A random walk model for infection on graphs: Spread of epidemics & rumours with mobile agents

Discrete Event Dynamic Systems: Theory and Applications

Volumn 21, Issue 1, 2011, Pages 41-61

  Draief, Moez ^a   Ganesh, Ayalvadi ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Erdos R nyi graph; Infection time; Power law graphs; Random walks on graphs; Regular graphs

Indexed keywords

ARBITRARY GRAPHS; COMPLETE GRAPHS; CONNECTIVITY PATTERN; CONVERGENCE TIME; DEGREE DISTRIBUTIONS; INFECTION TIME; NETWORK TOPOLOGY; POWER-LAW; POWER-LAW GRAPH; POWER-LAW GRAPHS; PRELIMINARY ANALYSIS; RANDOM WALK; RANDOM WALK MODELS; RANDOM WALKERS; REGULAR GRAPHS; UNDERLYING NETWORKS; UPPER BOUND;

COMPUTER VIRUSES; ELECTRIC NETWORK TOPOLOGY; GRAPHIC METHODS; INFORMATION DISSEMINATION; MOBILE AGENTS; PHASE TRANSITIONS; RANDOM PROCESSES; VIRUSES;

GRAPH THEORY;

EID: 79951553269     PISSN: 09246703     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10626-010-0092-5     Document Type: Conference Paper

References (41)

