Contact network epidemiology: Bond percolation applied to infectious disease prediction and control

Bulletin of the American Mathematical Society

Volumn 44, Issue 1, 2007, Pages 63-86

  Meyers, Lauren Ancel ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547299719     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-06-01148-7     Document Type: Article

References (70)

1. H. Abbey, An examination of the reed-frost theory of epidemics, Human Biology 24 (1952). no. 3. 201-233.
2. R. M. Anderson and R. M. May. Infectious Diseases of Humans. Dynamics and Control, Oxford University Press, Oxford, 1991.
3. L. A. N. Amaral and J. M. Ottino. Complex networks - augmenting the framework for the study of complex systems, Eur. Phys. J. B. 38 (2004). 147-162.
4. A. L. Barabasi and R. Albert, Emergence of scaling in random networks, Science 286 (1999), no. 5439, 509. MR2091634
5. N. T. J. Bailey, The Mathematical Theory of Infectious Diseases and Its Applications. Hafner Press. New York. 1975. MR0452809 (56:11084)
6. D. Bernoulli and S. Blower, An attempt at a new analysis of lhe mortality caused by smallpox and of the advantages of inoculation to prevent it. Reviews in Medical Virology 14 (2004). no. 5. 275-288.
7. N. Becker, Estimation for discrete time branching processes with application to epidemics, Biometrics 33 (1977), no. 3, 515-522. MR0654337 (58:31657)
8. Designated hospitals in Beijing meeting SARS treatment demands, People's Daily Online. 2003.
9. F. Ball. D. Mollison. and G. Scalia-Tomba. Epidemics with two levels of mixing. The Annals of Applied Probability 7 (1997), 46. MR1428749 (99a:92033)
10. C. M. Booth, L. M. Matukas, G. A. Tomlinson. A. R. Rachlis, D. B. Rose, H. A. Dwosh. S. L. Walmsley. T. Mazzulli, M. Avendano. P. Derkach. I. E. Ephtimios. I. Kitai. B. D. Mederski, S. B. Shadowitz. W. L. Gold. L. A. Hawryluck. E. Rea. J. S. Chenkin, D. W. Cescon, S. M. Poutanen. and A. S. Detsky, Clinical features and short-term outcomes of 144 patients with SARS in the greater Toronto area. JAMA (2003), 289.21.JOC30885.
11. S. Bansal. B. Pourbohloul. and L. A. Meyers. .4 comparative analysis of influenza vaccination programs. PLoS Medicine 3 (2006), e387.
12. T. Britton and P. D. O'Neill, Bayesian inference for stochastic epidemics in populations with random social structure, Scandanavian Journal of Statistics 29 (2002). no. 3, 375-390. MR1925565
13. CDC, Efficiency of quarantine during an epidemic of severe acute respiratory syndrome-Beijing, China, 2003, Morbidity and Mortality Weekly Report 52 (2003). no. 43. 1037-1040.
14. CDC informational bulletin. Public health guidance for community-level preparedness and response to severe acute respiratory syndrome (SARS) version 2, supplement D: Community containment measures, including nonhospital isolation and quarantine, 2004. http://www.cdc.gov/ncidod/sars/ guidance/D/pdf/ lessons.pdf
15. G. Chowell, J. M. Hyman, S. Eubank, and C. Castillo-Chavez, Scaling laws for the movement of people between locations in a large city, Physical Review E 68 (2003), 066102.
16. CNN.com, Berkeley turns away students from SARS-hit regions, 2003.
17. CNN.com, SARS closing Beijing schools, 2003.
18. O. Diekmann, M. C. M. de Jong, and J. A. J. Metz, A deterministic epidemic model taking account of repeated contacts between the same individuals, J. Appl. Prob. 35 (1998), 448-462. MR1641833:(99k:92041) :
19. C. A. Donnelly, A. C. Ghani, G. M. Leung, A. J. Hedley, C. Fraser, S. Riley, L. J. Abu-Raddad, L-M. Ho, T-Q. Thach, P. Chau, K-P. Chan, T-H. Lam, L-Y. Tse, T. Tsang, S-H. Liu, J. H. B. Kong, E. M. C. Lau, N. M. Ferguson, and R. M. Anderson, Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. The Lancet (2003), 1.
20. K. Dietz and J. A. P. Heesterbeek, Daniel Bernoulli's epidemiological model revisited, Mathematical Biosciences 180 (2002), 1-21. MR1950745 (2003m-92070)
21. R. Durrett, Stochastic spatial models, SIAM Review 41 (1999), no. 4, 677-718. MR1722998::(2000h:60086)
22. S. Eubank, H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai, and N. Wang, Modelling disease outbreaks in realistic urban social networks, Nature 429 (2004), 180-184.
