On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling

OGUNMOLA ADENIYI OYEWOLE

doi:doi:10.11648/j.ajam.20140201.14

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On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling

OGUNMOLA ADENIYI OYEWOLE

Published in American Journal of Applied Mathematics (Volume 2, Issue 1)

Received: 31 December 2013 Published: 28 February 2014

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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.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 1)
DOI	10.11648/j.ajam.20140201.14
Page(s)	21-28
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Discrete Time, Markov Process, HIV/AIDS, Susceptible, Infective, Models

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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APA Style

OGUNMOLA ADENIYI OYEWOLE. (2014). On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling. American Journal of Applied Mathematics, 2(1), 21-28. https://doi.org/10.11648/j.ajam.20140201.14

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ACS Style

OGUNMOLA ADENIYI OYEWOLE. On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling. Am. J. Appl. Math. 2014, 2(1), 21-28. doi: 10.11648/j.ajam.20140201.14

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AMA Style

OGUNMOLA ADENIYI OYEWOLE. On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling. Am J Appl Math. 2014;2(1):21-28. doi: 10.11648/j.ajam.20140201.14

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@article{10.11648/j.ajam.20140201.14,
  author = {OGUNMOLA ADENIYI OYEWOLE},
  title = {On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {21-28},
  doi = {10.11648/j.ajam.20140201.14},
  url = {https://doi.org/10.11648/j.ajam.20140201.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140201.14},
  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.},
 year = {2014}
}

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TY  - JOUR
T1  - On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling
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Y1  - 2014/02/28
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T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
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AB  - 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.
VL  - 2
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Author Information

OGUNMOLA ADENIYI OYEWOLE

Department of Mathematics and Statistics, Faculty of Pure and Natural Science, Federal University Wukari, Taraba State

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APA Style

OGUNMOLA ADENIYI OYEWOLE. (2014). On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling. American Journal of Applied Mathematics, 2(1), 21-28. https://doi.org/10.11648/j.ajam.20140201.14

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ACS Style

OGUNMOLA ADENIYI OYEWOLE. On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling. Am. J. Appl. Math. 2014, 2(1), 21-28. doi: 10.11648/j.ajam.20140201.14

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AMA Style

OGUNMOLA ADENIYI OYEWOLE. On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling. Am J Appl Math. 2014;2(1):21-28. doi: 10.11648/j.ajam.20140201.14

Copy | Download

@article{10.11648/j.ajam.20140201.14,
  author = {OGUNMOLA ADENIYI OYEWOLE},
  title = {On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {21-28},
  doi = {10.11648/j.ajam.20140201.14},
  url = {https://doi.org/10.11648/j.ajam.20140201.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140201.14},
  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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - On the use of Discrete – Time Markov Process for HIV/AIDs Epidemic Modelling
AU  - OGUNMOLA ADENIYI OYEWOLE
Y1  - 2014/02/28
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140201.14
DO  - 10.11648/j.ajam.20140201.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 21
EP  - 28
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140201.14
AB  - 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.
VL  - 2
IS  - 1
ER  -

Copy | Download