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The Effect of Concurrency on Epidemic Threshold in Time-Varying Networks

  • Tomokatsu Onaga
  • James P. Gleeson
  • Naoki MasudaEmail author
Chapter
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Part of the Computational Social Sciences book series (CSS)

Abstract

Various epidemic spreading processes are considered to take place on time-varying networks. One key factor that alters epidemic spreading on time-varying networks is concurrency, the number of neighbours that a node has at a given time point. In this chapter, we present a theoretical study of the effects of concurrency on the susceptible-infected-susceptible epidemic processes on a class of temporal network models. By theoretical analysis that explicitly takes into account stochastic dying-out effects, we show that network dynamics increase the epidemic threshold (i.e., suppress epidemics), compared to that for the time-averaged network when the nodes’ concurrency is low, but also decrease the epidemic threshold (i.e., enhance epidemics) when the concurrency is high.

Keywords

SIS model Concurrency Epidemic threshold Phase transition Activity-driven model Stochastic extinction 

Notes

Acknowledgements

T.O. acknowledges the support provided through JSPS KAKENHI Grant Number JP19K14618 and JP19H01506. J.G. acknowledges the support provided through Science Foundation Ireland (Grants No. 16/IA/4470 and No. 16/RC/3918). N.M. acknowledges the support provided through JST, CREST, and JST, ERATO, Kawarabayashi Large Graph Project.

References

  1. 1.
    Bansal, S., Read, J., Pourbohloul, B., Meyers, L.A.: J. Biol. Dyn. 4, 478–489 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Masuda, N., Holme, P.: F1000Prime Rep. 5, 6 (2013)Google Scholar
  3. 3.
    Holme, P.: Eur. Phys. J. B 88, 234 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    Masuda, N., Holme, P. (eds.): Temporal Network Epidemiology. Springer, Singapore (2017)zbMATHGoogle Scholar
  5. 5.
    Morris, M., Kretzschmar, M.: Soc. Networks 17, 299–318 (1995)CrossRefGoogle Scholar
  6. 6.
    Kretzschmar, M., Morris, M.: Math. Biosci. 133, 165–195 (1996)CrossRefGoogle Scholar
  7. 7.
    Morris, M., Kretzschmar, M.: AIDS 11, 641–648 (1997)CrossRefGoogle Scholar
  8. 8.
    Perra, N., Gonçalves, B., Pastor-Satorras, R., Vespignani, A.: Sci. Rep. 2, 469 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Onaga, T., Gleeson, J.P., Masuda, N.: Phys. Rev. Lett. 119, 108301 (2017)ADSCrossRefGoogle Scholar
  10. 10.
    Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: In: Proceedings of the Thirteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 717–726. ACM, New York (2007)Google Scholar
  11. 11.
    Stehlé, J., Barrat, A., Bianconi, G.: Phys. Rev. E 81, 035101(R) (2010)Google Scholar
  12. 12.
    Zhao, K., Karsai, M., Bianconi, G.: PLoS One 6, e28116 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    Liberzon, D.: Switching in systems and control. In: Systems and Control: Foundations and Applications. Birkhäuser, Boston (2003)Google Scholar
  14. 14.
    Masuda, N., Klemm, K., Eguíluz, V.M.: Phys. Rev. Lett. 111, 188701 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    Hasler, M., Belykh, V., Belykh, I.: SIAM J. Appl. Dyn. Syst. 12, 1031–1084 (2013)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Speidel, L., Klemm, K., Eguíluz, V.M., Masuda, N.: New J. Phys. 18, 073013 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Rev. Mod. Phys. 87, 925–979 (2015)ADSGoogle Scholar
  18. 18.
    Keeling, M.J., Ross, J.V.: J. R. Soc. Interface 5, 171–181 (2008)CrossRefGoogle Scholar
  19. 19.
    Simon, P.L., Taylor, M., Kiss, I.Z.: J. Math. Biol. 62, 479–508 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hindes, J., Schwartz, I.B.: Phys. Rev. Lett. 117, 028302 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Kiss, I.Z., Miller, J.C., Simon, P.L.: Mathematics of Epidemics on Networks: From Exact to Approximate Models. Springer, Cham (2017)CrossRefGoogle Scholar
  22. 22.
    Van Mieghem, P., Omic, J., Kooij, R.: IEEE Trans. Netw. 17, 1–14 (2009)CrossRefGoogle Scholar
  23. 23.
    De Oliveira, M.M., Dickman, R.: Phys. Rev. E 71, 016129 (2005)ADSCrossRefGoogle Scholar
  24. 24.
    Alessandretti, L., Sun, K., Baronchelli, A., Perra, N.: Phys. Rev. E 95, 052318 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    Pozzana, I., Sun, K., Perra, N.: Phys. Rev. E 96, 042310 (2017)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tomokatsu Onaga
    • 1
  • James P. Gleeson
    • 2
  • Naoki Masuda
    • 3
    Email author
  1. 1.The Frontier Research Institute for Interdisciplinary Sciences and Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  3. 3.Department of Engineering MathematicsUniversity of BristolBristolUK

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