Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic

Mathematical Biosciences and Engineering

Volumn 6, Issue 2, 2009, Pages 363-376

  Musgrave, Jeff ^a   Watmough, James ^a  

^a UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Control reproduction number; Disease transmission model; Epidemiology

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; CONDOM; EPIDEMIC; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; INCIDENCE; METHODOLOGY; RISK ASSESSMENT; RISK FACTOR; STATISTICS; UTILIZATION REVIEW;

COMPUTER SIMULATION; CONDOMS; DISEASE OUTBREAKS; HIV INFECTIONS; HUMANS; INCIDENCE; MODELS, BIOLOGICAL; RISK ASSESSMENT; RISK FACTORS;

HUMAN IMMUNODEFICIENCY VIRUS;

EID: 67650477858     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2009.6.363     Document Type: Article

References (29)

1. D. Greenhalgh, M. Doyle and F. Lewis, A mathematical treatment of AIDS and condom use, IMA Journal of Mathematics Applied in Medicine and Biology, 18 (2001), 225-262.
2. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
3. R. McLeod, J. Brewster, A. Gumel, D. Slonowsky, Sensitivity and uncertainity analyses for a SARS model with time-varying inputs and outputs, Mathematical Biosciences and Engineering, 3 (2006), 527-544.
4. Z. Mukandavire and W. Garira, Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe, Journal of Mathematical Biology, 54 (2007), 669- 699.
5. A. Gumel, C. McCluskey and P. van den Driescche, Mathematical study of a staged- progression HIV model with imperfect vaccine, Bulletin of Mathematical Biology, 68 (2006), 2105-2128.
6. R. Breban, I. McGowan, C. Topaz, E. Schwartz, P. Anton and S. Blower, Modeling the potential impact of rectal microbicides to reduce HIV transmission in bathhouses, Mathematical Biosciences and Engineering, 3 (2006), 459-466.
7. AIDS vaccine still long way off; researchers, experts still optimistic, The Body: The Complete HIV/AIDS Resource http://www.thabody.com/content/confs/ aids2006/art7907.html.
8. D. R. Burton, R. C. Desrosiers, R. W. Doms, M. B. Feinberg, R. C. Gallo, B. Hahn, J. A. Hoxie, E. Hunter, B. Korber, A. Landay, M. M. Lederman, J. Lieberman, J. M. McCune, J. P. Moore, N. Nathanson, L. Picker, D. Richman, C. Rinaldo, M. Stevenson, D. I.Watkins, S. M.Wolinsky and J. A. Zack, A sound rationale needed for phase III HIV-1 vaccine trials, Science, 303 (2004), 316.
9. C. for Disease Control and Prevention, http://www.cdc.gov/hiv/topics/ basic/index.htm (20 July 2007).
10. AVERT, http://www.avert.org/worldstats.htm (20 July 2007).
11. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, John A. Jacquez memorial volume, Mathematical Biosciences, 180 (2002), 29-48.
12. S. Moghadas, A. Gumel, R. Mcleod and R. Gordon, Could condoms stop the AIDS epidemic?, Journal of Theoretical Medicine, 5 (2003, 171-181.
13. M. Nowak and R. May, Mathematical biology of HIV infections: Antigenic variation and diversity threshold, Mathematical Biosciences, 106 (1991), 1-21.
14. F. Brauer, The Kermack-McKendrick epidemic model revisited, Mathematical Biosciences, 198 (2005), 119-131.
15. L. Fischetti, O. Opare-Sem, D. Candotti, H. Lee and J.-P. Allain, Higher viral load may explain the dominance of CRF02-AG in the molecular epidemiology of HIV in Ghana, AIDS, 18 (2004), 1208-1210.
16. S. Ahmed, T. Lutaloa, M. Wawerb, D. Serwaddac, N. K. Sewankamboc, F. Nalugodaa, F. Makumbia, F. Wabwire-Mangenc, N. Kiwanukaa, G. Kigozia, M. Kiddugavua and R. Gray, Hiv incidence and sexually transmitted disease prevalence associated with condom use: a population study in rakai, Uganda, AIDS, 15 (2001), 2171-2179.
17. M. Bracher, G. Santow and S. C. Watkins, Assessing the potential of condom use to prevent the spread of HIV: a microsimulation study, Studies in Family Planning, 35 (2004), 48-64.
18. K. R. Davis and S. C. Weller, The effectiveness of condoms in reducing heterosexual transmission of HIV, Family Planning Perspectives, 31 (1999), 272-279.
19. N. Hearst and S. Chen, Condom promotion for AIDS in the developing world: Is it working,Studies in Family Planning, 35 (2004), 39-47.
20. J. Hale, "Studies in Ordinary Differential Equations," Vol. 14 of MAA studies in Mathematics, The Mathematical Association of America, United States of America, 1969.
21. J. M. Hyman, J. Li and E. A. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Math. Biosci., 155 (1999), 77-109.
22. K. Senior, AIDS epidemic still not under control, The Lancet Infectious Diseases, 6 (2006),10.
23. R. Steinbrook, HIV in India - a complex epidemic, The New England Journal of Medicine, 356 (2007), 1089.
24. W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. London, 115 (1927), 700-721.
25. J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, A final size relation for epidemic models, Mathematical Biosciences and Engineering, 4 (2007), 159-175 (electronic).
26. J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, Simple models for containment of a pandemic, Journal of the Royal Society Interface, 3 (2006,) 453-457.
27. H. Caswell, "Matrix Population Models: Construction, Analysis and Interpretation," Sinauer Associates, Sunderland, Mass., 2001.
28. L. Forster, One-third of sexually active older adults with HIV/AIDs has unprotected sex. [29] P. D. Cleary, N. V. Devanter, T. F. Rogers, E. Singer, R. Shipton-Levy, M. Steilen, A. Stuart, J. Avom and J. Pindyck, Behavior changes after notification of hiv infection, American Journal of Public Health, 81 (1991), 1586-1590.
29. G. J. P. van Griensven, E. M. M. de Vroome, J. Goudsmit and R. A. Coutinho, Changes insexual behaviour and the fall in incidence of HIV infection among homosexual men, Br. Med. J., 298 (1989), 218-221.