Volume 4, Issue 5, October 2016, Page: 222-234
Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment
Ram Singh, Department of Mathematical Sciences, Baba Ghulam Shah Badshah, University, Rajouri, Jammu and Kashmir, India
Shoket Ali, Department of Mathematical Sciences, Baba Ghulam Shah Badshah, University, Rajouri, Jammu and Kashmir, India
Madhu Jain, Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttrakhand, India
Rakhee , Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, India
Received: Aug. 30, 2016;       Accepted: Sep. 23, 2016;       Published: Oct. 14, 2016
DOI: 10.11648/j.ajam.20160405.14      View  3146      Downloads  150
Abstract
The mathematical model for analyzing the transmission dynamics of HIV/AIDS epidemic with treatment is studied by considering the three latent compartments for slow, medium and fast progresses of developing the AIDS. By constructing the system of differential equations for the different population groups namely susceptible, three types of latent individuals, symptomatic stage group and full blown AIDS individuals, the mathematical analysis is carried out in order to understand the dynamics of disease spread. By determining the basic reproduction number (R0), the model examines the two equilibrium points (i) the disease free equilibrium and (ii) the endemic equilibrium. It is established that if R0 <1, the disease free equilibrium is locally and globally asymptotically stable. The stability of endemic equilibrium has also been discussed.
Keywords
Transmission Dynamic, HIV/AIDS, Latent Compartments, Reproduction Number, Stability
To cite this article
Ram Singh, Shoket Ali, Madhu Jain, Rakhee , Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment, American Journal of Applied Mathematics. Vol. 4, No. 5, 2016, pp. 222-234. doi: 10.11648/j.ajam.20160405.14
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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