HIV/AIDS remains an important global cause of morbidity and mortality. While medical male circumcision and condom and microbicides use hold great promise for helping to stem the tide of new HIV infections, theoretically providing further evidence of the potential long-term population-level benefit of their combined effects is viable. A deterministic sex-structured model is formulated, the expected lifetime disease reproductive output of an individual (or epidemiological birth) is determined, and the stability of steady states is investigated. To complement HIV treatment with antiretrovirals, which is not yet fully accessible to all those in need, microbicides and nontherapeutic measures such as male circumcision and condoms provide additional potential impact on curtailing the spread of HIV/AIDS. 1. Introduction “Globally, HIV/AIDS has killed more than 25 million people, making it one of the most destructive epidemics in recorded history with sub-Saharan Africa carrying the highest burden of the disease. Since its emergence in 1981, HIV continues to be a significant social-economic and public health burden around the globe. Its main transmission route is heterosexual, representing up to 90% of all transmission.” For the estimated 33.3 million (27.1–30.3 million) people living with HIV after nearly 30 years into a very complex epidemic, the gains are real but still fragile, even as the number of annual AIDS-related deaths worldwide has steadily decreased from the peak of 2.1 million [1.9–2.3 million] in 2004 to an estimated 1.8 million [1.6–2.0 million] in 2009 [1]. Various preventative and therapeutic measures have been embarked upon, aiming at combating one of the greatest pandemic in modern times. These include the use of life-saving antiretroviral drugs (ARVs), condoms, HIV testing, mutual monogamy, counseling, and abstinence (WHO/UNAIDS, 2005) [2, 3]. Various degrees of success of these controls have been limited to very few countries [4]. Consistent use of latex condoms which is advocated as a primary prevention for HIV infection [5, 6] has suffered from problems of stigma, myths and fertility decline which are key social issues in sub-Saharan Africa [4]. Although the use of antiretroviral drugs has led to significant reduction in HIV burden in many nations, their accessibility and efficient delivery in resource-poor nations remain low. These together with the absence of an anti-HIV vaccine, call for use of other affordable programs for controlling HIV spreading especially in nations with limited resources and inadequate public health services.
References
[1]
WHO/UNAIDS, “UNAIDS report on the global AIDS epidemic 2010,” UNAIDS/10. 11E JC1958E, 2010.
[2]
D. P. Wilson, P. M. Coplan, M. A. Wainberg, and S. M. Blower, “The paradoxical effects of using antiretroviral-based microbicides to control HIV epidemics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 105, no. 28, pp. 9835–9840, 2008.
[3]
S. M. Moghadas, A. B. Gumel, R. G. McLeod, and R. Gordon, “Could condoms stop the AIDS epidemic?” Journal of Theoretical Medicine, vol. 5, no. 3-4, pp. 171–181, 2003.
[4]
Zambia Report, Second Joint Annual Programme Review of National HIV/AIDS/STI/TB Intervention Strategic Plan 2002–2005, Government of Republic of Zambia, 2005.
[5]
I. De Vincenzi, “A longitudinal study of human immunodeficiency virus transmission by heterosexual partners,” The New England Journal of Medicine, vol. 331, no. 6, pp. 341–346, 1994.
[6]
S. D. Pinkerton and P. R. Abramson, “Effectiveness of condoms in preventing HIV transmission,” Social Science and Medicine, vol. 44, no. 9, pp. 1303–1312, 1997.
[7]
B. Auvert, D. Taljaard, E. Lagarde, J. Sobngwi-Tambekou, R. Sitta, and A. Puren, “Randomized, controlled intervention trial of male circumcision for reduction of HIV infection risk: the ANRS 1265 trial,” PLoS Medicine, vol. 2, no. 11, article e298, 2005.
[8]
R. C. Bailey, S. Moses, C. B. Parker et al., “Male circumcision for HIV prevention in young men in Kisumu, Kenya: a randomised controlled trial,” The Lancet, vol. 369, no. 9562, pp. 643–656, 2007.
[9]
A. J. Fink, “A possible explanation for heterosexual male infection with AIDS,” The New England Journal of Medicine, vol. 315, no. 18, p. 1167, 1986.
[10]
J. Hutchinson, “On the influence of circumcision on prevention of syphilis,” The Medical Times and Gazette, vol. 1, pp. 542–543, 1885.
[11]
S. Moses, R. C. Bailey, and A. R. Ronald, “Male circumcision: assessment of health benefits and risks,” Sexually Transmitted Infections, vol. 74, no. 5, pp. 368–373, 1998.
