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The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission

Received: 25 May 2018     Accepted: 26 June 2018     Published: 2 August 2018
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Abstract

Malaria is one of infectious diseases and has become the most public health issue especially in developing countries. Mathematically, the spread of malaria can be modeled to predict the dynamics of the outbreak of the disease. The present research studies the impact of migration of susceptible population on the dynamics of malaria transmission. In this paper an improved mathematical model is constructed based on a set of reasonable assumptions. Validity of the model is proved by verifying positivity of the solution. Mathematical analysis is carried out including equilibrium point analysis. Basic reproduction number of the model is determined so as to study the effect of migration parameter on the malaria outbreak. It has been observed that the migration parameter is directly proportional to the malaria outbreak. Hence, it is suggested that in order to keep the malaria outbreak under control, the migration parameter is required to be minimized. That is, migration of populations is recommended to reduce so as to reduce the impact of malaria outbreak.

Published in American Journal of Applied Mathematics (Volume 6, Issue 3)
DOI 10.11648/j.ajam.20180603.13
Page(s) 117-127
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), 2018. Published by Science Publishing Group

Keywords

Malaria Outbreak, Reproduction Number, Migration Parameter, Numerical Simulation

References
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[6] Plemmons W. R., “Mathematical study of malaria models of Ross and Ngwa”, Master Thesis, University of Florida, pp. 1-69, 2006.
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[14] Ferreira M. U., H. M. Yang, “Assessing the effects of global warming and local social and economic conditions on the malaria transmission”, Revista de SaudePublica, vol. 34, pp. 214-222, 2000.
[15] Koella J. C. and R. Antia, “Epidemiological models for the spread of anti-malarial resistance”, Malaria Journal, vol. 2, 2003.
[16] Welch, J. Li, R. M., U. S. Nair, T. L. Sever, D. E. Irwin, C.Cordon-Rosales, N. Padilla, “Dynamic malaria models with environmental changes”, in Proceedings of the Thirty-fourth southeastern symposium on system theory, Huntsville, pp. 396-400, 2014.
[17] Bacaer N. and C. Sokhna. “A reaction-diffusion system modeling the spread of resistance to an antimalarial drug”, Math. Biosci. Engrg, vol. 2, pp. 227-238, 2005.
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Cite This Article
  • APA Style

    Alemu Geleta Wedajo, Boka Kumsa Bole, Purnachandra Rao Koya. (2018). The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission. American Journal of Applied Mathematics, 6(3), 117-127. https://doi.org/10.11648/j.ajam.20180603.13

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    ACS Style

    Alemu Geleta Wedajo; Boka Kumsa Bole; Purnachandra Rao Koya. The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission. Am. J. Appl. Math. 2018, 6(3), 117-127. doi: 10.11648/j.ajam.20180603.13

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    AMA Style

    Alemu Geleta Wedajo, Boka Kumsa Bole, Purnachandra Rao Koya. The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission. Am J Appl Math. 2018;6(3):117-127. doi: 10.11648/j.ajam.20180603.13

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  • @article{10.11648/j.ajam.20180603.13,
      author = {Alemu Geleta Wedajo and Boka Kumsa Bole and Purnachandra Rao Koya},
      title = {The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission},
      journal = {American Journal of Applied Mathematics},
      volume = {6},
      number = {3},
      pages = {117-127},
      doi = {10.11648/j.ajam.20180603.13},
      url = {https://doi.org/10.11648/j.ajam.20180603.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180603.13},
      abstract = {Malaria is one of infectious diseases and has become the most public health issue especially in developing countries. Mathematically, the spread of malaria can be modeled to predict the dynamics of the outbreak of the disease. The present research studies the impact of migration of susceptible population on the dynamics of malaria transmission. In this paper an improved mathematical model is constructed based on a set of reasonable assumptions. Validity of the model is proved by verifying positivity of the solution. Mathematical analysis is carried out including equilibrium point analysis. Basic reproduction number of the model is determined so as to study the effect of migration parameter on the malaria outbreak. It has been observed that the migration parameter is directly proportional to the malaria outbreak. Hence, it is suggested that in order to keep the malaria outbreak under control, the migration parameter is required to be minimized. That is, migration of populations is recommended to reduce so as to reduce the impact of malaria outbreak.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission
    AU  - Alemu Geleta Wedajo
    AU  - Boka Kumsa Bole
    AU  - Purnachandra Rao Koya
    Y1  - 2018/08/02
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ajam.20180603.13
    DO  - 10.11648/j.ajam.20180603.13
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 117
    EP  - 127
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20180603.13
    AB  - Malaria is one of infectious diseases and has become the most public health issue especially in developing countries. Mathematically, the spread of malaria can be modeled to predict the dynamics of the outbreak of the disease. The present research studies the impact of migration of susceptible population on the dynamics of malaria transmission. In this paper an improved mathematical model is constructed based on a set of reasonable assumptions. Validity of the model is proved by verifying positivity of the solution. Mathematical analysis is carried out including equilibrium point analysis. Basic reproduction number of the model is determined so as to study the effect of migration parameter on the malaria outbreak. It has been observed that the migration parameter is directly proportional to the malaria outbreak. Hence, it is suggested that in order to keep the malaria outbreak under control, the migration parameter is required to be minimized. That is, migration of populations is recommended to reduce so as to reduce the impact of malaria outbreak.
    VL  - 6
    IS  - 3
    ER  - 

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Author Information
  • Department of Mathematics, Wollega University, Nekemte, Ethiopia

  • Department of Mathematics, Wollega University, Nekemte, Ethiopia

  • Department of Mathematics, Hawassa University, Hawassa, Ethiopia

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