American Journal of Applied Mathematics

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Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process

Received: 06 September 2016    Accepted: 23 September 2016    Published: 15 October 2016
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Abstract

The spread of the Human Immunodeficiency Virus (HIV) and the resulting Acquired Immune Deficiency syndrome (AIDS) is a major health concern. Mathematical models are therefore commonly applied to understand the spread of the HIV epidemic. In this study, HIV dynamics is analyzed using a Stochastic Discrete-Time Markov Chain Mathematical Model. Demographic and epidemiological parameters that affect the model population dynamics were investigated. Well posedness of the model determined and the conditions for the existence and stability of disease-free and endemic equilibrium points proved, using the next generation matrix technique. The effect of various intervention strategies, were simulated by varying the parameters representing the possible strategies and comparing the respective values of the reproductive ratio R_0. The numerical simulation results using intervention transition matrix showed that vertical transmission is the most sensitive parameter standing at 0.6 followed by the use of HAART at 0.4. This indicates the strategy which requires much effort to avert progression of infected individual to AIDS.

DOI 10.11648/j.ajam.20160405.15
Published in American Journal of Applied Mathematics (Volume 4, Issue 5, October 2016)
Page(s) 235-246
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), 2024. Published by Science Publishing Group

Keywords

Markov Chain, Reproductive Ratio, Stability, Transition Matrix

References
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[21] Piot, P. and Bartos, M., 2002The epidemiology of HIV and AIDS, AIDS in Africa, Springer, pp. 200-217.
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  • Department of Center for Teacher Education, Moi University, Eldoret, Kenya

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    Rotich Kiplimo Titus. (2016). Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process. American Journal of Applied Mathematics, 4(5), 235-246. https://doi.org/10.11648/j.ajam.20160405.15

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    ACS Style

    Rotich Kiplimo Titus. Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process. Am. J. Appl. Math. 2016, 4(5), 235-246. doi: 10.11648/j.ajam.20160405.15

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    AMA Style

    Rotich Kiplimo Titus. Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process. Am J Appl Math. 2016;4(5):235-246. doi: 10.11648/j.ajam.20160405.15

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  • @article{10.11648/j.ajam.20160405.15,
      author = {Rotich Kiplimo Titus},
      title = {Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {5},
      pages = {235-246},
      doi = {10.11648/j.ajam.20160405.15},
      url = {https://doi.org/10.11648/j.ajam.20160405.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20160405.15},
      abstract = {The spread of the Human Immunodeficiency Virus (HIV) and the resulting Acquired Immune Deficiency syndrome (AIDS) is a major health concern. Mathematical models are therefore commonly applied to understand the spread of the HIV epidemic. In this study, HIV dynamics is analyzed using a Stochastic Discrete-Time Markov Chain Mathematical Model. Demographic and epidemiological parameters that affect the model population dynamics were investigated. Well posedness of the model determined and the conditions for the existence and stability of disease-free and endemic equilibrium points proved, using the next generation matrix technique. The effect of various intervention strategies, were simulated by varying the parameters representing the possible strategies and comparing the respective values of the reproductive ratio R_0. The numerical simulation results using intervention transition matrix showed that vertical transmission is the most sensitive parameter standing at 0.6 followed by the use of HAART at 0.4. This indicates the strategy which requires much effort to avert progression of infected individual to AIDS.},
     year = {2016}
    }
    

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    AB  - The spread of the Human Immunodeficiency Virus (HIV) and the resulting Acquired Immune Deficiency syndrome (AIDS) is a major health concern. Mathematical models are therefore commonly applied to understand the spread of the HIV epidemic. In this study, HIV dynamics is analyzed using a Stochastic Discrete-Time Markov Chain Mathematical Model. Demographic and epidemiological parameters that affect the model population dynamics were investigated. Well posedness of the model determined and the conditions for the existence and stability of disease-free and endemic equilibrium points proved, using the next generation matrix technique. The effect of various intervention strategies, were simulated by varying the parameters representing the possible strategies and comparing the respective values of the reproductive ratio R_0. The numerical simulation results using intervention transition matrix showed that vertical transmission is the most sensitive parameter standing at 0.6 followed by the use of HAART at 0.4. This indicates the strategy which requires much effort to avert progression of infected individual to AIDS.
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