Networks and epidemic models

Journal of the Royal Society Interface

Volumn 2, Issue 4, 2005, Pages 295-307

  Keeling, Matt J ^a   Eames, Ken T D ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b Department of Zoology ^*  (United Kingdom)

Author keywords

Contact tracing; Infection; Random network; Scale free network; Small world network; Transmission

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; COMPUTER SIMULATION; DISEASE PREDISPOSITION; DISEASE TRANSMISSION; EPIDEMIC; EPIDEMIOLOGY; HUMAN; INCIDENCE; METHODOLOGY; POPULATION DYNAMICS; PREVALENCE; RISK ASSESSMENT; RISK FACTOR; SOCIAL SUPPORT; STATISTICS;

ANIMALS; COMMUNICABLE DISEASES, EMERGING; COMPUTER SIMULATION; DISEASE OUTBREAKS; DISEASE SUSCEPTIBILITY; DISEASE TRANSMISSION; EPIDEMIOLOGIC METHODS; HUMANS; INCIDENCE; MODELS, BIOLOGICAL; POPULATION DYNAMICS; PREVALENCE; RISK ASSESSMENT; RISK FACTORS; SOCIAL SUPPORT;

EID: 33646893242     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2005.0051     Document Type: Review

References (99)

1. Albert, R., Jeong, H. & Barabási, A.-L. 1999 Diameter of the world-wide web. Nature 401, 130-131.
2. Albert, R., Jeong, H. & Barabási, A.-L. 2000 Error and attack tolerance of complex networks. Nature 406, 378-381.
3. Anderson, R. M. 1988 The epidemiology of HIV infection: variable incubation plus infectious periods and heterogeneity in sexual activity. J.R. Stat. Soc. A 151, 66-98.
4. Anderson, R. M. & May, R. M. 1992 Infectious diseases of humans. Oxford: Oxford University Press.
5. Bailey, N. T. J. 1957 The mathematical theory of epidemics. London: Griffin.
6. Bak, P., Chen, K. & Tang, C. 1990 A forest-fire model and some thoughts on turbulence. Phys. Lett. A 147, 297-300.
7. Barabási, A. L. & Albert, R. 1999 Emergence of scaling in random networks. Science 286, 509-512.
8. Barbour, A. & Mollison, D. 1990 Epidemics and random graphs. In Stochastic processes in epidemic theory (ed. J.-P. Gabriel, C. Lefèvre & P. Picard), pp. 86-89. New York: Springer.
9. Bearman, P. S., Moody, J. & Stovel, K. 2004 Chains of affection: the structure of adolescent romantic and sexual networks. Am. J. Sociol. 110, 44-91.
10. Bollobás, B. 1979 Graph theory. New York: Springer.
11. Bollobás, B. 1985 Random graphs. London: Academic Press.
12. Boots, M. & Sasaki, A. 1999 'Small worlds' and the evolution of virulence: infection occurs locally and at a distance. Proc. R. Soc. B 266, 1933-1938. (doi:10.1098/rspb.1999.0869.)
13. De, P., Singh, A. E., Wong, T., Yacoub, W. & Jolly, A. M. 2004 Sexual network analysis of a gonorrhoea outbreak. Sex. Transm. Infect. 80, 280-285.
14. Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. 1998 A deterministic epidemic model taking account of repeated contacts between the same individuals. J. Appl. Prob. 35, 462-468.
15. Dietz, K. & Hadeler, K. P. 1988 Epidemiological models for sexually transmitted diseases. J. Math. Biol. 26, 1-25.
16. Doherty, I. A., Padian, N. S., Marlow, C. & Aral, S. O. 2005 Determinants and consequences of sexual networks as they affect the spread of sexually transmitted infections. J. Infect. Dis. 191, S42-S54.
17. Eames, K. T. D. & Keeling, M. J. 2002 Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proc. Natl Acad. Sci. USA 99, 13330-13335.
18. Eames, K. T. D. & Keeling, M. J. 2003 Contact tracing and disease control. Proc. R. Soc. B 270, 2565-2571. (doi:10.1098/rspb.2003.2554.)
19. Eames, K. T. D. & Keeling, M. J. 2004 Monogamous networks and the spread of sexually transmitted diseases. Math. Biosci. 189, 115-130.
