Epidemic processes on complex networks: The effect of topology on the spread of epidemics

Physica A: Statistical Mechanics and its Applications

Volumn 363, Issue 1, 2006, Pages 120-131

  Draief, Moez ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Duration of an epidemic; Epidemic threshold; Final size of an epidemic; Isoperimetric constant; Reed Frost model; SIS model; Spectral radius

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; PROBABILISTIC LOGICS; TOPOLOGY;

DURATION OF AN EPIDEMIC; EPIDEMIC THRESHOLD; FINAL SIZE OF AN EPIDEMIC; ISOPERIMETRIC CONSTANT; REED-FROST MODEL; SIS MODEL; SPECTRAL RADIUS;

EPIDEMIOLOGY;

EID: 33645145011     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.01.054     Document Type: Article

References (48)

1. S.N. Dorogovtsev, and J.F.F. Mendes Evolution of Networks: from Biological Nets to the Internet and WWW 2002 Oxford University Press UK
2. D.J. Watts Small Worlds: The Dynamic on Networks between Order and Randomness 1999 Princeton University Press USA
3. M. Faloutsos, P. Faloutsos, C. Faloutsos, On power-law relationships of the Internet topology, Proceedings of ACM SIGCOMM Computer Communication Review, vol. 29, 1999, p. 251.
4. R. Pastor-Satorras, and A. Vespignani Internet: structure et évolution 2004 Belin France
5. S. Lawrence, and C.L. Giles Searching the World Wide Web Science 280 1998 98 100
6. M.E.J. Newman, D.J. Watts, and S.H. Strogatz Random graphs of social networks Proc. Natl. Acad. Sci. USA 99 1 2002 2566 2572
7. J.M. Montoya, R.V. Solé, Small world patterns in food webs, J. Theoret. Biol. 214 (2002) 405-412.
8. H. Jeong, B. Tombor, R. Albet, Z.N. Oltvai, and A.-L. Barabási The large-scale organisation of metabolic networks Nature 407 2000 651 654
9. J.O. Kephart, S.R. White, Measuring and modeling computer virus prevalence, Proceedings of the IEEE Computer Society Symposium on Research in Security and Privacy, 1993, pp. 2-15.
10. P. Eugster, R. Guerraoui, A.-M. Kermarrec, and L. Massoulié From epidemics to distributed computing IEEE Comput. Mag. 37 5 2004 60 67
11. A.-M. Kermarrec, L. Massoulié, and A. Ganesh Probabilistic reliable dissemination in large-scale systems IEEE Trans. Parallel Distributed Syst. 14 3 2003
12. R. van Renesse, Y. Minsky, M. Hayden, A gossip-style failure detection service, Proceedings of the IFIP Conference on Distributed Systems Platforms and Open Distributed Processing, 1998.
13. I. Gupta, R. van Renesse, K. Birman, Scalable fault-tolerant aggregation in large process groups, Proceedings of the International Conference on Dependable Systems and Networks, July 2001.
14. R. van Renesse, K. Birman, and W. Vogels Astrolabe: a robust and scalable technology for distributed systems monitoring, management and data mining ACM Trans. Comput. Syst. 21 3 2003
15. A.J. Demers, D.H. Greene, C. Hauser, W. Irish, J. Larson, Epidemic algorithms for replicated database maintenance, Proceedings of the Sixth Annual ACM Symposium on Principles of Distributed Computing, 1987, pp. 1-12.
16. N.T.J. Bailey The Mathematical Theory of Infectious Diseases and its Applications 1975 Griffin London
17. D.J. Daley, and J. Gani Epidemic Modelling: An Introduction 2001 Cambridge University Press Cambridge
18. R. Pastor-Satorras, and A. Vespignani Epidemic threshold in scale-free networks Phys. Rev. Lett. 86 14 2001 3200 3203
19. M. Boguña, R. Pastor-Satorras, A. Vespignani, Absence of epidemic threshold in scale-free networks with degree correlations, Phys. Rev. Lett. 90(2) (2003).
