Volume 3, Issue 6, December 2015, Page: 271-282
Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size
Udoo Iorlumun Joseph Martins, Department of Mathematics, School of Sciences, College of Education, Zing, Taraba State, Nigeria
Kimbir Richard Anande, Department of Mathematics, Statistics and Computer Science, Federal University of Agriculture, Makurdi, Benue State, Nigeria
Remilekun Mathew Odekunle, Department of Mathematics, School of Pure and Applied Sciences, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria
Received: Oct. 6, 2015;       Accepted: Oct. 23, 2015;       Published: Nov. 24, 2015
DOI: 10.11648/j.ajam.20150306.16      View  3311      Downloads  103
Abstract
A mathematical model of the transmission dynamics of HIV/AIDS, incorporating counselling, vaccination and antiretroviral therapy (ART) in a varying population, is presented. The existence and stability of the disease-free equilibrium states of the variants of the model are investigated, from which threshold values for vaccination and ART administration rates are established. Furthermore, numerical experiments are carried out to illustrate the effects of vaccination and ART, separately and in combination, on the transmission dynamics of HIV/AIDS in such populations.
Keywords
HIV/AIDS, Counselling, Vaccination, ART, Mathematical Model, Stability, Eradication, Threshold Values
To cite this article
Udoo Iorlumun Joseph Martins, Kimbir Richard Anande, Remilekun Mathew Odekunle, Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size, American Journal of Applied Mathematics. Vol. 3, No. 6, 2015, pp. 271-282. doi: 10.11648/j.ajam.20150306.16
Copyright
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Anzala, O., Mutua, G. N., Oyugi, F. J. O., Mohamed, B. F., Achia, T., and Stover, J.(2012). What impact would an HIV/AIDS vaccine have on the HIV/AIDS epidemic in kenya? Open Journal of Immunology Vol. 2, No. 4, 195-201.
[2]
AVERT (2010): Averting HIV/AIDS Epidemic: Worldwide HIV and AIDS Statistics Commentary.
[3]
Beltrami, E. (1989): Mathematics for dynamic modeling. Academic Press. N. Y.
[4]
Blower, S.M. and Mclean, A. R. (1994): Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco. Science 265, 1451-1454.
[5]
Centres for Disease Control and Prevention (CDC, 1982): Update on Acquire Immunodeficiency Syndrome (AIDS): United State-Morbidity and Mortality Weekly Report, 31, pp 507-514.
[6]
Centres for Disease Control and Prevention (CDC, 1999): HIV and its transmission. Atlanta. U.S.A.
[7]
Elizabeth Glaser Pediatric AIDS Foundation (EGPAF, 2013). Issue Brief: Pediatric HIV and AIDS.
[8]
Garcia-Calleja, J. M., Gouws, E., and Ghys, P. D. (2006): National population based HIV prevalence survey in sub-Saharan Africa: results and implications for HIV and AIDS estimates. Sexually transmitted Infections, 82: 64-70.
[9]
Greenhalgh, D., Doyle, M., and Lewis, F. (2001): A Mathematical treatment of AIDS and Condom use. IMA. J. Math. Appl. Med. Biol., 18, no.3, pp225-262.
[10]
Hsieh, Y. H. (1996): A two sex model for treatment of AIDS and behaviour changes in a Population of varying size. IMA. J. Math. Appl. Biol. Med., 13, 151-173.
[11]
IAVI (2011). International AIDS vaccine Initiative: “The Potential Impact of an AIDS vaccine in Low-and Middle-Income Countries”—Technical Report. New York.
[12]
Kai Sun, Shuntai Zhou, Ray Y. Chen, Myron S. Cohen, and Fujie Zhang (2010): Recent Key advances in human immunodeficiency virus medicine and implications for China, AIDS Research and Therapy, 7:12.
[13]
Kgosimore M. and Lungu E. M. (2004): The effects of vaccination and treatment on the spread of HIV/AIDS. Journal of Biological Systems, Vol. 12.No. 4, 399-417
[14]
Kimbir, A. R. and Aboiyar, T. (2003). A mathematical model for the prevention of HIV / AIDS in a varying population. Journal of Nigerian Mathematical Society 22, 43- 55.
[15]
Kimbir, A. R. and Oduwole H. K. (2008): A Mathematical Model of HIV/AIDS Transmission Dynamics Considering Counselling and Antretroviral Therapy. J. Modern Mathe. Stat., 2(5): 166-169.
[16]
Koob, J. J. and Harvan J. S. (2003): AIDS instruction in US Schools of Social Work: 20 years into the epidemics. Social Work Education, 22: 309-319.
[17]
Kribs-Zaleta, C. M., and Velasco-Hernandez, J. X. (2000): A simple vaccination model with multiple endemic states. Math. Biosci. 164, no. 2,183-201.
[18]
Medley, G. F., Anderson, R. M., Cox, D. R., and Billard, L. (1987): Incubation period of AIDS in patients infected via bloodtransfusion. Nature, 328, pp718-724.
[19]
Mugisha J.Y.T. (2005): Balancing Treatment and Prevention: The case of HIV/AIDS. American Journal of Applied Sciences 2(10): 1380-1388.
[20]
Mukandavire Z., Bowa K., and Garira W. (2007): Modeling Circumcision and Condom use as HIV/AIDS preventive control strategies, Mathematical and Computer Modelling 46, 1353-1372.
[21]
Putzel J. (2003): “Institutionalizing an Emergency Response: HIV/AIDS and Governance in Uganda and Senegal.” Department of International Development, 5-14.
[22]
Richard A. Kimbir, Martins J. I. Udoo and Terhemen Aboiyar (2012): A Mathematical Model for the Transmission Dynamics of HIV/AIDS in a two-sex Population considering Counseling and Antiretroviral Therapy (ART). J. Math. Comput. Sci. 2, No.6, 1671-1684.
[23]
Swanson, C. E., Tindall, B. and Cooper, D. A. (1994): Efficacy of Zidivudine treatment in homosexual men with AIDS-related complex: factors influencing development of AIDS, survival and drug tolerance-AIDS.Vol.9, 625-634.
[24]
UNAIDS (2008): Report on the global AIDS epidemic. Geneva.
[25]
UNAIDS (2009): AIDS epidemic update.
[26]
UNAIDS (2010): 2010 Report on global AIDS epidemic. Geneva.
[27]
UNAIDS (2012): UNAIDS REPORT ON THE GLOBAL AIDS EPIDEMIC.
[28]
UNAIDS (2013): UNAIDS 2013 Global Fact Sheet.
[29]
Velasco-Hernandez J. X., Gershengorn H. B., and Blower S. M. (2002): Could widespread use of combination antiretroviral therapy eradicate HIV epidemics? The Lancet 2, 487-493.
[30]
Williams B. G., Lloyd-Smith J. O., Gouws E., Hankins C., Getz W. M., Hargrove J., de Zoysa I., and Auvert B. (2006): The Potential Impact of Male Circumcision on HIV in sub-Saharan Africa, PLoS Medecine 3, 1032-1040.
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