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Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan

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  • Ullah, Saif
  • Khan, Muhammad Altaf
  • Farooq, Muhammad
  • Gul, Taza

Abstract

In this paper, we present a mathematical model on the dynamics of Tuberculosis (TB) in Khyber Pakhtunkhwa, province of Pakistan. The model is parameterized using TB infected cases reported from the year 2002 to 2017 in Khyber Pakhtunkhwa. The basic reproduction number R0 for the given period is estimated as R0≈1.3419. Mathematical analysis of the model in terms of stability analysis is derived and discussed in detail. The model at the disease free case is locally as well as globally asymptotically stable when the basic reproduction number R0<1. Further, when the basic reproduction number R0>1, then the model is stable locally as well as globally. Moreover, the sensitivity analysis of the model parameters are performed and their corresponding graphical results are presented. Finally, the numerical results for the sensitive parameters are plotted and their effects are shown on the disease elimination.

Suggested Citation

  • Ullah, Saif & Khan, Muhammad Altaf & Farooq, Muhammad & Gul, Taza, 2019. "Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 181-199.
    • Handle: RePEc:eee:matcom:v:165:y:2019:i:c:p:181-199
    DOI: 10.1016/j.matcom.2019.03.012
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    References listed on IDEAS

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    1. Wang, Yi & Cao, Jinde, 2014. "Global dynamics of multi-group SEI animal disease models with indirect transmission," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 81-89.
    2. Yang, Yali & Li, Jianquan & Ma, Zhien & Liu, Luju, 2010. "Global stability of two models with incomplete treatment for tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 79-85.
    3. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
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