20. R.M. May, and A.L. Lloyd Infectious dynamics on scale networks Phys. Rev. E 64 2001 066112
21. R. Pastor-Satorras, and A. Vespignani Epidemic and immunisation in scale-free networks S. Bornholdt H.G. Schuster Handbook of Graphs and Networks: From the Genome to the Internet 2002 Wiley Berlin 113 132
22. R. Pastor-Satorras, and A. Vespignani Epidemic spreading in finite scale-free networks Phys. Rev. E 65 2002
23. M. Boguña, R. Pastor-Satorras, and A. Vespignani Epidemic spreading in complex networks with degree correlations J.M. Rubi Proceedings of the XVIII Sitges Conference "Statistical Mechanics of Complex Networks" 2003 Springer Berlin
24. D. Volchenkov, L. Volchenkov, and P. Blanchard Epidemic spreading in a variety of scale-free networks Phys. Rev. E 66 2002 046137
25. T.E. Harris Contact interactions on a lattice Ann. Probab. 2 1974 969 988
26. T.M. Liggett Stochastic Interacting Systems: Contact, Voter and Exclusion Processes 1999 Springer Berlin
27. C. Bezuidenhout, and G. Grimmett The critical process dies out Ann. Probab. 18 1990 1462 1482
28. R. Durrett On the growth of one-dimensional contact processes Ann. Probab. 8 1980 890 907
29. R. Pemantle The contact process on trees Ann. Probab. 20 1992 2089 2116
30. A. Barabási, and R. Albert Emergence of scaling in random networks Science 286 1999 509 512
31. N. Berger, C. Borgs, J. Chayes, A. Saberi, The epidemic threshold in scale-free graphs, Proceedings of SODA, 2005.
32. A. Ganesh, L. Massoulié, D. Towsley, The effect of network topology on the spread of epidemics, Proceedings of IEEE Infocom, 2005.
33. Y. Wang, D. Chakrabarti, C. Wang, C. Faloutsos, Epidemic spreading in real networks: an eigenvalue viewpoint, 22nd Symposium on Reliable Distributed Computing, 2003.
34. W. Feller, An Introduction to Probability Theory and its Applications, vol. 1, third ed., Wiley, New York, 1957.
35. E. Coffman, J. Ge, V. Misra, D. Towsley, Network resilience: exploring cascading failures in BGP, Proceedings of 40th Annual Allerton Conference on Communications, Computing and Control, 2002.
36. R.A. Horn, and C.R. Johnson Matrix Analysis 1990 Cambridge University Press UK
37. S. Janson, T. Łuczak, A. Ruciński, Random Graphs, Wiley-Interscience in Discrete Mathematics and Optimisation, Wiley, New York, 2000.
38. B. Bollobás, and O. Riordan The diameter of a scale-free random graph Combinatorica 4 2004 5 34
39. F. Chung, and L. Lu The average distances in random graphs with given expected degrees Internet Math. 1 2003 91 114
40. F. Chung, L. Lu, and V. Vu Eigenvalues of random power law graphs Ann. Combin. 7 2003 21 33
41. W.O. Kermack, and A.G. McKendrick A contribution to the mathematical theory of epidemics Proc. R. Soc. London A 115 1927 700 721
42. H. Andersson, T. Britton, Stochastic Epidemic Models and their Statistical Analysis, Springer Lecture Notes in Statistics, vol. 151. Springer, New York, 2000.
43. M. Draief, A. Ganesh, L. Massoulié, Threshold for virus spread on networks, preprint, 2005.
44. F. Ball, D. Mollison, and G. Scalia-Tomba Epidemics with two levels of mixing Ann. Appl. Probab. 7 1997 46 89
45. P. Erdös, and A. Rényi On the evolution of random graphs Mat Kutato Int. Közl 5 1960 17 60
46. F. Chung, and L. Lu Connected components in random graphs with given degree sequences Ann. Combin. 6 2002 125 145
47. L. Lovász, B. Szegedy, Limits of dense graph sequences, Technical Report TR-2004-79, Microsoft Research, 2004.
48. B. Bollobás, S. Janson, O. Riordan, The phase transition in inhomogeneous random graphs, Technical Report 2005:18, Uppsala University, 2005.