On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling
American Journal of Applied Mathematics
Volume 2, Issue 1, February 2014, Pages: 21-28
Received: Dec. 31, 2013; Published: Feb. 28, 2014
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Author
OGUNMOLA ADENIYI OYEWOLE, Department of Mathematics and Statistics, Faculty of Pure and Natural Science, Federal University Wukari, Taraba State
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Abstract
In this research, a discrete-time Markov process for HIV/AIDs epidemic modeling, which takes into account the dynamic of the HIV; the number of susceptible contracting HIV, the number of infective developing AIDS and the parameters influencing these outcomes is designed. This is to determine the behaviour of the epidemic and to keep it under control. Each parameter in the model was varied at different values while others are kept constant to determine the effects of the parameter on the disease states, and to ultimately determine the more important parameter(s) necessary to control the epidemic. By simulation, it was revealed that the susceptible people in a population depletes in a negative exponential form after contracting HIV, the infectives grow and decay in a log logistic form, while the AIDS people in the population grow in a positive exponential form. The rate at which susceptible becomes infective and the rate at which infective becomes AIDS are crucial parameters which when kept low, the epidemic is kept under control.
Keywords
Discrete Time, Markov Process, HIV/AIDS, Susceptible, Infective, Models
To cite this article
OGUNMOLA ADENIYI OYEWOLE, On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling, American Journal of Applied Mathematics. Vol. 2, No. 1, 2014, pp. 21-28. doi: 10.11648/j.ajam.20140201.14
References
[1]
Coffin, J. et al. (1986). Human Immunodeficiency Viruses. World Scientific Publishing Company Limited.
[2]
Druten Van, J. A. M., DeBoo, Th., Reintjes, A.g.M., Jager, J. C., Heisterkamp, S. H., Continho, R. A., Bos, J. M. and Ruitenberg, E. J. (1987). Reconstruction and prediction of spread of HIV infection in populations of homosexual men.
[3]
Isham Valerie (1988). Mathematical Modelling of the Transmission Dynamics of HIV Infection and AIDS.
[4]
Londa J. S. Allen and Amy M. Burgin (1998) Comparism of deterministic and stochastic SIS and SIR models in discrete time.
[5]
Nasidi A, Henry T.O., Ajose Coker O.O., and et al. Evidence of LAV/HTLV III Infection and AIDS related complex in Lagos, Nigeria.
[6]
Tan, W. Y. and Xing, Z. H. (1999). Modeling the HIV epidemic with variable infection in homosexual populations by state space model.
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