[12]
N. Siegfried, M. Muller, J. Deeks et al., “HIV and male circumcision - A systematic review with assessment of the quality of studies,” The Lancet Infectious Diseases, vol. 5, no. 3, pp. 165–173, 2005.
[13]
B. G. Williams, J. O. Lloyd-Smith, E. Gouws et al., “The potential impact of male circumcision on HIV in sub-Saharan Africa,” PLoS Medicine, vol. 3, no. 7, article e262, 2006.
[14]
R. H. Gray, G. Kigozi, D. Serwadda et al., “Male circumcision for HIV prevention in men in Rakai, Uganda: a randomised trial,” The Lancet, vol. 369, no. 9562, pp. 657–666, 2007.
R. Breban, I. McGowan, C. Topaz, E. J. Schwartz, P. Anton, and S. Blower, “Modeling the potential impact of rectal microbicides to reduce HIV transmission in bathhouses,” Mathematical Biosciences and Engineering, vol. 3, no. 3, pp. 459–466, 2006.
[17]
C. Watts and P. Vickerman, “The impact of microbicides on HIV and STD transmission: model projections,” AIDS, vol. 15, pp. S43–S44, 2001.
[18]
R. J. Smith, E. N. Bodine, D. P. Wilson, and S. M. Blower, “Evaluating the potential impact of vaginal microbicides to reduce the risk of acquiring HIV in female sex workers,” AIDS, vol. 19, no. 4, pp. 413–421, 2005.
[19]
S. McCormack, “Microbicides: where are we now and what next?” HIV Therapy, vol. 4, no. 6, pp. 615–618, 2010.
[20]
Z. Mukandavire, K. Bowa, and W. Garira, “Modelling circumcision and condom use as HIV/AIDS preventive control strategies,” Mathematical and Computer Modelling, vol. 46, no. 11-12, pp. 1353–1372, 2007.
[21]
C. N. Podder, O. Sharomi, A. B. Gumel, and S. Moses, “To cut or not to cut: a modeling approach for assessing the role of male circumcision in HIV control,” Bulletin of Mathematical Biology, vol. 69, no. 8, pp. 2447–2466, 2007.
[22]
R. M. Anderson and R. M. May, Infectious Diseases of Humans, Oxford University Press, Oxford, UK, 1991.
[23]
C. Castillo-Chavez and S. Busenberg, “On the solution of the two-sex mixing problem,” in Differential Equations Models in Biology, Epidemiology and Ecology, Proceedings, Claremont 1990, S. Busenberg and M. Martelli, Eds., vol. 92 of Lecture Notes in Biomathematics, pp. 80–98, Springer, New York, NY, USA, 1991.
[24]
V. Hutson and K. Schmitt, “Permanence and the dynamics of biological systems,” Mathematical Biosciences, vol. 111, no. 1, pp. 1–71, 1992.
[25]
P. Van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002.
[26]
O. Diekmann, J. A. Heesterbeek, and J. A. Metz, “On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990.
[27]
R. M. May and R. M. Anderson, “The transmission dynamics of Human Immunodeficiency Virus (HIV),” Philosophical Transactions of the Royal Society of London B, vol. 321, no. 1207, pp. 565–607, 1988.
[28]
V. Lakshmikantham, S. Leela, and A. Martynyuk, Stability Analysis of Nonlinear Systemsand Basel, Marcel Dekker, New York, NY, USA, 1989.
[29]
H. R. Thieme, “Persistence under relaxed point-dissipativity (with application to an endemic model),” SIAM Journal on Mathematical Analysis, vol. 24, no. 2, pp. 405–435, 1993.
[30]
H. R. Thieme, “Uniform persistence and permanence for non-autonomous semiflows in population biology,” Mathematical Biosciences, vol. 166, no. 2, pp. 173–201, 2000.
[31]
J. Dushoff, W. Huang, and C. Castillo-Chavez, “Backwards bifurcations and catastrophe in simple models of fatal diseases,” Journal of Mathematical Biology, vol. 36, no. 3, pp. 227–248, 1998.
[32]
C. M. Kribs-Zaleta and J. X. Velasco-Hernández, “A simple vaccination model with multiple endemic states,” Mathematical Biosciences, vol. 164, no. 2, pp. 183–201, 2000.
[33]
E. Mtisi, H. Rwezaura, and J. M. Tchuenche, “A mathematical analysis of malaria and tuberculosis co-dynamics,” Discrete and Continuous Dynamical Systems B, vol. 12, no. 4, pp. 827–864, 2009.