23. M. Ferrari, S. Bansal, L. A. Meyers, and O. N. Bjornstad, Network frailty and the geometry of herd immunity, Proceedings of the Royal Society (London) B (in press).
24. N. M. Ferguson and G. P. Garnett, More realistic models of sexually transmitted disease transmission dynamics: sexual partnership networks, pair models, and moment closure, Sex. Transm. Dis. 27 (2000), no. 10, 600.
25. J. P. Fox, C. E. Hall, M. K. Cooney, and H. M. Foy, hifluenza virus infections in Seattle families, 1975-1979, American Journal of Epidmiology 116 (1982), 212-227.
26. C. P. Farrington, M. N. Kanaan, and N. J. Gay, Branching process models for surveillance of infectious diseases controlled by mass vaccination, Biostatistics 4 (2003), no. 2, 279-295.
27. W. P. Glezen, Emerging infections: pandemic influenza, Epidemiology Reviews 18 (1996), no. 1, 64-76.
28. P. Grassberger, Critical behavior of the general epidemic process and dynamical percolation, Mathematical Biosciences 63 (1983), no. 2, 157-172.
29. W. H. Hamer, Epidemic disease in England-the evidence of variability and persistency of type, The Lancet i (1906), 733-739.
30. H. W. Hethcote, Mathematics of infectious diseases, SIAM Review 42 (2000), 599. MR1814049 (2002c-92034)
31. H. W. Hethcote and J. A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics, vol. 56, Springer-Verlag, Berlin, 1984. MR0766910::(86a:92002):
32. L. C. Jennings and J. A. R. Miles, A study of acute respiratory disease in the community of Port Chalmers, Journal of Hygiene 81 (1978), 67-75.
33. A. Kleczkowski and B. T. Grenfell, Mean field-type equations for spread of epidemics: the 'small world' model, Physica A 274 (1999), no. 1-2, 1-385.
34. W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society (London) A 115 (1927), 700-721.
35. M. J. Keeling, D. A. Rand, and A. J. Morris, Correlation models for childhood diseases, Proceedings of the Royal Society (London) B 264 (1997), 1149-1156.
36. M. J. Keeling, M. E. Woolhouse, R. M. May, G. Davies, and B. T. Grenfell, Modelling vaccination strategies against foot-and-mouth disease, Nature 421 (2003), no. 6919, 136-42.
37. M. Lipsitch, T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, G. Gopalakrishna, S. K. Chew, C. C. Tan, M. H. Samore, D. Fisman, and M. Murray, Transmission dynamics and control of severe acute respiratory syndrome, Science (2003), 1086616.
38. Y. S. Leo, M. Chen, B. H. Heng, C. C. Lee, N. Paton, B. Ang, P. Choo, S. W. Lim, A. E. Ling, M. L. Ling, B. K. Tay, P. A. Tambyah, Y. T. Lim, G. Gopalakrishna, S. Ma, L. James, P. L. Ooi, S. Lim, K. T. Goh, Sk. K. Chew, and C. C. Tan, Severe acute respiratory syndrome - Singapore, 2003, Morbidity and Mortality Weekly Report 52 (2003), no. 18, 405.
39. F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Aberg, The web of human sexual contacts, Nature 411 (2001), 907-908.
40. F. Liljeros, C. R. Edling, and L. A. N. Amaral, Sexual networks: implications for the transmission of sexually transmitted diseases, Microbes (2003).
41. I. M. Longini and M. E. Halloran, Strategy for distribution of influenza vaccine to high-risk groups and children, American Journal of Epidemiology 161 (2005), 303-306.
42. I. M. Longini, M. E. Halloran, A. Nizam, and Y. Yang, Containing pandemic influenza with antiviral agents, American Journal of Epidemiology 159 (2004), 623-633.
43. I. M. Longini, J. S. Koopman, A. S. Monto, and J. P. Fox, Estimating house-hold and community transmission parameters of influenza, American Journal of Epidemiology 115 (1982), 736-751.
44. A. L. Lloyd and R. M. May, Epidemiology. How viruses spread among computers and people, Science 292 (2001), no. 5520, 1316.
45. I. M. Longini, A mathematical model for predicting the geographic spread of new infectious agents, Math. Biosci. 90 (1988), 367. MR0958149 (89h:92052)
46. C. Lefevre and P. Picard, On the formulation of discrete-time epidemic models, Math. Biosci. 95 (1989), no. 1, 27-35. MR1001289 (90e:92068)
47. A. S. Monto, J. S. Koopman, and I. M. Longini, The Tecumseh study of illness. XIII. Influenza infection and disease, 1976-1981, American Journal of Epidemiol-ogy 121 (1985), 811-822.