20. Earn, D. J. D., Rohani, P., Bolker, B. M. & Grenfell, B. T. 2000 A simple model for complex dynamical transitions in epidemics. Science 287, 667-670.
21. Edmunds, W. J., Medley, G. F. & O'Callaghan, C. J. 1997a Social ties and susceptibility to the common cold. J. Am. Med. Assoc. 278, 1231.
22. Edmunds, W. J., O'Callaghan, C. J. & Nokes, D. J. 19976 Who mixes with whom? A method to determine the contact patterns of adults that may lead to the spread of airborne infections. Proc. R. Soc. B 264, 949-957. (doi:10.1098/rspb.1997.0131.)
23. Eichner, M. 2003 Case isolation and contact tracing can prevent the spread of smallpox. Am. J. Epidemiol. 158, 118-128.
24. Eubank, S., Guclu, H., Kumar, V. S. A., Marathe, M. V., Srinivasan, A., Toroczkai, Z. & Wang, N. 2004 Modelling disease outbreaks in realistic urban social networks. Nature 429, 180-184.
25. Ferguson, N. M. & Garnett, G. P. 2000 More realistic models of sexually transmitted disease transmission dynamics: sexual partnership networks, pair models, and moment closure. Sex. Transm. Dis. 27, 600-609.
26. Ferguson, N. M., Donnelly, C. A. & Anderson, R. M. 2001 The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions. Science 292, 1155-1160.
27. Frank, O. & Strauss, D. 1986 Markov Graphs. J. Am. Stat. Soc. 81, 832-842.
28. Fraser, C., Riley, S., Anderson, R. M. & Ferguson, N. M. 2004 Factors that make an infectious disease outbreak controllable. Proc. Natl Acad. Sci. USA 101, 6146-6151.
29. Garnett, G. P. & Anderson, R. M. 1996 Sexually transmitted diseases and sexual behavior: insights from mathematical models. J. Infect. Dis. 174, S150-S161.
30. Ghani, A. C. & Garnett, G. P. 1998 Measuring sexual partner networks for transmission of sexually transmitted diseases. J. R. Stat. Soc. A 161, 227-238.
31. Ghani, A. C. & Garnett, G. P. 2000 Risks of acquiring and transmitting sexually transmitted diseases in sexual partner networks. Sex. Transm. Dis. 27, 579-587.
32. Ghani, A. C., Swinton, J. & Garnett, G. P. 1997 The role of sexual partnership networks in the epidemiology of gonorrhea. Sex. Transm. Dis. 24, 45-56.
33. Gilbert, M., Mitchell, A., Bourn, D., Mawdsley, J., Clifton-Hadley, R. & Wint, W. 2005 Cattle movements and bovine tuberculosis in Great Britain. Nature 435, 491-496.
34. Grassberger, P. 1983 On the critical behaviour of the general epidemic process and dynamical percolation. Math. Biosci. 63, 157-172.
35. Grenfell, B. T. 1992 Chance and chaos in measles dynamics. J. R. Stat. Soc. B 54, 383-398.
36. Grenfell, B. T., Bjornstad, O. N. & Kappey, J. 2001 Travelling waves and spatial hierarchies in measles epidemics. Nature 414, 716-723.
37. Grimmett, G. 1989 Percolation. Berlin: Springer.
38. Halloran, M. E., Longini Jr. I. M., Nizam, A. & Yang, Y. 2002 Containing bioterrorist smallpox. Science 298, 1428-1432.
39. Handcock, M. S. & Jones, J. H. 2004 Likelihood-based inference for stochastic models of sexual network formation. Theor. Popul. Biol. 65, 413-422.
40. Harary, F. 1969 Graph theory. Reading, MA: Addison-Wesley.
41. Harris, T. E. 1974 Contact interactions on a lattice. Ann. Probab. 2, 969-988.
42. Haydon, D. T., Chase-Topping, M., Shaw, D. J., Matthews, L., Friar, J. K., Wilesmith, J. & Woolhouse, M. E. J. 2003 The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak. Proc. R. Soc. B 270, 121-127. (doi:10.1098/rspb.2002.2191.)
43. Hethcote, H. W. & Yorke, J. A. 1984 Gonorrhea transmission dynamics and control. Springer Lecture Notes in Biomathematics. Berlin: Springer.
44. Jeong, H., Tombar, B., Albert, R., Oltvai, Z. N. & Barabasi, A.-L. 2000 The large-scale organization of metabolic networks. Nature 407, 651-654.
