(formula presented.)

Journal of Mathematical Biology

Volumn 71, Issue 1, 2015, Pages 1-56

  Leung, Ka Yin ^a,b   Kretzschmar, Mirjam ^b,c   Diekmann, Odo ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITY MEDICAL CENTER UTRECHT   (Netherlands)

^c NATIONAL INSTITUTE FOR PUBLIC HEALTH AND THE ENVIRONMENT   (Netherlands)

Author keywords

(formula presented.)infection; (formula presented.); Concurrency; Dynamic network; Mean field at distance one

Indexed keywords

AFRICA SOUTH OF THE SAHARA; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; BIOLOGY; COMPUTER SIMULATION; DISEASE PREDISPOSITION; EPIDEMIC; FEMALE; HIV INFECTIONS; HOMOSEXUALITY; HUMAN; MALE; MATHEMATICAL PHENOMENA; SEXUALITY; SEXUALLY TRANSMITTED DISEASES; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; TRANSMISSION;

AFRICA SOUTH OF THE SAHARA; BASIC REPRODUCTION NUMBER; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; DISEASE SUSCEPTIBILITY; EPIDEMICS; FEMALE; HIV INFECTIONS; HOMOSEXUALITY; HUMANS; LINEAR MODELS; MALE; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; SEXUAL PARTNERS; SEXUALLY TRANSMITTED DISEASES;

EID: 84929223067     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-014-0808-5     Document Type: Article

References (39)

1. Altmann M (1995) Susceptible-infected-removed epidemic models with dynamic partnerships. J Math Biol 33:661–675
2. Altmann M (1998) The deterministic limit of infectious disease models with dynamic partners. Math Biosci 150:153–175
3. Ball F, Neal P (2008) Network epidemic models with two levels of mixing. Math Biosci 212:69–87
4. Bansal S, Read J, Pourbohloul B, Meyers LA (2010) The dynamic nature of contact networks in infectious disease epidemiology. J Biol Dyn 4:478–489
5. Barbour AD, Reinert G (2013) Approximating the epidemic curve. Electron J Probab 18:1–30
6. Britton T, Lindholm M (2010) Dynamic random networks in dynamic populations. J Stat Phys 139:518–535
7. Britton T, Lindholm M, Turova T (2011) A dynamic network in a dynamic population: asymptotic properties. J Appl Probab 48:1163–1178
8. Decreusefond L, Dhersin J-S, Moyal P, Tran VC (2012) Large graph limit for an SIR process in random network with heterogeneous connectivity. Ann Appl Probab 22:541–575
9. Diekmann O, de Jong MCM, Metz JAJ (1998) A deterministic epidemic model taking account of repeated contacts between the same individuals. J Appl Probab 35:448–462
10. Diekmann O, Heesterbeek JAP, Britton T (2013) Mathematical tools for understanding infectious disease dynamics. Princeton University Press, Princeton
11. Dietz K, Hadeler KP (1988) Epidemiological models for sexually transmitted diseases. J Math Biol 26:1–25
12. Eaton JW, Hallett TB, Garnett GP (2011) Concurrent sexual partnerships and primary HIV infection: a critical interaction. AIDS Behav 15:687–692
13. Ferguson NM, Garnett GP (2000) More realistic models of sexually transmitted disease transmission dynamics. Sex Transm Dis 27:600–609
14. Goodreau SM (2011) A decade of modelling research yields considerable evidence for the importance of concurrency: a response to Sawers and Stillwaggon. J Int AIDS Soc 14:12
15. Haccou P, Jagers P, Vatutin VA (2005) Branching processes. Variation, growth, and extinction of populations. Cambridge University Press, Cambridge
16. Heijne JC, Althaus CL, Herzog SA, Kretzschmar M, Low N (2011) The role of reinfection and partner notification in the efficacy of Chlamydia screening programs. J Infect Dis 203:372–377
17. House T, Keeling MJ (2011) Insights from unifying modern approximations to infections on networks. J R Soc Interface 8:67–73
18. Inaba H (1997) Advances in mathematical population dynamics: molecules, cells and man. Calculating $$R_0$$R0 for HIV infection via pair formation. World Scientific, pp 355–382
19. Jagers P (1975) Branching processes with biological applications. Wiley, New York
20. Kamp C (2010) Untangling the interplay between epidemic spread and transmission network dynamics. PLoS Comput Biol 6:e1000984
21. Kenyon C, Colebunders R (2012) Strong association between point-concurrency and peak HIV prevalence. J Infect Dis 16:e826–e827
22. Kiss IZ, Berthouze L, Taylor TJ, Simon PL (2012) Modelling approaches for simple dynamic networks and applications to disease transmission models. Proc R Soc A 468:1332–1355
23. Kretzschmar M, Dietz K (1998) The effect of pair formation and variable infectivity on the spread of an infection without recovery. Math Biosci 148:83–113
24. Kretzschmar M, Morris M (1996) Measures of concurrency in networks and the spread of infectious disease. Math Biosci 133:165–195
25. Kretzschmar M, Jager JC, Reinking DP, Van Zessen G, Brouwers H (1994) The basic reproduction ratio R0 for a sexually transmitted disease in a pair formation model with two types of pairs. Math Biosci 124:181–205
26. Leung KY, Kretzschmar MEE, Diekmann O (2012) Dynamic concurrent partnership networks incorporating demography. Theor Popul Biol 82:229–239
27. Lindquist J, Ma J, van den Driessche P, Willeboordse FH (2011) Effective degree network disease models. J Math Biol 62:143–164
28. Lurie MN, Rosenthal S (2010) Concurrent partnerships as a driver of the HIV epidemic in sub-Saharan Africa? The evidence is limited. AIDS Behav 14:17–24
29. Miller JC, Volz EM (2013) Incorporating disease and population structure into models of SIR disease in contact networks. PLoS ONE 8:e69162–e69162
30. Miller JC, Slim AC, Volz EM (2012) Edge-based compartmental modelling for infectious disease spread. J R Soc Interface 9:890–906
31. Morris M, Kretzschmar M (1997) Concurrent partnerships and the spread of HIV. AIDS 11:641–648
32. Morris M, Kretzschmar M (2000) A microsimulation study of the effects of concurrent partnerships on the spread of HIV in Uganda. Math Popul Studies 8:109–133
33. Powers KA, Ghani AC, Miller WC et al (2011) The role of acute and early HIV infection in the spread of HIV and implications for transmission prevention strategies in Lilongwe, Malawi: a modelling study. Lancet 378:256–268
34. Reniers G, Watkins S (2010) Polygyny and the spread of HIV in sub-Saharan Africa: a case of benign concurrency. AIDS 24:299–307
35. Seneta E (1973) Non-negative matrices. An introduction to theory and applications. George Allen & Unwin Ltd, London
36. Tanser F, Barnighausen T, Hund L, Garnett GP, McGrath N, Newell ML (2011) Effect of concurrent sexual partnerships on rate of new HIV infections in a high-prevalence, rural South African population: a cohort study. Lancet 378:247–255
37. Taylor M, Simon PL, Green DM, House T, Kiss IZ (2012) From Markovian to pairwise epidemic models and the performance of moment closure approximations. J Math Biol 64:1021–1042
38. Watts CH, May RM (1992) The influence of concurrent partnerships on the dynamics of HIV/AIDS. Math Biosci 108:89–104
39. Xiridou M, Geskus R, De Wit J, Coutinho R, Kretzschmar M (2003) The contribution of steady and casual partnerships to the incidence of HIV infection among homosexual men in Amsterdam. AIDS 17:1029–1038