48. L. A. Meyers, M. E. J. Newman, M. Martin, and S. Schrag, Applying network theory to epidemics: Control measures for mycoplasma pneumoniae outbreaks, Emerging Infectious Diseases 9 (2003), no. 2, 204.
49. L. A. Meyers, M. E. J. Newman, and B. Pourbohloul, Predicting epidemics on directed contact networks, Journal of Theoretical Biology 240 (2006), 400-418.
50. M. Morris, Data driven network models for the spread of disease, Epidemic Models: Their Structure and Relation to Data (D. Mollison, ed.), Cambridge University Press, Cambridge, 1995, pp. 302-322.
51. L. A. Meyers, B. Pourbohloul, M. E. J. Newman, D. M. Skowronski, and R. C. Brunham, Network theory and SARS: predicting outbreak diversity, Journal of Theoretical Biology 232 (2005), 71-81. MR2106112
52. M. E. J. Newman, Spread of epidemic disease on networks, Physical Review E 66 (2002), no. 1, art. no. 016128. MR1919737:(2003e:60223)
53. _, Threshold effects for two pathogens spreading on a network, Physical Review Letters 95 (2005).
54. World Health Organization, Severe acute respiratory syndrome (SARS), 2003.
55. B. Pourbohloul, L. A. Meyers, D. M. Skowronski, M. Krajden, D. M. Patrick, and R. C. Brunham, Modeling control strategies of respiratory pathogens, Emerg. Infect. Dis. 11 (2005), no. 8, 1249-1256.
56. R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett. 86 (2001), no. 14, 3200.
57. N. Paneth and P. Vinten-Johansen, A rivalry of foulness: Official and unofficial investigations of the London cholera epidemic of 1854, American Journal of Public Health 88 (1998), no. 10, 1545-1553.
58. S. Riley, C. Fraser, C. A. Donnelly, A. C. Ghani, L. J. Abu-Raddad, A. J. Hedley, G. M. Leung, L-M. Ho, T-H. Lam, T. Q. Thach, P. Chau, K-P. Chan, S-V. Lo, P-Y. Leung, T. Tsang, W. Ho, K-H. Lee, E. M. C. Lau, N. M. Ferguson, and R. M. Anderson, Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions, Science (2003), 1086478.
59. R. B. Rothenberg, How a net works: implications of network structure for the persistence and control of sexually transmitted diseases and HIV, Sexually Transmitted Diseases 28 (2001), 63-68.
60. T. A. Reichart, N. Sugaya, D. S. Fedson, W. P. Glezen, L. Simonsen, and M. Tashiro, The Japanese experience with vaccinating school-children against influenza, New England Journal of Medicine 344 (2001), 889-896.
61. R. B. Rothenberg, C. Sterk, K. Toomey, J. Potterat, D. Johnson, M. Schrader, and S. Hatch, Using social network and ethnographic tools to evaluate syphilis transmission, Sexually Transmitted Diseases 25 (1997), no. 3, 154-160.
62. Smallpox: A great and terrible scourge, 2002, National Library of Medicine (National Institutes of Health) website: http://www.nlm.nih.gov/ exhibition/ smallpox/sp.variolation.html
63. L. Sattenspiel and C. P. Simon, The spread and persistence of infectious diseases in structured populations, Math. Biosci. 90 (1988), 341. MR0958148 (89m:92045)
64. L. M. Sander, C. P. Warren, I. M. Sokolov, C. Simon, and J. Koopman, Percolation on heterogeneous networks as a model for epidemics, Mathematical Biosciences 180 (2002), 293-305. MR1950759 (2003m:92080):
65. L. H. Taber, A. Paredes, W. P. Glezen, and R. B. Couch, Infection with influenza A/Victoria virus in Houston families, 1976, Journal of Hygiene 86 (1982), 303-313.
66. C. P. B. Van der Ploeg, C. van Vliet, S. J. de Vlas, J. O. Ndinya-Achola, L. Fransen, G. J. van Oortmarssen, and J. D. F. Habbema, A microsimulation model for decision support in STD control, Interfaces 28 (1998), 84-100.
67. E. Volz, SIR dynamics structured populations with heterogeneous connectivity, Journal of Mathematical Biology (in press).
68. D. J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press, Princeton, 1999. MR1716136 (2001a:91064)
69. D. Weycker, J. Edelsberg, M. E. Halloran, I. M. Longini, A. Nizam, V. Ciuryla, and G. Oster, Population-wide benefits of routine vaccination of children against influenza, Vaccine 23 (2005), no. 10, 1284-1293.
70. R-H. Xu, J-F. He, M. R. Evans, G-W. Peng, H. E. Field, D-W. Yu, C-K. Lee, H-M. Luo, W-S. Lin, P. Lin, L-H. Li, W-J. Liang, J-Y. Lin, and A. Schnur, Epidemiologic clues to SARS origin in China, Emerg. Infect. Dis. 10 (2004), no. 6.