45. Jolly, A. M. & Wylie, J. L. 2002 Gonorrhoea and chlamydia core groups and sexual networks in Manitoba. Sex. Transm. Infect. 78, i45-i51.
46. Karlberg, M. 1997 Testing transitivity in graphs. Soc. Networks 19, 325-343.
47. Keeling, M. J. 1997 Modelling the persistence of measles. Trends Microbiol. 5, 513-518.
48. Keeling, M. J. 1999 The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. B 266, 859-867. (doi:10.1098/rspb.1999. 0716.)
49. Keeling, M. J. 2005 Implications of network structure for epidemic dynamics. Theor. Popul. Biol. 67, 1-8.
50. Keeling, M. J., Rand, D. A. & Morris, A. J. 1997 Correlation models for childhood epidemics. Proc. R. Soc. B 264, 1149-1156. (doi:10.1098/rspb.1997. 0159.)
51. Keeling, M. J., Rohani, P. & Grenfell, B. T. 2001 Seasonally-forced disease dynamics explored as switching between attractors. Physica D 148, 317-335.
52. Kermack, W. O. & McKendrick, A. G. 1927 A contribution to the mathematical theory of epidemics. Proc. R. Soc. A 115, 700-721.
53. Klovdahl, A. S. 1985 Social networks and the spread of infectious diseases: the AIDS example. Soc. Sci. Med. 21, 1203-1216.
54. Klovdahl, A. S. 2001 Networks and pathogens. Sex. Transm. Dis. 28, 25-28.
55. Klovdahl, A. S., Dhofier, Z., Oddy, G., O'Hara, J., Stoutjesdijk, S. & Whish, A. 1977 Social networks in an urban area: first Canberra study Aust. N. Z. J. Sociol. 13, 169-172.
56. Kretzschmar, M., van Duynhoven, Y. T. H. P. & Severijnen, A. J. 1996 Modeling prevention strategies for gonorrhea and chlamydia using stochastic network simulations. Am. J. Epidem. 144, 306-317.
57. Kuperman, M. & Abramson, G. 2001 Small world effects in an epidemiological model. Phys. Rev. Lett. 86, 2909-2912.
58. Leinhardt, S. (ed.) 1977 Social networks: a developing paradigm. New York: Academic Press.
59. Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley, H. E. & Aberg, Y. 2001 The web of human sexual contacts. Nature 411, 907-908.
60. Liljeros, F., Edling, C. R. & Amaral, L. A. N. 2003 Sexual networks: implications for the transmission of sexually transmitted infections. Microbes Infect. 5, 189-196.
61. Lloyd, A. L. & May, R. M. 2001 How viruses spread among computers and people. Science 292, 1316-1317.
62. 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.
63. Milgram, S. 1967 The small world problem. Psychol. Today 1, 61-67.
64. Mollison, D. 1977 Spatial contact models for ecological and epidemic spread. J. R. Stat. Soc. 39, 283-326.
65. Moore, C. & Newman, M. 2000 Epidemics and percolation in small-world networks. Phys. Rev. E 61, 5678-5682.
66. Morris, M. 1997 Sexual networks and HIV. AIDS 11, S209-S216.
67. Müller, J., Kretzschmar, M. & Dietz, K. 2000 Contact tracing in stochastic and deterministic epidemic models. Math. Biosci. 164, 39-64.
68. National Audit Office 2003 Identifying and tracking livestock in England. London: The Stationary Office.
69. Newman, M. E. J. 2001 The structure of scientific collaboration networks. Proc. Natl Acad. Sci. USA 98, 404-409.
70. Newman, M. E. J. 2002 Spread of epidemic disease on networks. Phys Rev. E 66, 016128.
71. Newman, M. E. J. & Watts, D. J. 1999 Scaling and percolation in the small-world network model. Phys Rev. E 60, 7332-7342.
72. Olsen, L. F., Truty, G. L. & Schaffer, W. M. 1986 Oscillations and chaos in epidemics: a nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark. Theor. Pop. Biol. 33, 344-370.
73. Pastor-Satorras, R. & Vespignani, A. 2001 Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200-3203.
74. Potterat, J. J., Rothenberg, R. B. & Muth, S. Q. 1999 Network structural dynamics and infectious disease propagation. Int. J. STD AIDS 10, 182-185.