1. D Aldous 1991 Meeting times for independent Markov chains Stoch Process Their Appl 38 185 193 0737.60061 10.1016/0304-4149(91)90090-Y 1119980
2. Aldous D, Fill J (2002) Reversible Markov chains ans random walks on graphs. Monograph available at http://www.stat.berkeley.edu/~aldous/RWG
3. Amini H, Draief M, Lelarge M (2009) Marketing in a random network. In: Network Central and Optimization, LNCS, NET-COOP'08. Springer, Berlin, pp 17-25
4. A-L Barabási R Albert 1999 Emergence of scaling in random networks Science 286 509 512 10.1126/science.286.5439.509 2091634
5. B Bollobás O Riordan 2004 "The diamet (Pubitemid 38706499)
6. Bui M, Bernard T, Sohier D, Bui A (2004) Random walks in distributed computing: a survey. In: Proc. IICS, 1-14
7. A Chaintreau P Hui J Scott R Gass J Crowcroft C Diot 2007 Impact of human mobility on opportunistic forwarding algorithms IEEE Trans Mob Comput 6 6 606 620 10.1109/TMC.2007.1060 (Pubitemid 46685740)
8. F Chung L Lu 2003 The average distances in random graphs with given expected degrees Internet Math 1 91 114 1065.05084 2076728
9. C Cooper A Frieze T Radzik 2009 Multiple random walks in random regular graphs SIAM J Discrete Math 22 4 1738 1761 2570201
10. D Coppersmith P Tetali P Winkler 1993 Collisions among random walks on a graph SIAM J Discrete Math 6 3 363 374 0776.60083 10.1137/0406029 1229691
11. Daley DJ, Gani J (2001) Epidemic modelling: an introduction. Cambridge University Press, Studies in mathematical biology
12. N Datta TC Dorlas 2004 Random walks on a complete graph: a model for infection J Appl Probab 41 1008 1021 1068.60070 10.1239/jap/1101840547 2122476 (Pubitemid 40317813)
13. T Dimitriou S Nikoletseas P Spirakis 2006 The infection time of graphs Discrete Appl Math 154 2577 2589 1119.60079 10.1016/j.dam.2006.04.026 2277961 (Pubitemid 44649209)
14. S Dolev E Schiller J Welch 2006 Random walk for self-stabilizing group communication in ad hoc networks IEEE Trans Mob Comput 5 7 893 905 10.1109/TMC.2006.104 (Pubitemid 44143938)
15. M Draief 2006 Epidemic processes on complex networks Physica A: Statistical Mechanics and its Applications 363 1 120 131 10.1016/j.physa.2006. 01.054
16. M Draief A Ganesh 2006 Efficient routing in poisson small-world networks J Appl Probab 43 3 678 686 1131.05083 10.1239/jap/1158784938 2274792
17. M Draief J Mairesse N O'Connell 2005 Queues, stores, and tableaux J Appl Probab 42 4 1145 1167 05036960 10.1239/jap/1134587823 2203829 (Pubitemid 43479536)
18. Draief M, Massoulié L (2010) Epidemics and rumours in complex networks. London mathematical society series, vol 369. Cambridge University Press
19. Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the Internet topology. In: Proceedings ACM Sigcomm
20. Friedman J (2003) A proof of Alons second eigenvalue conjecture. In: Proceedings of the thirty-fifth annual ACM symposium on theory of computing (STOC'03), pp 720-724
21. Ganesh A, Draief M (2009) A random walk model for infection on graphs. ACM Proc. Valuetools'09, article 34
22. AJ Ganesh A-M Kermarrec E Le Merrer L Massoulié 2007 Peer counting and sampling in overlay networks based on random walks Distrib Comput 20 4 267 278 10.1007/s00446-007-0027-z (Pubitemid 350005917)
23. Ganesh A, Massoulié L, Towsley D (2005) The effect of network topology on the spread of epidemics. In: Proc. INFOCOM, pp 1455-1466 (Pubitemid 41390795)
24. Gkantsidis C, Mihail M, Saberi A (2005) Hybrid search schemes for unstructured peer-to-peer networks. In: Proc. INFOCOM, pp 1526-1537 (Pubitemid 41390670)
25. Karger DR, Ruhl M (2004) Simple efficient load balancing algorithms for peer-to-peer systems. In: Proc. SPAA, pp 36-43
26. Kempe D, Kleinberg J, Demers A (2001) Spatial gossip and resource location protocols. In: Proc. STOC, pp 163-172 (Pubitemid 32865729)
27. Kephart J, White S (1991) Directed-graph epidemiological models of computer viruses. In: Proceedings of the IEEE computer symposium on research in security and privacy, pp 343-359
28. J Kleinberg 2007 The wireless epidemic Nature 449 287 288 10.1038/449287a (Pubitemid 47449550)
29. Kleinberg J (2000) The small-world phenomenon: an algorithm perspective. In: Proc. STOC, pp 163-170
30. Leavitt N (2005) Mobile phones: the next frontier for hackers? IEEE Computer Society Press, Los Alamitos, CA, vol 38, no 4, pp 20-23 (Pubitemid 40608419)
31. Lovász L (1993) Random Walks on Graphs: a survey. In: Combinatorics, Bolyai Society Mathematical Studies vol 2, pp 1-46
32. Mickens JW, Noble BD (2005) Modeling epidemic spreading in mobile environments. In: Proceedings of the 4th ACM workshop on Wireless security, pp 77-86 (Pubitemid 44447320)
33. Mohar B (1997) Some applications of Laplace eigenvalues of graphs. In: Hahn G, Sabidussi G (eds) Graph symmetry. Kluwer Academic Press, Dordrecht, pp 225-275
34. Mobile phone virus Cabir. http://www.dancewithshadows.com/tech/mobile- phone-virus-cabir.asp
35. M Nekovee 2007 Worm epidemics in wireless ad hoc networks New J Phys 9 189 10.1088/1367-2630/9/6/189 (Pubitemid 47146370)
36. Norris J (1997) Markov chains. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press
37. B Pittel 1987 On spreading a rumor SIAM J Appl Math 47 1 213 223 0619.60068 10.1137/0147013 873245
38. CJ Rhodes M Nekovee 2008 The opportunistic transmission of wireless worms between mobile devices Physica A: Statistical Mechanics and Its Applications 387 27 6837 6844 10.1016/j.physa.2008.09.017
39. Su J, Chan KKW, Miklas AG, Po K, Akhavan A, Saroiu S, de Lara E, Goel A (2006) A preliminary investigation of worm infections in a bluetooth environment. In: Proceedings of the 4th ACM workshop on Recurring malcode, WORM'06, pp 9-16 (Pubitemid 47117518)
40. P Wang M González C Hidalgo A-L Baranási 2009 Understanding the spreading patterns of mobile phone viruses Science 324 5930 1071 1076 10.1126/science.1167053
41. Yan G, Cuellar L, Eindenbenz S, Flores H, Hengartner N, Vu V (2007) Bluetooth worm propagation: mobility pattern matters! In: Proceedings of the 2nd ACM symposium on Information, computer and communications security, ASIACCS'07, pp 32-44 (Pubitemid 47479225)