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Immunization and epidemic dynamics in complex networks

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Abstract.

We study the behavior of epidemic spreading in networks, and, in particular, scale free networks. We use the Susceptible-Infected-Removed (SIR) epidemiological model. We give simulation results for the dynamics of epidemic spreading. By mapping the model into a static bond-percolation model we derive analytical results for the total number of infected individuals. We study this model with various immunization strategies, including random, targeted and acquaintance immunization.

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References

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

    Article  ADS  Google Scholar 

  2. R. Pastor-Satorras, A. Vespignani Phys. Rev. E 63, 066117 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. R. Albert, H. Jeong, A.-L. Barabási, Nature, 406, 378 (2000)

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 86, 3682 (2001)

    Article  ADS  Google Scholar 

  8. R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 65, 036104 (2002)

    Article  ADS  Google Scholar 

  9. Z. Dezso, A.-L. Barabási, Phys. Rev. E 65, 055103(R) (2002)

    Article  ADS  Google Scholar 

  10. R.M. Anderson, R.M. May, Infectious Diseases of Humans: Dynamics and Control (Oxford University Press, UK, 1992)

  11. P. Grassberger, Math. Biosci. 63, 157 (1983)

    Article  Google Scholar 

  12. C.P. Warren, L.M. Sander, I.M. Sokolov, Math. Biosci. 180, 293 (2002)

    Article  MathSciNet  Google Scholar 

  13. H.W. Hethcote, J.A. Yorke, Gonorrhea transmission dynamics and control, Vol. 56 of Lecture notes in Biomathematics (Springer-Verlag, Berlin, 1984)

  14. R.M. May, R.M. Anderson, Math. Biosci. 72, 83 (1984)

    Article  MathSciNet  Google Scholar 

  15. H.W. Hethcote, J.W. Van-Ark, Math. Biosci. 84, 85 (1987)

    Article  MathSciNet  Google Scholar 

  16. R. Pastor-Satorras, A. Vespignani, Evolution and structure in the Internet (Cambridge University Press, UK, 2004)

  17. A.L. Lloyd, R.M. May, Science 292, 1316 (2001)

    Article  Google Scholar 

  18. S.H. Strogatz, Nature 410, 268 (2000)

    Article  ADS  Google Scholar 

  19. R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  ADS  Google Scholar 

  20. S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)

    Article  ADS  Google Scholar 

  21. M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    Article  ADS  MathSciNet  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  24. A.-L. Barabási, H. Jeong, R. Ravasz, Z. Neda, T. Vicsek, A. Schubert, Physica A 311, 590 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  25. M.E.J. Newman, D.J. Watts, S.H. Strogatz, PNAS 99, 2566 (2002)

    Article  ADS  Google Scholar 

  26. S.-H. Yook, H. Jeong, A.-L. Barabási Proc. Nat. Acad. Sci. USA 99, 13382 (2002)

    Article  ADS  Google Scholar 

  27. A.L. Barabási, R. Albert, Science 286, 509 (1999)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. X. Guardiola, R. Guimera, A. Arenas, A. Diaz-Guilera, D. Streib, L.A.N. Amaral, cond-mat/0206240

  30. R. Cohen, S. Havlin, D. ben-Avraham, Phys. Rev. Lett. 91, 247901 (2003)

    Article  ADS  Google Scholar 

  31. S.L. Feld, Am. J. Soc. 96, 1464 (1991)

    Article  Google Scholar 

  32. M.E.J. Newman, Social Networks 25, 83 (2003); M.E.J. Newman, Nature 411, 41 (2001)

    Article  Google Scholar 

  33. M. Boguna, R. Pastor-Satorras, Phys. Rev. E 66, 047104 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. L.A.N. Amaral, A. Scala, M. Barthélémy, H.E. Stanley, PNAS 97, 11149 (2000)

    Article  ADS  Google Scholar 

  37. R.V. Solé, J.M. Montoya, Proc. Roy. Soc. Lond. B Bio. 268, 2039 (2001)

    Article  Google Scholar 

  38. J. Camacho, R. Guimerá, L.A.N. Amaral, Phys. Rev. Lett. 88, 228102 (2002)

    Article  ADS  Google Scholar 

  39. H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A.L. Barabási, Nature, 407, 651 (2000)

  40. H. Jeong, S. Mason, A.-L. Barabási, Z.N. Oltvai, Nature 411, 41 (2001)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Minerva Center and Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    N. Madar, T. Kalisky, R. Cohen & S. Havlin

  2. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel

    R. Cohen

  3. Department of Physics, Clarkson University, NY 13699-5820, Potsdam, USA

    D. ben-Avraham

Authors
  1. N. Madar
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  2. T. Kalisky
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  3. R. Cohen
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  4. D. ben-Avraham
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  5. S. Havlin
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Corresponding author

Correspondence to R. Cohen.

Additional information

Received: 3 November 2003, Published online: 14 May 2004

PACS:

02.50.Cw Probability theory - 02.10.Ox Combinatorics; graph theory - 89.20.Hh World Wide Web, Internet - 64.60.-i General studies of phase transitions

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Madar, N., Kalisky, T., Cohen, R. et al. Immunization and epidemic dynamics in complex networks. Eur. Phys. J. B 38, 269–276 (2004). https://doi.org/10.1140/epjb/e2004-00119-8

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  • DOI: https://doi.org/10.1140/epjb/e2004-00119-8

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