Epidemic threshold and phase transition in scale-free networks with asymmetric infection

Abstract.

We study the SIS epidemic dynamics on scale-freeweighted networks with asymmetric infection, by both analysis andnumerical simulations, with focus on the epidemic threshold aswell as critical behaviors. It is demonstrated that the asymmetryof infection plays an important role: we could redistribute theasymmetry to balance the degree heterogeneity of the network andthen to restore the epidemic threshold to a fnite value. On theother hand, we show that the absence of the epidemic threshold isnot so bad as commented previously since the prevalence grows veryslowly in this case and one could only protect a few vertices toprevent the diseases propagation.

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References

  1. R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 1 (2002)

    Google Scholar 

  2. M.E.J. Newman, SIAM Review 45, 167 (2003)

    Google Scholar 

  3. S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (OxfordUniversity Press, Oxford, 2003)

  4. R. Pastor-Satorras, A. Vespignani, Evolution andStruc- ture of the Internet: A Statistical Physics Approach (Cam-bridge University Press, 2004)

  5. D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts,Phys. Rev. Lett. 85, 5468 (2000)

    Google Scholar 

  6. R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett.85, 4626 (2000)

    Google Scholar 

  7. R. Pastor-Satorras, A. Vespignani, Phys. Rev. Lett. 86, 3200(2001)

  8. R.M. May, A.L. Lloyd, Phys. Rev. E 64, 066112 (2001)

    Google Scholar 

  9. M.E.J. Newman, Phys. Rev. E 66, 016128 (2002)

    Google Scholar 

  10. M. Boguñá, R. Pastor-Satorras, A. Vespignani, Phys. Rev.Lett. 90, 028701 (2003)

    Google Scholar 

  11. M.A. Serrano, M. Boguñá, Phys. Rev. Lett. 97, 088701(2006)

  12. N.T.J. Bailey, The Mathematical Theory of Infectious Diseases, 2nd edn.(Griffin, London, 1975); J.D. Murray, MathematicalBiology (Springer-Verlag, Berlin, 1993)

  13. S.R. White, in Proceeding of the Virus Bulletin Conference,Munich, 1998 http://www.research.ibm.com/antivirus/SciPapers.htm

  14. F. Liljeros, C.R. Edling, L.A.N. Amaral, H.E. Stanley, Y. Aberg, Nature (London) 411, 907 (2001)

    Google Scholar 

  15. H. Ebel, L.-I. Mielsch, S. Bornholdt, Phys. Rev. E 66,035103(R) (2002)

  16. M. Faloutsos, P. Faloutsos, C. Faloutsos, ACM ComputerCommunication Review 29, 251 (1999)

    Google Scholar 

  17. L. Hufnage, D. Brockmann, T. Geisel, Proc. Natl. Acad.Sci. USA 101, 15124 (2004)

    Google Scholar 

  18. V. Colizza, A. Barrat, M. Barthélemy, A. Vespignani,Proc. Natl. Acad. Sci. USA 103, 2015 (2006)

  19. A. Barrat, M. Barthélemy, R. Pastor-Satorras, A.Vespignani, Proc. Natl. Acad. Sci. USA 101, 3747 (2004)

    Google Scholar 

  20. For too large or too small α, λkiwij may be larger than 1. Inthis case, it can be rescaled by a small constant, and dose notalter the results. In this paper we focus on the epidemicthreshold and set -2 ≤α≤2 in oursimulations

  21. M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2002)

    Google Scholar 

  22. R. Pastor-Satorras, A. Vespignani, in Handbook of Graphsand Networks: From the Genome to the Internet, edited by S.Bornholdt, H.G. Schuster (Wiley-VCH, Berlin, 2002), pp.113–132

  23. K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701(2001)

  24. R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 65,035108(R) (2002)

  25. V. Colizza, R. Pastor-Satorras, A. Vespignani, NaturePhys. 3, 276 (2007)

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Yan, G., Fu, ZQ. & Chen, G. Epidemic threshold and phase transition in scale-free networks with asymmetric infection. Eur. Phys. J. B 65, 591 (2008). https://doi.org/10.1140/epjb/e2008-00370-y

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PACS.

  • 89.75.-k Complex systems
  • 89.75.Hc Networks and genealogical trees