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Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination

Received: 11 September 2015     Accepted: 26 September 2015     Published: 23 October 2015
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Abstract

In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if RC <1 and unstable if RC >1. We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all RCi >1 and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.

Published in Applied and Computational Mathematics (Volume 4, Issue 6)
DOI 10.11648/j.acm.20150406.16
Page(s) 431-444
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

Vaccination, Metapopulation, Measles, Bifurcation Analysis

References
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Cite This Article
  • APA Style

    Leopard C. Mpande, Damian Kajunguri, Emmanuel A. Mpolya. (2015). Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination. Applied and Computational Mathematics, 4(6), 431-444. https://doi.org/10.11648/j.acm.20150406.16

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    ACS Style

    Leopard C. Mpande; Damian Kajunguri; Emmanuel A. Mpolya. Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination. Appl. Comput. Math. 2015, 4(6), 431-444. doi: 10.11648/j.acm.20150406.16

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    AMA Style

    Leopard C. Mpande, Damian Kajunguri, Emmanuel A. Mpolya. Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination. Appl Comput Math. 2015;4(6):431-444. doi: 10.11648/j.acm.20150406.16

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  • @article{10.11648/j.acm.20150406.16,
      author = {Leopard C. Mpande and Damian Kajunguri and Emmanuel A. Mpolya},
      title = {Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {6},
      pages = {431-444},
      doi = {10.11648/j.acm.20150406.16},
      url = {https://doi.org/10.11648/j.acm.20150406.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.16},
      abstract = {In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if RC <1 and unstable if RC >1. We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all RCi >1 and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination
    AU  - Leopard C. Mpande
    AU  - Damian Kajunguri
    AU  - Emmanuel A. Mpolya
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    N1  - https://doi.org/10.11648/j.acm.20150406.16
    DO  - 10.11648/j.acm.20150406.16
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 431
    EP  - 444
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20150406.16
    AB  - In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if RC <1 and unstable if RC >1. We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all RCi >1 and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.
    VL  - 4
    IS  - 6
    ER  - 

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Author Information
  • Nelson Mandela African Institution of Science and Technology, School of CoCSE, Arusha, Tanzania

  • Nelson Mandela African Institution of Science and Technology, School of CoCSE, Arusha, Tanzania

  • Nelson Mandela African Institution of Science and Technology, School of LiSBE, Arusha, Tanzania

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