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Spread of epidemic disease on networks

M. E. J. Newman
Phys. Rev. E 66, 016128 – Published 26 July 2002
An article within the collection: Physical Review E 25th Anniversary Milestones
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  1. N. T. J. Bailey, The Mathematical Theory of Infectious Diseases and its Applications (Hafner Press, New York, 1975).
  2. R. M. Anderson and R. M. May, Infectious Diseases of Humans (Oxford University Press, Oxford, 1991).
  3. H.W. Hethcote, SIAM Rev. 42, 599 (2000).
  4. S.H. Strogatz, Nature (London) 410, 268 (2001).
  5. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
  6. D.J. Watts and S.H. Strogatz, Nature (London) 393, 440 (1998).
  7. L.A.N. Amaral, A. Scala, M. Barthélémy, and H.E. Stanley, Proc. Natl. Acad. Sci. USA 97, 11149 (2000).
  8. F. Liljeros, C.R. Edling, L.A.N. Amaral, H.E. Stanley, and Y. Åberg, Nature (London) 411, 907 (2001).
  9. M. Girvan and M. E. J. Newman, Proc. Natl. Acad. Sci. USA 99, 8271 (2002).
  10. J. Abello, A. Buchsbaum, and J. Westbrook, in Proceedings of the 6th European Symposium on Algorithms, edited by G. Bilardi, G. F. Italiano, A. Pietracaprina, and G. Pucci (Springer, Berlin, 1998).
  11. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 401, 130 (1999).
  12. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999).
  13. A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener, Comput. Netw. 33, 309 (2000).
  14. H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.-L. Barabási, Nature (London) 407, 651 (2000).
  15. H. Jeong, S. Mason, A.-L. Barabási, and Z.N. Oltvai, Nature (London) 411, 41 (2001).
  16. D.A. Fell and A. Wagner, Nat. Biotechnol. 18, 1121 (2000).
  17. R.J. Williams and N.D. Martinez, Nature (London) 404, 180 (2000).
  18. J.M. Montoya and R.V. Solé, J. Theor. Biol. 214, 405 (2002).
  19. C. Moore and M.E.J. Newman, Phys. Rev. E 61, 5678 (2000).
  20. M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001).
  21. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).
  22. Y. Moreno, R. Pastor-Satorras, and A. Vespignani, arXiv:cond-mat/0107267.
  23. C.P. Warren, L.M. Sander, and I. Sokolov, arXiv:cond-mat/0106450.
  24. C. P. Warren, L. M. Sander, I. Sokolov, C. Simon, and J. Koopman, Math. Biosci. (to be published).
  25. L. Sattenspiel and C.P. Simon, Math. Biosci. 90, 341 (1988).
  26. I.M. Longini, Math. Biosci. 90, 367 (1988).
  27. M. Kretzschmar and M. Morris, Math. Biosci. 133, 165 (1996).
  28. F. Ball, D. Mollison, and G. Scalia-Tomba, Ann. Appl. Probab. 7, 46 (1997).
  29. H.L. Frisch and J.M. Hammersley, J. Soc. Ind. Appl. Math. 11, 894 (1963).
  30. P. Grassberger, Math. Biosci. 63, 157 (1983).
  31. D.J. de S. Price, Science 149, 510 (1965).
  32. A.L. Lloyd and R.M. May, Science 292, 1316 (2001).
  33. E.A. Bender and E.R. Canfield, J. Comb. Theory, Ser. A 24, 296 (1978).
  34. M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995).
  35. M. Molloy and B. Reed, Combinatorics, Probab. Comput. 7, 295 (1998).
  36. M.E.J. Newman, S.H. Strogatz, and D.J. Watts, Phys. Rev. E 64, 026118 (2001).
  37. M.E.J. Newman, D.J. Watts, and S.H. Strogatz, Proc. Natl. Acad. Sci. USA 99, 2566 (2002).
  38. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000).
  39. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 86, 3682 (2001).
  40. D.S. Callaway, M.E.J. Newman, S.H. Strogatz, and D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000).
  41. S.N. Dorogovtsev, J.F.F. Mendes, and A.N. Samukhin, Phys. Rev. E 64, 025101 (2001).
  42. L.A. Adamic, R.M. Lukose, A.R. Puniyani, and B.A. Huberman, Phys. Rev. E 64, 046135 (2001).
  43. H. Wilf, Generatingfunctionology, 2nd ed. (Academic Press, London, 1994).
  44. C. Moore and M.E.J. Newman, Phys. Rev. E 62, 7059 (2000).
  45. M.E.J. Newman, Proc. Natl. Acad. Sci. U.S.A. 98, 404 (2001).
  46. R. Pastor-Satorras and A. Vespignani, Phys. Rev. E 65, 036104 (2002).
  47. T.B. Hyde, M. Gilbert, S.B. Schwartz, E.R. Zell, J.P. Watt, W.L. Thacker, D.F. Talkington, and R.E. Besser, J. Infect. Dis. 183, 907 (2001).
  48. H. W. Hethcote and J. A. Yorke, Gonorrhea Transmission Dynamics and Control (Springer, New York, 1984).
  49. L. W. Ancel, M. E. J. Newman, M. Martin, and S. Schrag, Santa Fe Institute Report No. 01-12-078, 2001 (unpublished).
  50. S. Gupta, R.M. Anderson, and R.M. May, AIDS 3, 807 (1989).
  51. A.S. Klovdahl, J.J. Potterat, D.E. Woodhouse, J.B. Muth, S.Q. Muth, and W.W. Darrow, Soc. Sci. Med. 38, 79 (1994).
  52. One should observe that the network studied in Ref. [8] is a cumulative network of actual sexual contacts—it represents the sum of all contacts over a specified period of time. Although this is similar to other networks of sexual contacts studied previously [50][51] it is not the network required by our models, which is the instantaneous network of connections (not contacts—see Sec. II). While the network measured may be a reasonable proxy for the network we need, it is not known if this is the case.
  53. It is also worth noting that networks of sexual contacts observed in sociometric studies [51] are often highly dendritic, with few short loops, indicating that the treelike components of our percolating clusters may be, at least in this respect, quite a good approximation to the shape of real STD outbreaks.

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