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IJSTR >> Volume 1 - Issue 9, October 2012 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Mathematical Model Approach To HIV/AIDS Transmission From Mother To Child

[Full Text]



Basavarajaiah.D. M. B. Narasimhamurthy, K. Maheshappa. B. Leelavathy



Key words: AIDS, HIV, PMTCT, DTSM, ARV’s, Vertical transmission, NACO



ABSTRACT:- AIDS is a devastating disease, more than 2.50 million of the infected populations died every year (NACO).For the control of diseases transmission need to be implementation of public health program, i.e., it helps to minimize the destruction caused by AIDS epidemic. Mathematical models and underlying transmission mechanism of the HIV can help the scientific, medical and researcher to understand and anticipate its spread in different population. Present study fitted mathematical models, which exhibit two equilibriums namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number R0 <1, the disease-free equilibrium is always locally asymptotically stable and in such a case the endemic equilibrium does not exist. If R0 >1, a unique equilibrium exist which locally asymptotically stable and becomes globally asymptotically stable under certain conditions showing that the disease becomes endemic due to vertical transmission.



1. Agarwala, B.D (2002), “On two ODE models for HIV/AIDS development in Canada and a logistic SEIR model”, Far East J, Appl. Math. 6 (1) (2002) 25–70..

2. Anderson, R.M., Medly G.F., May R.M., Johnson, A.M (1998), “A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS”, IMA J. Math. Appl. Med. Biol.3 (1986) 229–263.

3. Anderson, R.M (1998), “The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS”, J. AIDS 1 (1988) 241–256.Anndelman, R (2001),

4. Mother to child HIV transmission in Africa. Policy Fact. AVERT (2010), HIV treatment. http://www.avert.org/treatment.htm.Retrieved on 24th December 2010.

5. Busenberg and Cooke K.L (1995), “Vertically transmitted diseases models and dynamics”. Biomathematics, vol. 23

6. Springer-Verlag.Castillo-Chavez, C. and Song, B (2004), Dynamical models of Tuberculosis and their application. Math. Biosci. Eng. 1, 361404.

7. Coovadia, H (2004), “Antiretroviral agents—how best to protect infants from HIV and save their mothers from AIDS”, N. Engl. J. Med. 351 (3): 289–292.77

8. Cochrane Systematic Review on interventions for prevention of late postnatal mother-to-child transmission of HIVhttp://www.cochrane.org/reviews/en/ab006734.html. Retrieved on 4th January 2011

9. Csete. Joanne. Pears house. Richard. Symington. Alison. (2009), Vertical HIVtransmission should be excluded from criminal prosecution. Reproductive Health Matters. Department of Health and Human Services (2005)

10. GuidetoAdultHIV/AIDSTreatment. (http://www.hab.hrsa.gov/tools/hivpocketguide05/PktGARTtables.htm).Retrieved on 15th October 2010.

11. May, R.M., Anderson, R.M (1998), Transmission dynamic of human immunodeficiency virus (HIV). Phil. Trans. Roy. Soc.321, 565-607.

12. Mbabaz, D (2008), Population Dynamic Type Models in HIV Infection. African Institute for Mathematical Science.