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Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis

Received: 22 April 2020     Accepted: 15 May 2020     Published: 29 May 2020
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Abstract

In this work we considered nonlinear dynamical system to study the dynamics of two-strain Tuberculosis epidemic in Ethiopia. We proved that the solution of the considered dynamical system is positive and bounded. We found that the considered dynamical system has disease free and endemic equilibrium points. We proved that the local and global stability of disease free equilibrium point and endemic equilibrium point. We found the effective reproduction number of the dynamical system. Also, the effective reproduction number of the dynamical system which experience drug sensitive strain and the effective reproduction number of the dynamical system which experience multi drug resistance strain. Using real data collected from different health sectors from Ethiopia we found that the numerical value of the effective reproduction number of the drug sensitive tuberculosis is 1.03 and the effective reproduction number of the drug resistance tuberculosis is 4.78 and the effective reproduction number of the dynamical system max{1.03, 4.78}=4.78. So that MDR strain is spreads strongly than DS strain. Numerical simulation is also done to illustrate the influence of different parameters on the effective reproduction number. Using sensitive analysis we identify the most influential parameter to change the behavior of the solution of the considered dynamical system is the number of effective contacts of susceptible or vaccinated individuals make with an infectious individual.

Published in American Journal of Applied Mathematics (Volume 8, Issue 3)
DOI 10.11648/j.ajam.20200803.15
Page(s) 123-144
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), 2020. Published by Science Publishing Group

Keywords

Drug-sensitive Tuberculosis, Drug Resistance Tuberculosis, Effective Reproduction Number, Sensitivity Analysis, Numerical Analysis

References
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[3] C. P. Bhunu, A two strain tuberculosis transmission model with therapy and quarantine, 2010.
[4] D. Meressa Achieving high treatment success for multidrugresistant TB in Africa: initiation and scale-up of MDR TB care in Ethiopia—an observational cohort study, http://thorax.bmj.com/ on November 25, 2015.
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[7] FDREM-H Ethiopian Public Health Institute, 2014, https://www.who.int/globalchange/resources/wash-toolkit/review-of-policy-documents-on-climate-change-wash-and-public-health-in-ethiopia.pdf?ua=1.
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[21] M. Maliyani, P. M. Mwamtobe, S. D. Hove-Musekwa and J. M. Tchuenche: Modelling the role of diagnosis, Treatment and Health education on Multi-Drug resistant tuberculosis dynamics International Journal of Biomathematics and Systems Biology, 2015.
[22] Z. Gashu, The Yield of Community-Based “Retrospective” Tuberculosis Contact Investigation in a High Burden Setting in Ethiopia, DOI:10.1371/journal.pone.0160514, 2016.
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  • APA Style

    Shimelis Bekele Zerefe, Temesgen Tibebu Mekonnen. (2020). Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis. American Journal of Applied Mathematics, 8(3), 123-144. https://doi.org/10.11648/j.ajam.20200803.15

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    ACS Style

    Shimelis Bekele Zerefe; Temesgen Tibebu Mekonnen. Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis. Am. J. Appl. Math. 2020, 8(3), 123-144. doi: 10.11648/j.ajam.20200803.15

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    AMA Style

    Shimelis Bekele Zerefe, Temesgen Tibebu Mekonnen. Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis. Am J Appl Math. 2020;8(3):123-144. doi: 10.11648/j.ajam.20200803.15

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  • @article{10.11648/j.ajam.20200803.15,
      author = {Shimelis Bekele Zerefe and Temesgen Tibebu Mekonnen},
      title = {Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis},
      journal = {American Journal of Applied Mathematics},
      volume = {8},
      number = {3},
      pages = {123-144},
      doi = {10.11648/j.ajam.20200803.15},
      url = {https://doi.org/10.11648/j.ajam.20200803.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200803.15},
      abstract = {In this work we considered nonlinear dynamical system to study the dynamics of two-strain Tuberculosis epidemic in Ethiopia. We proved that the solution of the considered dynamical system is positive and bounded. We found that the considered dynamical system has disease free and endemic equilibrium points. We proved that the local and global stability of disease free equilibrium point and endemic equilibrium point. We found the effective reproduction number of the dynamical system. Also, the effective reproduction number of the dynamical system which experience drug sensitive strain and the effective reproduction number of the dynamical system which experience multi drug resistance strain. Using real data collected from different health sectors from Ethiopia we found that the numerical value of the effective reproduction number of the drug sensitive tuberculosis is 1.03 and the effective reproduction number of the drug resistance tuberculosis is 4.78 and the effective reproduction number of the dynamical system max{1.03, 4.78}=4.78. So that MDR strain is spreads strongly than DS strain. Numerical simulation is also done to illustrate the influence of different parameters on the effective reproduction number. Using sensitive analysis we identify the most influential parameter to change the behavior of the solution of the considered dynamical system is the number of effective contacts of susceptible or vaccinated individuals make with an infectious individual.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis
    AU  - Shimelis Bekele Zerefe
    AU  - Temesgen Tibebu Mekonnen
    Y1  - 2020/05/29
    PY  - 2020
    N1  - https://doi.org/10.11648/j.ajam.20200803.15
    DO  - 10.11648/j.ajam.20200803.15
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 123
    EP  - 144
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20200803.15
    AB  - In this work we considered nonlinear dynamical system to study the dynamics of two-strain Tuberculosis epidemic in Ethiopia. We proved that the solution of the considered dynamical system is positive and bounded. We found that the considered dynamical system has disease free and endemic equilibrium points. We proved that the local and global stability of disease free equilibrium point and endemic equilibrium point. We found the effective reproduction number of the dynamical system. Also, the effective reproduction number of the dynamical system which experience drug sensitive strain and the effective reproduction number of the dynamical system which experience multi drug resistance strain. Using real data collected from different health sectors from Ethiopia we found that the numerical value of the effective reproduction number of the drug sensitive tuberculosis is 1.03 and the effective reproduction number of the drug resistance tuberculosis is 4.78 and the effective reproduction number of the dynamical system max{1.03, 4.78}=4.78. So that MDR strain is spreads strongly than DS strain. Numerical simulation is also done to illustrate the influence of different parameters on the effective reproduction number. Using sensitive analysis we identify the most influential parameter to change the behavior of the solution of the considered dynamical system is the number of effective contacts of susceptible or vaccinated individuals make with an infectious individual.
    VL  - 8
    IS  - 3
    ER  - 

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Author Information
  • Department of Mathematics, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia

  • Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia

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