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Stability and Time-Scale Analysis of Malaria Transmission in Human-Mosquito Population

Received: 9 September 2016     Accepted: 4 November 2016     Published: 2 December 2016
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Abstract

More realistic human-mosquito mathematical model in which re-infected asymptomatic humans are considered is presented. The Next Generation Matrix technique is used to construct epidemiological threshold known as the reproduction number. Locally and globally asymptotically stable disease-free equilibrium conditions for the model are established. Possible time-scale of events for model transition from non-endemic to endemic is analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region.

Published in International Journal of Systems Science and Applied Mathematics (Volume 2, Issue 1)
DOI 10.11648/j.ijssam.20170201.11
Page(s) 1-9
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

Malaria Transmission, Stability Analysis, Mathematical Modeling

References
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  • APA Style

    Kodwo Annan, Cedrick Dizala Mukinay. (2016). Stability and Time-Scale Analysis of Malaria Transmission in Human-Mosquito Population. International Journal of Systems Science and Applied Mathematics, 2(1), 1-9. https://doi.org/10.11648/j.ijssam.20170201.11

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    ACS Style

    Kodwo Annan; Cedrick Dizala Mukinay. Stability and Time-Scale Analysis of Malaria Transmission in Human-Mosquito Population. Int. J. Syst. Sci. Appl. Math. 2016, 2(1), 1-9. doi: 10.11648/j.ijssam.20170201.11

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    AMA Style

    Kodwo Annan, Cedrick Dizala Mukinay. Stability and Time-Scale Analysis of Malaria Transmission in Human-Mosquito Population. Int J Syst Sci Appl Math. 2016;2(1):1-9. doi: 10.11648/j.ijssam.20170201.11

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  • @article{10.11648/j.ijssam.20170201.11,
      author = {Kodwo Annan and Cedrick Dizala Mukinay},
      title = {Stability and Time-Scale Analysis of Malaria Transmission in Human-Mosquito Population},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {2},
      number = {1},
      pages = {1-9},
      doi = {10.11648/j.ijssam.20170201.11},
      url = {https://doi.org/10.11648/j.ijssam.20170201.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20170201.11},
      abstract = {More realistic human-mosquito mathematical model in which re-infected asymptomatic humans are considered is presented. The Next Generation Matrix technique is used to construct epidemiological threshold known as the reproduction number. Locally and globally asymptotically stable disease-free equilibrium conditions for the model are established. Possible time-scale of events for model transition from non-endemic to endemic is analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region.},
     year = {2016}
    }
    

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    T2  - International Journal of Systems Science and Applied Mathematics
    JF  - International Journal of Systems Science and Applied Mathematics
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    UR  - https://doi.org/10.11648/j.ijssam.20170201.11
    AB  - More realistic human-mosquito mathematical model in which re-infected asymptomatic humans are considered is presented. The Next Generation Matrix technique is used to construct epidemiological threshold known as the reproduction number. Locally and globally asymptotically stable disease-free equilibrium conditions for the model are established. Possible time-scale of events for model transition from non-endemic to endemic is analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region.
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Author Information
  • School of Science and Technology, Georgia Gwinnett College, Lawrenceville, Georgia, USA

  • School of Science and Technology, Georgia Gwinnett College, Lawrenceville, Georgia, USA

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