75. Potterat, J. J., Philips-Plummer, L., Muth, S. Q., Rothenberg, R. B., Woodhouse, D. E., Maldonado-Long, T. S., Zimmerman, H. P. & Muth, J. B. 2002 Risk network structure in the early epidemic phase of HIV transmission in Colorado Springs. Sex. Transm. Infect. 78, i159-i163.
76. Rand, D. A. & Wilson, H. B. 1991 Chaotic stochasticity-a ubiquitous source of unpredictability in epidemics. Proc. R. Soc. B 246, 179-184.
77. Read, J. M. & Keeling, M. J. 2003 Disease evolution on networks: the role of contact structure. Proc. R. Soc. B 270, 699-708. (doi:10.1098/rspb.2002. 2305.)
78. Rhodes, C. J. & Anderson, R. M. 1997 Epidemic thresholds and vaccination in a lattice model of disease spread. Theor. Popul. Biol. 52, 101-118.
79. Rhodes, C. J., Jensen, H. J. & Anderson, R. M. 1997 On the critical behaviour of simple epidemics. Proc. R. Soc. B 264, 1639-1646. (doi:10.1098/rspb.1997.0228.)
80. Riley, S. et al. 2003 Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science 300, 1961-1966.
81. Robins, G., Pattison, P. & Woolcock, J. 2004 Missing data in networks: exponential random graph (p*) models for networks with non-respondents. Soc. Networks 26, 257-283.
82. Rohani, P., Earn, D. J. D. & Grenfell, B. T. 2000 The impact of immunisation on pertussis transmission in England and Wales. Lancet 355, 285-286.
83. Rothenberg, R. 2001 Commentary-how a net works-implications of network structure for the persistence and control of sexually transmitted diseases and HIV. Sex. Transm. Dis. 28, 63-68.
84. Rothenberg, R. 2003 STD transmission dynamics: some current complexities-2002 Thomas Parran Award Lecture. Sex. Transm. Dis. 30, 478-482.
85. Rothenberg, R. B., Potterat, J. J., Woodhouse, D. E., Muth, S. Q., Darrow, W. W. & Klovdahl, A. S. 1998 Social network dynamics and HIV transmission. AIDS 12, 1529-1536.
86. Rozenfeld, A. F., Cohen, R., ben-Avraham, D. & Havlin, S. 2002 Scale-free networks on lattices. Phys. Rev. Lett. 89, 218701.
87. Schwartz, I. B. 1985 Multiple recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models. J. Math. Biol. 18, 233-253.
88. Scott, J. 1991 Social network analysis: a handbook. London: SAGE Publications.
89. Snijders, T. A. B. 2001 The statistical evaluation of social network dynamics. Sociol. Methodol. 31, 361-395.
90. Szendroi, B. & Csányi, G. 2004 Polynomial epidemics and clustering in contact networks. Proc. R. Soc. B 271, S364-S366. (doi:10.1098/rsbl.2004.0188.)
91. Travers, J. & Milgram, S. 1969 An experimental study of the small world problem. Sociometry 32, 425-443.
92. Wallinga, J., Edmunds, W. J. & Kretzschmar, M. 1999 Perspective: human contact patterns and the spread of airborne infectious diseases. Trends Microbiol. 7, 372-377.
93. Warren, C. P., Sander, L. M. & Sokolov, I. M. 2002 Geography in a scale-free network model. Phys. Rev. E 66, 056105.
94. Wasserman, S. & Faust, K. 1994 Social network analysis. Cambridge: Cambridge University Press.
95. Watts, D. J. 1999 Small worlds: the dynamics of networks between order and randomness. Princeton: Princeton University Press.
96. Watts, D. J. & Strogatz, S. H. 1998 Collective dynamics of 'small-world' networks. Nature 393, 440-442.
97. West, D. B. 1996 Introduction to graph theory. Upper Saddle River, NJ: Prentice Hall.
98. Woodhouse, D. E. et al. 1994 Mapping a social network of heterosexuals at high risk for HIV infection. AIDS 8, 1331-1336.
99. Wylie, J. L. & Jolly, A. 2001 Patterns of chlamydia and gonorrhea infection in sexual networks in Manitoba, Canada. Sex. Transm. Dis. 28, 14-24.