

Hanlin Sun

Giacomo Rapisardi

Alex Arenas

  • School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom and The Alan Turing Institute, 96 Euston Rd., London NW1 2DB, United Kingdom

  • School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom

  • Barcelona Supercomputing Center (BSC) and Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain

  • Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain

PDF

Phys. Rev. Research 3, L012014 – Published 8 February, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012014

Abstract

With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message-passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (34)

  1. A.-L. Barabási, Network Science (Cambridge University Press, Cambridge, UK, 2016).
  2. M. Newman, Networks: An Introduction (Oxford University Press, New York, 2018).
  3. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Critical phenomena in complex networks, Rev. Mod. Phys. 80, 1275 (2008).
  4. R. Cohen and S. Havlin, Complex Networks: Structure, Robustness and Function (Cambridge University Press, Cambridge, UK, 2010).
  5. A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, UK, 2008).
  6. R. Albert, H. Jeong, and A.-L. Barabási, Error and attack tolerance of complex networks, Nature (London) 406, 378 (2000).
  7. R. Cohen, K. Erez, D. ben Avraham, and S. Havlin, Resilience of the Internet to Random Breakdowns, Phys. Rev. Lett. 85, 4626 (2000).
  8. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Structure of Growing Networks with Preferential Linking, Phys. Rev. Lett. 85, 4633 (2000).
  9. M. E. J. Newman, Spread of epidemic disease on networks, Phys. Rev. E 66, 016128 (2002).
  10. R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, Epidemic processes in complex networks, Rev. Mod. Phys. 87, 925 (2015).
  11. L. Ferretti, C. Wymant, M. Kendall, L. Zhao, A. Nurtay, L. Abeler-Dörner, M. Parker, D. Bonsall, and C. Fraser, Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing, Science 368, eabb6936 (2020).
  12. M. Chinazzi, J. T. Davis, M. Ajelli, C. Gioannini, M. Litvinova, S. Merler, A. Pastore y Piontti, K. Mu, L. Rossi, K. Sun, C. Viboud, X. Xiong, H. Yu, M. E. Halloran, I. M. Longini, and A. Vespignani, The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak, Science 368, 395 (2020).
  13. C. Fraser, S. Riley, R. M. Anderson, and N. M. Ferguson, Factors that make an infectious disease outbreak controllable, Proc. Natl. Acad. Sci. USA 101, 6146 (2004).
  14. S. Kojaku, L. Hébert-Dufresne, and Y.-Y. Ahn, The effectiveness of contact tracing in heterogeneous networks, arXiv:2005.02362 (2020).
  15. B. Karrer and M. E. J. Newman, Message passing approach for general epidemic models, Phys. Rev. E 82, 016101 (2010).
  16. B. Karrer, M. E. J. Newman, and L. Zdeborová, Percolation on Sparse Networks, Phys. Rev. Lett. 113, 208702 (2014).
  17. G. Bianconi, Multilayer Networks: Structure and Function (Oxford University Press, New York, 2018).
  18. F. Radicchi and G. Bianconi, Redundant Interdependencies Boost the Robustness of Multiplex Networks, Phys. Rev. X 7, 011013 (2017).
  19. G. T. Cantwell and M. E. J. Newman, Message passing on networks with loops, Proc. Natl. Acad. Sci. USA 116, 23398 (2019).
  20. F. Altarelli, A. Braunstein, L. Dall'Asta, J. R. Wakeling, and R. Zecchina, Containing Epidemic Outbreaks by Message-Passing Techniques, Phys. Rev. X 4, 021024 (2014).
  21. L. Lü, D. Chen, X.-L. Ren, Q.-M. Zhang, Y.-C. Zhang, and T. Zhou, Vital nodes identification in complex networks, Phys. Rep. 650, 1 (2016).
  22. S. Mugisha and H.-J. Zhou, Identifying optimal targets of network attack by belief propagation, Phys. Rev. E 94, 012305 (2016).
  23. F. Krzakala, C. Moore, E. Mossel, J. Neeman, A. Sly, L. Zdeborová, and P. Zhang, Spectral redemption in clustering sparse networks, Proc. Natl. Acad. Sci. USA 110, 20935 (2013).
  24. T. Martin, X. Zhang, and M. E. J. Newman, Localization and centrality in networks, Phys. Rev. E 90, 052808 (2014).
  25. S. Moore and T. Rogers, Predicting the Speed of Epidemics Spreading in Networks, Phys. Rev. Lett. 124, 068301 (2020).
  26. T. Rogers, Assessing node risk and vulnerability in epidemics on networks, Europhys. Lett. 109, 28005 (2015).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012014 for further details on the analytical derivations, on the used algorithms and on the numerical results discussed in the main body of the paper.
  28. A. Y. Lokhov, M. Mézard, H. Ohta, and L. Zdeborová, Inferring the origin of an epidemic with a dynamic message-passing algorithm, Phys. Rev. E 90, 012801 (2014).
  29. F. Altarelli, A. Braunstein, L. Dall'Asta, A. Lage-Castellanos, and R. Zecchina, Bayesian Inference of Epidemics on Networks Via Belief Propagation, Phys. Rev. Lett. 112, 118701 (2014).
  30. S. Melnik, A. Hackett, M. A. Porter, P. J. Mucha, and J. P. Gleeson, The unreasonable effectiveness of tree-based theory for networks with clustering, Phys. Rev. E 83, 036112 (2011).
  31. C. Granell, S. Gómez, and A. Arenas, Competing spreading processes on multiplex networks: Awareness and epidemics, Phys. Rev. E 90, 012808 (2014).
  32. B. Rozemberczki, R. Davies, R. Sarkar, and C. Sutton, GEMSEC: Graph embedding with self clustering, in Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ACM, New York, USA, 2019), pp. 65–72.
  33. R. Zafarani and H. Liu, Social Computing Data Repository at ASU, Arizona State University, School of Computing, Informatics and Decision Systems Engineering, 2009, http://socialcomputing.asu.edu.
  34. F. Morone and H. A. Makse, Influence maximization in complex networks through optimal percolation, Nature (London) 524, 65 (2015).

Outline

Information

Phys. Rev. Research 3, L012014– Published 8 February, 2021
  • Received 10 July 2020
  • Revised 15 November 2020
  • Accepted 24 December 2020
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation