Spreading dynamics on small-world networks with connectivity fluctuations and correlations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 5, 2006, Pages

  Vazquez, Alexei ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER VIRUSES; CORRELATION METHODS; DISEASES; ELECTRONIC MAIL;

COMPUTER MALWARES; CONNECTIVITY CORRELATIONS; CONNECTIVITY FLUCTUATIONS; POWER LAW GROWTH;

COMPUTER NETWORKS;

EID: 33750578875     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.056101     Document Type: Article

References (43)

1. R. M. Anderson and R. M. May, Infectious Diseases of Humans (Oxford University Press, New York, 1991).
2. O. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (John Wiley & Sons, New York, 2000).
3. M. Barthélemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.178701 92, 178701 (2004).
4. P. Jagers, Branching Processes with Biological Applications (Wiley, London, 1975).
5. C. J. Mode and C. K. Sleeman, Stochastic Processes in Epidemiology (World Scientific, Singapore, 2000).
6. N. M. Ferguson, Nature (London) NATUAS 0028-0836 10.1038/nature02007 425, 681 (2003).
7. C. Fraser, S. Riley, R. Anderson, and N. M. Ferguson, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0307506101 101, 6146 (2004).
8. A. Vazquez, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 70, 163 (2006).
9. A. Vazquez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96. 038702 96, 038702 (2006).
10. T. E. Harris, The Theory of Branching Processes (Springer-Verlag, Berlin, 2002).
11. R. Pastor-Satorras, A. Vazquez, and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.258701 87, 258701 (2001).
12. M. E. J. Newman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 89.208701 89, 208701 (2002).
13. S. Maslov and K. Sneppen, Science SCIEAS 0036-8075 10.1126/science. 1065103 296, 910 (2002).
14. P. L. Krapivsky and S. Redner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.066123 63, 066123 (2001).
15. M. Boguña, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.028701 90, 028701 (2003).
16. A. Vazquez and Y. Moreno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.015101 67, 015101 (R) (2003).
17. A. Vazquez and M. Weigt, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.027101 67, 027101 (R) (2003).
18. F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Berg, Nature (London) NATUAS 0028-0836 10.1038/35082140 411, 907 (2001).
19. A.-L. Barabási and R. Albert, Science SCIEAS 0036-8075 10.1126/science.286.5439.509 286, 509 (1999).
20. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. CCRED2 0146-4833 10.1145/316194.316229 29, 251 (1999).
21. H. Ebel, L.-I. Mielsch, and S. Bornholdt, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.035103 66, R35103 (2002).
22. J.-P. Eckmann, E. Moses, and D. Sergi, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0405728101 101, 14333 (2004).
23. A. Barrat, M. Barthelemy, R. Pastor-Satorras, and A. Vespignani, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0400087101 101, 3747 (2004).
24. M. Boguña and R. Pastor-Satorras, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.036112 68, 036112 (2003).
25. A. Vazquez, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.056104 67, 056104 (2003).
26. S. Batiston and M. Catanzaro, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00127-8 38, 345 (2004).
27. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
28. D. J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, NJ, 1999).
29. S. Milgram, Psychol. Today PSTOAM 0033-3107 2, 60 (1967).
30. F. Chung and L. Lu, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.252631999 99, 15879 (2002).
31. B. Bollobás and O. M. Riordan, in Handbook of Graphs and Networks: From the Genome to the Internet, edited by, S. Bornholdt, and, H. G. Schuster, (Wiley-VCH, Weinheim, 2003), pp. 1-34.
32. R. Cohen and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.058701 90, 058701 (2003).
33. R. Cohen, D. Dolev, S. Havlin, T. Kalisky, O. Mokryn, and Y. Shavitt, e-print cond-mat/0305582.
34. P. Echenique, J. Gomez-Gardenes, Y. Moreno, and A. Vazquez, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.035102 71, 035102 (2005).
35. W. O. Kermack and A. G. McKendrick, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 115, 700 (1927).
36. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3200 86, 3200 (2001).
37. C. Moore and M. E. J. Newman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.5678 61, 5678 (2000).
38. J. H. Jones and M. S. Handcock, Nature (London) NATUAS 0028-0836 10.1038/423605a 423, 605 (2003).
39. J. H. Jones and M. S. Handcock, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 10.1098/rspb.2003.2369 270, 1123 (2003).
40. A. Schneeberger, C. H. Mercer, S. A. Gregson, N. M. Fergurson, C. A. Nyamukapa, R. M. Anderson, A. M. Johnson, and G. P. Garnett, Sex Transm. Dis. ZZZZZZ 0148-5717 31, 380 (2004).
41. R. Brookmeyer and M. H. Gail, AIDS Epidemiology: A Quantitative Apprach (Oxford University Press, New York, 1994).
42. B. Szendriöi and G. Csányi, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 10.1098/rsbl.2004.0188 271, S364 (2004).
43. S. Eubank, H. Guclu, V. S. A. Kumar, M. Marathe, A. Srinivasan, Z. Toroczcai, and N. Wang, Nature (London) NATUAS 0028-0836 10.1038/nature02541 429, 180 (2004).