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A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles

Received: 10 August 2015     Accepted: 7 September 2015     Published: 29 September 2015
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Abstract

Despite the availability of measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. Elimination of measles requires maintaining the effective reproduction number less than unity, Re <1 as well as achieving low levels of susceptibility. Infectious diseases are great field for mathematical modeling, and for connecting mathematical models to primary or secondary data. In this project, we concentrated on the mathematical model for control and elimination of transmission dynamics of measles. We have obtained disease free equilibrium (DFE) point, effective reproduction number and basic reproduction number for the model. Simulations of different variables of the model have been performed and sensitivity analysis of different embedded parameters has been done. MATLAB has been used in simulations of the ordinary differential equations (ODEs) as well as the reproduction numbers.

Published in Applied and Computational Mathematics (Volume 4, Issue 6)
DOI 10.11648/j.acm.20150406.12
Page(s) 396-408
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), 2015. Published by Science Publishing Group

Keywords

Measles, Vaccination, Immunity, Mathematical Modelling, Herd Immunity

References
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Cite This Article
  • APA Style

    Stephen Edward, Kitengeso Raymond E., Kiria Gabriel T., Felician Nestory, Mwema Godfrey G., et al. (2015). A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles. Applied and Computational Mathematics, 4(6), 396-408. https://doi.org/10.11648/j.acm.20150406.12

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    ACS Style

    Stephen Edward; Kitengeso Raymond E.; Kiria Gabriel T.; Felician Nestory; Mwema Godfrey G., et al. A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles. Appl. Comput. Math. 2015, 4(6), 396-408. doi: 10.11648/j.acm.20150406.12

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    AMA Style

    Stephen Edward, Kitengeso Raymond E., Kiria Gabriel T., Felician Nestory, Mwema Godfrey G., et al. A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles. Appl Comput Math. 2015;4(6):396-408. doi: 10.11648/j.acm.20150406.12

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  • @article{10.11648/j.acm.20150406.12,
      author = {Stephen Edward and Kitengeso Raymond E. and Kiria Gabriel T. and Felician Nestory and Mwema Godfrey G. and Mafarasa Arbogast P.},
      title = {A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {6},
      pages = {396-408},
      doi = {10.11648/j.acm.20150406.12},
      url = {https://doi.org/10.11648/j.acm.20150406.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.12},
      abstract = {Despite the availability of measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. Elimination of measles requires maintaining the effective reproduction number less than unity, Re <1 as well as achieving low levels of susceptibility. Infectious diseases are great field for mathematical modeling, and for connecting mathematical models to primary or secondary data. In this project, we concentrated on the mathematical model for control and elimination of transmission dynamics of measles. We have obtained disease free equilibrium (DFE) point, effective reproduction number and basic reproduction number for the model. Simulations of different variables of the model have been performed and sensitivity analysis of different embedded parameters has been done. MATLAB has been used in simulations of the ordinary differential equations (ODEs) as well as the reproduction numbers.},
     year = {2015}
    }
    

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    AB  - Despite the availability of measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. Elimination of measles requires maintaining the effective reproduction number less than unity, Re <1 as well as achieving low levels of susceptibility. Infectious diseases are great field for mathematical modeling, and for connecting mathematical models to primary or secondary data. In this project, we concentrated on the mathematical model for control and elimination of transmission dynamics of measles. We have obtained disease free equilibrium (DFE) point, effective reproduction number and basic reproduction number for the model. Simulations of different variables of the model have been performed and sensitivity analysis of different embedded parameters has been done. MATLAB has been used in simulations of the ordinary differential equations (ODEs) as well as the reproduction numbers.
    VL  - 4
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Author Information
  • Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania

  • Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania

  • Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania

  • Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania

  • Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania

  • Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma (UDOM), Dodoma, Tanzania

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