Competing epidemics on complex networks

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

Volumn 84, Issue 3, 2011, Pages

  Karrer, Brian ^a   Newman, M E J ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CO-EXISTENCE REGIME; COMPLEX NETWORKS; DYNAMICAL TRANSITION; HUMAN DISEASE; NETWORK SIZE; RELATIVE RATES; STOCHASTIC FLUCTUATION; ANALYTIC-AND-NUMERICAL METHODS; RECENT RESEARCHES; STRONG DEPENDENCES;

NUMERICAL METHODS; PHASE DIAGRAMS; STOCHASTIC SYSTEMS;

DISPLAY DEVICES; COMPLEX NETWORKS;

EID: 80052994416     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.036106     Document Type: Article

References (25)

1. R. M. Anderson and R. M. May, Infectious Diseases of Humans (Oxford University Press, Oxford, 1992).
2. H. W. Hethcote, SIAM Rev. SIREAD 0036-1445 10.1137/S0036144500371907 42, 599 (2000).
3. M. J. Keeling and K. T. James, J. R. Soc. Interface SIREAD 1742-5689 10.1098/rsif.2005.0051 2, 295 (2005).
4. F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Åberg, Nature (London) NATUAS 0028-0836 10.1038/35082140 411, 907 (2001). (Pubitemid 32601479)
5. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3200 86, 3200 (2001). (Pubitemid 32317894)
6. M. E. J. Newman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.016128 66, 016128 (2002). (Pubitemid 40599061)
7. S. Bansal, B. T. Grenfell, and L. A. Meyers, J. R. Soc. Interface PRLTAO 1742-5689 10.1098/rsif.2007.1100 4, 879 (2007). (Pubitemid 47523493)
8. E. Kenah and J. C. Miller, Interdiscip. Perspect. Infect. Dis. PRLTAO 1687-708X 10.1155/2011/543520 2011, 543520 (2011).
9. P. S. Dodds and D. J. Watts, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.218701 92, 218701 (2004).
10. D. Mollison, J. R. Stat. Soc. B 39, 283 (1977).
11. P. Grassberger, Math. Biosci. MABIAR 0025-5564 10.1016/0025-5564(82) 90036-0 63, 157 (1983). (Pubitemid 13085555)
12. L. M. Sander, C. P. Warren, I. Sokolov, C. Simon, and J. Koopman, Math. Biosci. MABIAR 0025-5564 10.1016/S0025-5564(02)00117-7 180, 293 (2002). (Pubitemid 35304359)
13. M. E. J. Newman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 95.108701 95, 108701 (2005). (Pubitemid 41505818)
14. S. Funk and V. A. A. Jansen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.036118 81, 036118 (2010).
15. Y.-Y. Ahn, H. Jeong, N. Masuda, and J. D. Noh, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.066113 74, 066113 (2006). (Pubitemid 46013215)
16. M. Molloy and B. Reed, Random Struc. Algorithms PRLTAO 1042-9832 10.1002/rsa.3240060204 6, 161 (1995).
17. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.026118 64, 026118 (2001).
18. For technical reasons we also require that the first and second moments of the degree distribution be finite, which excludes some networks with heavy-tailed distributions.
19. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4626 85, 4626 (2000). (Pubitemid 32024907)
20. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5468 85, 5468 (2000). (Pubitemid 32089658)
21. b takes its maximum value of 1.
22. V. Marceau, P.-A. Noël, L. Hébert-Dufresne, A. Allard, and L. J. Dubé, Phys. Rev. E. PLEEE8 1539-3755 10.1103/PhysRevE.84.026105 84, 026105 (2011).
23. rk because the initial carriers of the diseases are chosen at random and not infected via a neighbor. In real life, on the other hand, all infections are acquired via a neighbor, so the equations should always be correct. These subtleties do not affect our arguments, however, so we ignore them here.
24. A naive implementation of this scheme would be computationally wasteful, and also somewhat arbitrary since one would have to decide a threshold level of infection below which a disease would be deemed to have died out. In our simulations we mitigate these problems somewhat by first generating the bond percolation clusters for the entire network and starting the simulated spread of the two diseases at vertices chosen from the giant clusters. This does not guarantee that both diseases will produce an epidemic in the coexistence region but it reduces substantially the number of cases where a disease dies out.
25. B. Karrer and M. E. J. Newman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.016101 82, 016101 (2010).