Epidemic threshold and immunization on generalized networks

Physica A: Statistical Mechanics and its Applications

Volumn 389, Issue 3, 2010, Pages 549-560

  Peng, Chengbin ^a,b   Jin, Xiaogang ^a,b   Shi, Meixia ^c  

^a ZHEJIANG UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY   (China)

^c ZHEJIANG UNIVERSITY   (China)

Author keywords

Complex networks; Eigenvalue; Epidemic threshold; Immunization; SIS model

Indexed keywords

COMPLEX NETWORKS; EIGENVALUES AND EIGENFUNCTIONS; IMMUNIZATION; MATRIX ALGEBRA;

CONTACT NETWORKS; EIGEN-VALUE; EPIDEMIC DYNAMICS; EPIDEMIC THRESHOLD; GENERALIZED NETWORKS; SIS MODEL; STATISTICAL PROPERTIES; SUSCEPTIBLE-INFECTED-SUSCEPTIBLE MODEL;

EPIDEMIOLOGY;

EID: 70350571231     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.09.047     Document Type: Article

References (45)

1. Hethcote H.W. The mathematics of infectious diseases. SIAM Review 42 4 (2000) 599-653
2. Lloyd A.L., and May R.M. Epidemiology: How viruses spread among computers and people. Science 292 5520 (2001) 1316-1317
3. Barthélemy M., Barrat A., Pastor-Satorras R., and Vespignani A. Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. Journal of Theoretical Biology 235 2 (2005) 275-288
4. Pastor-Satorras R., and Vespignani A. Epidemic spreading in scale-free networks. Physical Review Letters 86 14 (2001) 3200-3203
5. Mollison D. Epidemic Models: Their Structure and Relation to Data (1995), Cambridge University Press
6. Rhodes C.J., and Anderson R.M. Dynamics in a lattice epidemic model. Physics Letters A 210 3 (1996) 183-188
7. Boguñá M., and Pastor-Satorras R. Epidemic spreading in correlated complex networks. Physical Review E 66 4 (2002) 047104
8. Pastor-Satorras R., and Vespignani A. Epidemic dynamics and endemic states in complex networks. Physical Review E 63 6 (2001) 066117
9. Yan G., Zhou T., Wang J., Fu Z.Q., and Wang B.H. Chinese Physics Letters 22 (2005) 510
10. Boccaletti S., Latora V., Moreno Y., Chavez M., and Hwang D.-U. Complex networks: Structure and dynamics. Physics Reports 424 4-5 (2006) 175-308
11. Y. Wang, D. Chakrabarti, C. Wang, C. Faloutsos, Epidemic spreading in real networks: An eigenvalue viewpoint, in: IEEE Symposium on Reliable Distributed Systems, 2003, pp. 25-34
12. Chakrabarti D., Wang Y., Wang C., Leskovec J., and Faloutsos C. Epidemic thresholds in real networks. ACM Transactions on Information and System Security 10 4 (2008) 1-26
13. Hethcote H. An immunization model for a heterogeneous population. Theoretical population biology 14 3 (1978) 338
14. Draief M. Epidemic processes on complex networks. Information and Material Flows in Complex Networks. Physica A: Statistical Mechanics and its Applications 363 1 (2006) 120-131 10.1016/j.physa.2006.01.054
15. Newman M.E.J. Analysis of weighted networks. Physical Review E 70 (2004) 056131
16. Meyers L.A., Newman M., and Pourbohloul B. Predicting epidemics on directed contact networks. Journal of Theoretical Biology 240 3 (2006) 400-418
17. R. Pastor-Satorras, A. Vespignani, Epidemics and immunization in scale-free networks, Arxiv preprint cond-mat/~0205260
18. Eames K., Read J., and Edmunds W. Epidemic prediction and control in weighted networks. Epidemics 1 1 (2009) 70-76
19. Zanette D., and Kuperman M. Effects of immunization in small-world epidemics. Physica A: Statistical Mechanics and its Applications 309 3-4 (2002) 445-452 10.1016/S0378-4371(02)00618-0
