A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

Journal of Mathematical Biology

Volumn 45, Issue 5, 2002, Pages 375-395

  Bauch, C T ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Moment closure approximation; Network model; Pair approximation; Sexually transmitted diseases; Steady casual partnership network

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPUTER SIMULATION; DISEASE TRANSMISSION; EPIDEMIOLOGY; FEMALE; HUMAN; MALE; SEXUAL BEHAVIOR; SEXUALITY; SEXUALLY TRANSMITTED DISEASE; STATISTICS;

COMPUTER SIMULATION; EPIDEMIOLOGIC METHODS; FEMALE; HUMANS; MALE; MODELS, BIOLOGICAL; SEXUAL BEHAVIOR; SEXUAL PARTNERS; SEXUALLY TRANSMITTED DISEASES; STOCHASTIC PROCESSES;

EID: 0037950616     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s002850200153     Document Type: Article

References (38)

1. Altmann, M.: Susceptible-infected-removed epidemic models with dynamic partnerships. J. Math. Biol., 33, 661-675 (1995)
2. Altmann, M.: The deterministic limit of infectious disease models with dynamic partners. Math. Biosci., 150, 153-175 (1998)
3. Anderson, R.M., Gupta, S., Ng, W.: The significant of sexual partner contact networks for the transmission dynamics of HIV. J. Acquir. Immune Defic. Syndr., 3, 417-429 (1990)
4. Anderson, R.M., May, R.M.: Infectious Diseases of Humans. Oxford Science Publications, OUP, 1991
5. Andersson, H.: Epidemic models on graphs and lattices: A short survey. Manuscript, 1998
6. Bauch, C.T.: Moment Closure Approximations in Epidemiology. PhD thesis, University of Warwick, August 2000
7. Bauch, C.T., Rand, D.A.: A moment closure model for sexually transmitted disease transmission through a concurrent partnership network. Proc. R. Soc. Lond. B, 267(1456), 2019-2027 (2000)
8. Bethe, H.A.: Proc. R. Soc. Lond., A 150, 552+ (1935)
9. Blanchard, P.H., Bolz, G.F., Krüger, T.: Modelling the aids-epidemic or any veneral disease on random graphs. In J.P. Gabriel, C. Lefévre, and P. Picard, editors, Stochastic Processes in Epidemic Theory, 104-117. Springer-Verlag, 1990
10. Cooke, K.L., Yorke, J.A.: Some equations modelling growth processes and gonorrhea epidemics. Math. Biosci., 16, 75-101 (1973)
11. Day, S., Ward, H., Ghani, A. et al.: Sexual histories, partnerships and networks associated with the transmission of gonorrhoea, Int. J. STD AIDS, 9, 666-671 (1998)
12. Diekmann, O., DeJong, M.C.M., Metz, J.A.J.: A deterministic epidemic model taking account of repeated contacts between the same individuals. J. Appl. Prob., 35, 448-462 (1998)
13. Dietz, K., Hadeler, K.P.: Epidemiological models for sexually transmitted diseases. J. Math. Biol., 26, 1-25 (1988)
14. Dietz, K., Tudor, D.: Triangles in heterosexual HIV transmission: AIDS Epidemiology: Methodological Issues, 143-155 (1992)
15. Cleland, J. et al.: Looking deeper into the HIV epidemic: A questionnaire for tracing sexual networks. Technical report, UNAids, 1998
16. Ferguson, N.M., Garnett, G.P.: More realistic models of sexually transmitted disease transmission dynamics: Sexual partnership networks, pair models and moment closure. Sex. Trans. Dis., 27(10), 600-609 (2000)
17. Filipe, J.A.N., Gibson, G.J.: Studying and approximating spatio-temporal models for epidemic spread and control. Phil. Trans. R. Soc. Lond. B, 353, 2153-2162 (1998)
18. Gupta, S., Garnett, G.: Risks of acquiring and transmitting sexually transmitted diseases in sexual partnership networks. Sex. Trans. Dis., 27(10), 579-587 (2000)
19. Ying-Hen Hsieh.: personal communication, 2001
20. Keeling, M.J., Rand, D.A., Morris, A.: Correlation models for childhood epidemics. Proc. R. Soc. Lond. B, 264, 1149-1156 (1997)
21. Klovdahl, A.S.: Social networks and the spread of infectious diseases: the aids example. Soc. Sci. Med., 21, 1203-1216 (1985)
22. Kretzschmar, M.: Deterministic and stochastic pair formation models for the spread of sexually transmitted diseases. J. Biol. Systems, 3, 789-801 (1995)
23. 0 for a sexually transmitted disease in a pair formation model with two types of pairs. Math. Biosci., 124, 181-205 (1994)
24. Kretzschmar, M., Morris, M.: Measures of concurrency in networks and the spread of infectious disease. Math. Biosci., 133, 165-195 (1996)
25. Kretzschmar, M., Reinking, D.P., Brouwers, H., van Zessen, G., Jager, J. C.: Network models: from paradigm to mathematical tool. In E.H. Kaplan and M. Brandeau, editors, Modeling the AIDS Epidemic. 1994
26. Kretzschmar, M., van Duynhoven, Y., Severijnen, A.: Modeling prevention strategies for gonorrhea and chlamydia using stochastic network simulations. Am. J. Epidemiol., 144, 306-317 (1996)
27. Levin, S.A., Durrett, R.: From individuals to epidemics. Phil. Trans. R. Soc. Lond. B, 351, 1615-1621 (1996)
28. Matsuda, H.: Conditions for the evolution of altruism. In Y. Ito, J.P. Brown, and J. Kikkawa, editors, Animal Societies: Theories and Facts, pages 67-80. Tokyo: Japanese Scientific Society Press, 1987
29. Matsuda, H., Ogita, N., Sasaki, A., Sato, K.: Statistical mechanics of population. Prog. Theor. Physics, 88, 1035-1049 (1992)
30. Morris, A.J.: Representing Spatial Interactions in Simple Ecological Models. PhD thesis, University of Warwick, September 1997
31. Morris, M.: Sexual networks and HIV, AIDS. 11, S1-S8 (1997)
32. Morris, M., Kretzschmar, M.: Concurrent partnerships and the spread of HIV, AIDS, 11(5), 1-7 (April 1997)
33. Rand, D.A.: Correlation equations and pair approximations for spatial ecologies. In J. McGlade, editor. Advanced Ecological Theory. Principles and Applications, 100-142. Blackwell Science, 1999
34. Rand, D.A., Keeling, M.J., Wilson, H.B.: Invasion, stability and evolution to criticality in spatially extended host-pathogen systems. Proc. R. Soc. Lond. B, 259, 55-63 (1995)
35. Sato, K., Matsuda, H., Sasaki, A.: Pathogen invasion and host extinction in lattice structured populations. J. Math. Biol., 32, 251-268 (1994)
36. van Baalen, M., Rand, D.A.: The unit of selection in viscous populations and the evolution of altruism. J. Theor. Biol., 193, 631-648 (1998)
37. Watts, C.H., May, R.M.: The influence of concurrent partnerships on the dynamics of HIV/AIDS. Math. Biosci., 108, 89-104 (1992)
38. Kuznetsov, Y.A., Levitin, V.V.: Content: A multiplatform environment for continuation and bifurcation analysis of dynamical systems (software under development). Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands, 1997