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Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process
American Journal of Applied Mathematics
Volume 4, Issue 5, October 2016, Pages: 235-246
Received: Sep. 6, 2016; Accepted: Sep. 23, 2016; Published: Oct. 15, 2016
Author
Rotich Kiplimo Titus, Department of Center for Teacher Education, Moi University, Eldoret, Kenya
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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.
Keywords
Markov Chain, Reproductive Ratio, Stability, Transition Matrix
Rotich Kiplimo Titus, Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process, American Journal of Applied Mathematics. Vol. 4, No. 5, 2016, pp. 235-246. doi: 10.11648/j.ajam.20160405.15
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