Network frailty and the geometry of herd immunity

Proceedings of the Royal Society B: Biological Sciences

Volumn 273, Issue 1602, 2006, Pages 2743-2748

  Ferrari, Matthew J ^a   Bansal, Shweta ^b   Meyers, Lauren A ^b,c   Björnstad, Ottar N ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c SANTA FE INSTITUTE   (United States)

Author keywords

Epidemiology; Frailty; Herd immunity; Social network; Vaccination

Indexed keywords

DISEASE SPREAD; DISEASE TRANSMISSION; EPIDEMIC; GEOMETRY; IMMUNITY; IMMUNIZATION; INFECTIOUS DISEASE;

ARTICLE; DISEASE TRANSMISSION; GEOMETRY; HERD IMMUNITY; IMMUNIZATION; POISSON DISTRIBUTION; PRIORITY JOURNAL; SOCIAL NETWORK; VACCINATION;

EID: 33750551765     PISSN: 09628452     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rspb.2006.3636     Document Type: Article

References (24)

1. Albert, R. & Barabasi, A. L. 2002 Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97. (doi:10. 1103/RevModPhys.74.47)
2. Albert, R., Jeong, H. & Barabasi, A. L. 2000 Error and attack tolerance of complex networks. Nature 406, 378-382. (doi:10.1038/35019019)
3. Anderson, R. M. & May, R. M. 1990 Immunization and herd-immunity. Lancet 335, 641-645. (doi:10.1016/0140-6736(90)90420-A)
4. Anderson, R. M. & May, R. M. 1991 Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press.
5. Bailey, N. T. J. 1957 The mathematical theory of epidemics. London, UK: Griffin.
6. Barabasi, A. L., Albert, R. & Jeong, H. 1999 Mean-field theory for scale-free random networks. Physica A 272, 173-187. (doi:10.1016/S0378-4371(99) 00291-5)
7. Barthelemy, M., Barrat, A., Pastor-Satorras, R. & Vespignani, A. 2005 Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. J. Theor. Biol. 235, 275-288. (doi:10.1016/j.jtbi.2005.01.011)
8. Bonabeau, E., Dagorn, L. & Freon, P. 1999 Scaling in animal group-size distributions. Proc. Natl Acad. Sci. USA 96, 4472-4477. (doi:10.1073/pnas.96.8.4472)
9. Hougaard, P. 1984 Life table methods for heterogeneous populations: distributions describing the heterogeneity. Biometrika 71, 75-83. (doi:10.2307/2336399)
10. Keeling, M. 2005 The implications of network structure for epidemic dynamics. Theor. Popul. Biol. 67, 1-8. (doi:10.1016/j.tpb.2004.08.002)
11. McCallum, H., Barlow, N. & Hone, J. 2001 How should pathogen transmission be modelled? Trends Ecol. Evol. 16, 295-300. (doi:10.1016/S0169- 5347(01)02144-9)
12. Meyers, L. A., Pourbohloul, B., Newman, M. E. J., Skowronski, D. M. & Brunham, R. C. 2005 Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232, 71-81. (doi:10.1016/j.jtbi.2004.07.026)
13. Moore, C. & Newman, M. E. J. 2000 Epidemics and percolation in small-world networks. Phys. Rev. E 61, 5678-5682. (doi:10.1103/PhysRevE.61.5678)
14. Newman, M. E. J. 2002 Spread of epidemic disease on networks. Phys. Rev. E 66, 016128. (doi:10.1103/PhysRevE.66.016128)
15. Newman, M. E. J. 2005 Threshold effects for two pathogens spreading on a network. Phys. Rev. Lett. 95, 108701. (doi:10.1103/PhysRevLett.95.108701)
16. Newman, M. E. J. & Watts, D. J. 1999 Scaling and percolation in the small-world network model. Phys. Rev. E 60, 7332-7342. (doi:10.1103/PhysRevE.60. 7332)
17. Newman, M. E. J., Watts, D. J. & Strogatz, S. H. 2002 Random graph models of social networks. Proc. Natl Acad. Sci. USA 99, 2566-2572. (doi:10.1073/pnas.012582999)
18. Pastor-Satorras, R. & Vespignani, A. 2001 Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200-3203. (doi:10.1103/PhysRevLett. 86.3200)
19. Pourbohloul, B., Meyers, L. A., Skowronski, D. M., Krajden, M., Patrick, D. M. & Brunham, R. C. 2005 Modeling control strategies of respiratory pathogens. Emerg. Infect. Dis. 11, 1249-1256.
20. Sjoberg, M., Albrectsen, B. & Hjalten, J. 2000 Truncated power laws: a tool for understanding aggregation patterns in animals? Ecol. Lett. 3, 90-94. (doi:10.1046/j.1461-0248.2000.00113.x)
21. Vaupel, J. W., Manton, K. G. & Stallard, E. 1979 The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, 439-454.
22. Volchenkov, D., Volchenkova, L. & Blanchard, P. 2002 Epidemic spreading in a variety of scale free networks. Phys. Rev. E 66, 046137. (doi:10.1103/PhysRevE.66.046137)
23. Volz, E. 2004 Random networks with tunable degree distribution and clustering. Phys. Rev. E 70, 056115. (doi:10.1103/PhysRevE.70.056115)
24. Watts, D. J. & Strogatz, S. H. 1998 Collective dynamics of 'small-world' networks. Nature 393, 440-442. (doi:10.1038/30918)