A contact-network-based formulation of a preferential mixing model

Bulletin of Mathematical Biology

Volumn 71, Issue 4, 2009, Pages 888-905

  Kiss, Istvan Z ^a   Simon, Péter L ^b   Kao, Rowland R ^c  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Epidemics; Final epidemic size; Preferential mixing

Indexed keywords

ARTICLE; BASIC REPRODUCTION NUMBER; CONTACT EXAMINATION; DISEASE TRANSMISSION; EPIDEMIC; FEMALE; HUMAN; MALE; SEXUALLY TRANSMITTED DISEASE; STATISTICAL MODEL;

BASIC REPRODUCTION NUMBER; CONTACT TRACING; DISEASE OUTBREAKS; FEMALE; HUMANS; MALE; MODELS, STATISTICAL; SEXUALLY TRANSMITTED DISEASES;

EID: 64449084685     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9386-2     Document Type: Article

References (34)

1. R.M. Anderson G. Garnett 2000 Mathematical models of the transmission and control of sexually transmitted disease Sex. Transm. Dis. 27 636 643
2. R.M. Anderson S. Gupta W. Ng 1990 The significance of sexual partner contact networks for the transmission of HIV J. AIDS 3 417 429
3. Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, London.
4. M. Barthélemy A. Barrat R. Pastoras-Satorras A. Vespignani 2005 Dynamical patterns of epidemic outbreaks in complex heterogeneous networks J. Theor. Biol. 235 257 288
5. M. Boguñá R. Pastor-Satorras A. Vespignani 2003 Absence of epidemic threshold in scale-free networks with degree-correlations Phys. Rev. Lett. 90 028701
6. Boguñá, M., Pastor-Satorras, R., Vespignani, A., 2003b. Epidemics spreading in complex networks with degree correlations. In: Pastor-Satorras, R., Rubi, J.M., Guilera, A.D. (Eds.), Statistical Mechanics of Complex Networks, Lecture Notes in Physics, vol. 625, pp. 127-147. Springer, Berlin
7. J.A. Catania T.J. Coates S. Kegels M.T. Fullilove 1992 Condom use in multi-ethnic neighborhoods of San Francisco: the population-based AMEN (AIDS in Multi- Ethnic Neighborhoods) study Am. J. Publ. Health 82 284 287
8. Diekmann, O., Heesterbeek, J.A.P., 2000. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, New York.
9. S. Eubank H. Guclu V.S.A. Kumar M.V. Marathe A. Srinivasan Z. Toroczkai N. Wang 2004 Modelling disease outbreaks in realistic urban social networks Nature 429 180 184 10.1038/nature02541
10. N.M. Ferguson C.A. Donnelly R.M. Anderson 2001 The foot-and mouth epidemic in Great Britain: pattern of spread and impact of interventions Science 292 1155 1160 10.1126/science.1061020
11. N.M. Ferguson D.A.T. Cummings S. Cauchemez C. Fraser S. Riley A. Meeyai S. Iamsirithaworn D.S. Burke 2005 Strategies for containing an emerging influenza pandemic in South East Asia Nature 437 209 214 10.1038/nature04017
12. A. Ghani J. Swinton G. Garnett 1997 The role of sexual partnership networks in the epidemiology of gonorrhea Sex. Transm. Infect. 24 45 56
13. D.M. Green I.Z. Kiss R.R. Kao 2006 Modelling the initial spread of foot-and-mouth disease through animal movements Proc. R. Soc. B 273 2729 2735 10.1098/rspb.2006.3648
14. S. Gupta R.M. Anderson R.M. May 1989 Networks of sexual contacts: implications for the pattern of spread of HIV AIDS 3 807 818
15. Hethcote, H.W., Yorke, J.A., 1984. Gonorrhea Transmission Dynamics and Control. Lecture Notes in Biomathematics, vol. 56. Springer, New York.
16. L. Hufnagel D. Brockmann T. Geisel 2004 Forecast and control of epidemics in a globalized world Proc. Natl. Acad. Sci. USA 101 15∈124 15∈129 10.1073/pnas.0308344101
17. H.J. Jones M.S. Handcock 2003 An assessment of preferential attachment as a mechanism for human sexual network formation Proc. R. Soc. B 270 1123 1128 10.1098/rspb.2003.2369
18. 0 in heterogeneous populations J. Theor. Biol. 242 634 642
19. R.R. Kao L. Danon D.M. Green I.Z. Kiss 2006 Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain Proc. R. Soc. B 273 1999 2007 10.1098/rspb.2006.3505
20. M.J. Keeling 2001 Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape Science 294 813 817 10.1126/science.1065973
21. I.Z. Kiss D.M. Green R.R. Kao 2005 Disease contact tracing in random and clustered networks Proc. R. Soc. B 272 1407 1414
22. I.Z. Kiss D.M. Green R.R. Kao 2006 The network of sheep movements within Great Britain: network properties and their implications for infectious disease spread J. R. Soc. Interface 3 669 677 10.1098/rsif.2006.0129
23. I.Z. Kiss D.M. Green R.R. Kao 2006 The effect of network heterogeneity and multiple routes of transmission on final epidemic size Math. Biosci. 203 124 136 10.1016/j.mbs.2006.03.002
24. I.Z. Kiss D.M. Green R.R. Kao 2008 The effect of network mixing patterns on epidemic dynamics and the efficacy of disease contact tracing J. R. Soc. Interface 5 791 799 10.1098/rsif.2007.1272
25. M. Kretzschmar Y.T.H.P. van Duynhoven A.J. Severijnen 1996 Modeling prevention strategies for gonorrhea and chlamydia using stochastic network simulations Am. J. Epidemiol. 144 306 317
26. F. Liljeros C.R. Edling L.A.N. Amaral H.E. Stanley Y. Aberg 2001 The web of human sexual networks Nature 411 907 908 10.1038/35082140
27. M. Lipsitch 2003 Transmission dynamics and control of severe acute respiratory syndrome Science 300 1966 1970 10.1126/science.1086616
28. R.M. May A.L. Lloyd 2001 Infection dynamics on scale-free networks Phys. Rev. E 64 066112
29. L.A. Meyers B. Pourbohloul M.E.J. Newman D.M. Skowronski R.C. Brunham 2005 Network theory and SARS: predicting outbreak diversity J. Theor. Biol. 232 71 81 10.1016/j.jtbi.2004.07.026
30. Y. Moreno J.B. Gómez A.F. Pacheco 2003 Epidemic incidence in correlated complex networks Phys. Rev. E 68 035103(R)
31. M.E.J. Newman 2002 Assortative mixing in networks Phys. Rev. E 89 208701
32. M.E.J. Newman 2003 Mixing patterns in networks Phys. Rev. E 67 026126
33. R. Pastor-Satorras A. Vazquez A. Vespignani 2001 Dynamical and correlation properties of the internet Phys. Rev. Lett. 87 0258701 10.1103/PhysRevLett.87.258701
34. P. van den Driessche J.J. Watmough 2002 Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 180 29 48