20. Liu Z., Lai Y.C., and Ye N. Propagation and immunization of infection on general networks with both homogeneous andheterogeneous components. Physical Review E 67 3 (2003) 031911 10.1103/PhysRevE.67.031911
21. Madar N., Kalisky T., Cohen R., Ben-Avraham D., and Havlin S. Immunization and epidemic dynamics in complex networks. The European Physical Journal B - Condensed Matter and Complex Systems 38 2 (2004) 269-276
22. C. Wang, J. Knight, M. Elder, On computer viral infection and the effect of immunization, in: Computer Security Applications, ACSAC '00, 16th Annual Conference, 2000, pp. 246-256
23. Bai W.J., Zhou T., and Wang B.H. Immunization of susceptible-infected model on scale-free networks. Physica A: Statistical Mechanics and its Applications 384 2 (2007) 656-662 10.1016/j.physa.2007.04.107
24. Cohen R., Havlin S., and Ben Avraham D. Efficient immunization strategies for computer networks and populations. Physical Review Letters 91 24 (2003) 247901
25. Wan Y., Roy S., and Saberi A. Designing spatially heterogeneous strategies for control of virus spread. IET Systems Biology 2 4 (2008) 184-201
26. Harris C.J., and Miles J.F. Stability of linear systems: Some aspects of kinematic similarity. Mathematics in Science and Engineering vol. 153 (1980), Academic Press, London, New York
27. Berman A., and Plemmons R.J. Nonnegative matrices in the mathematical sciences (1994), Society for Industrial Mathematics
28. Erdos P., and Renyi A. On random graphs. Publicationes Mathematicae Debrecen 6 290 (1959)
29. Barabási A., and Albert R. Emergence of scaling in random networks. Science 286 5439 (1999) 509-512
30. Pastor-Satorras R., and Vespignani A. Immunization of complex networks. Physical Review E 65 3 (2002) 036104
31. Dezso{double acute} Z., and Barabási A.-L. Halting viruses in scale-free networks. Physical Review E 65 5 (2002) 055103
32. Varga R.S. Matrix Iterative Analysis (2000), Springer
33. Mathias R. Spectral perturbation bounds for positive definite matrices. SIAM Journal on Matrix Analysis and Applications 18 4 (1997) 959-980
34. Wang Y., Xiao G., Hu J., Cheng T., and Wang L. Imperfect targeted immunization in scale-free networks. Physica A: Statistical Mechanics and its Applications 388 12 (2009) 2535-2546 10.1016/j.physa.2009.02.036
35. Holme P. Efficient local strategies for vaccination and network attack. Europhysics Letters 68 6 (2004) 908-914
36. Boyd S.P., and Vandenberghe L. Convex Optimization (2004), Cambridge University Press
37. Tuy H., and Hoang T. Convex Analysis and Global Optimization (1998), Kluwer Academic Pub.
38. Lewis A., and Overton M. Eigenvalue optimization. Acta Numerica 5 (2008) 149-190
39. W. Fulton, Eigenvalues of sums of hermitian matrices, Seminaire Bourbaki 40, Exposé No. 845, 1998, p. 15
40. Vandenberghe L., and Boyd S. Semidefinite programming. SIAM Review 38 1 (1996) 49-95
41. Boyd S., Ghosh A., and Prabhakar B. Randomized gossip algorithms. IEEE/ACM Transactions on Networking (TON) 14 (2006) 2508-2530
42. Grant M., and Boyd S. Graph implementations for nonsmooth convex programs. Lecture Notes in Control and Information Sciences vol. 371 (2008) 95
43. M. Grant, S. Boyd, Matlab software for disciplined convex programming (web page and software), February 2009. URL http://stanford.edu/~boyd/cvx
44. Burke J.V., Lewis A.S., and Overton M.L. A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM Journal on Optimization 15 3 (2005) 751-779
45. Horn R.A., and Johnson C.R. Matrix Analysis (1990), Cambridge University Press