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.
Published in | American Journal of Applied Mathematics (Volume 4, Issue 5) |
DOI | 10.11648/j.ajam.20160405.15 |
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), 2016. Published by Science Publishing Group |
Markov Chain, Reproductive Ratio, Stability, Transition Matrix
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APA Style
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
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
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
@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://article.sciencepublishinggroup.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} }
TY - JOUR T1 - Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process AU - Rotich Kiplimo Titus Y1 - 2016/10/15 PY - 2016 N1 - https://doi.org/10.11648/j.ajam.20160405.15 DO - 10.11648/j.ajam.20160405.15 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 235 EP - 246 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20160405.15 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. VL - 4 IS - 5 ER -