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Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment

Received: 30 August 2016     Accepted: 23 September 2016     Published: 14 October 2016
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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.

Published in American Journal of Applied Mathematics (Volume 4, Issue 5)
DOI 10.11648/j.ajam.20160405.14
Page(s) 222-234
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

Keywords

Transmission Dynamic, HIV/AIDS, Latent Compartments, Reproduction Number, Stability

References
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[17] Wang J., Zhang R. and Kuniya T., “Global dynamics for a class of age-infection HIV models with nonlinear infection rate”, Math. Analysis and Appl. 432 (1), 289-313 (2015).
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[19] Huo H. F., Chen R. and Wang X. Y., “Modelling and stability of HIV/AIDS epidemic model with treatment”, Appl. Math. Model. 40(13-14), 6550–6559 (2016).
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Cite This Article
  • APA Style

    Ram Singh, Shoket Ali, Madhu Jain, Rakhee. (2016). Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment. American Journal of Applied Mathematics, 4(5), 222-234. https://doi.org/10.11648/j.ajam.20160405.14

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    ACS Style

    Ram Singh; Shoket Ali; Madhu Jain; Rakhee. Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment. Am. J. Appl. Math. 2016, 4(5), 222-234. doi: 10.11648/j.ajam.20160405.14

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    AMA Style

    Ram Singh, Shoket Ali, Madhu Jain, Rakhee. Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment. Am J Appl Math. 2016;4(5):222-234. doi: 10.11648/j.ajam.20160405.14

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  • @article{10.11648/j.ajam.20160405.14,
      author = {Ram Singh and Shoket Ali and Madhu Jain and Rakhee},
      title = {Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {5},
      pages = {222-234},
      doi = {10.11648/j.ajam.20160405.14},
      url = {https://doi.org/10.11648/j.ajam.20160405.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160405.14},
      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.},
     year = {2016}
    }
    

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    T1  - Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment
    AU  - Ram Singh
    AU  - Shoket Ali
    AU  - Madhu Jain
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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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    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20160405.14
    AB  - 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.
    VL  - 4
    IS  - 5
    ER  - 

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Author Information
  • Department of Mathematical Sciences, Baba Ghulam Shah Badshah, University, Rajouri, Jammu and Kashmir, India

  • Department of Mathematical Sciences, Baba Ghulam Shah Badshah, University, Rajouri, Jammu and Kashmir, India

  • Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttrakhand, India

  • Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, India

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