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A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations

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  • Khan, Hasib
  • Alam, Khurshaid
  • Gulzar, Haseena
  • Etemad, Sina
  • Rezapour, Shahram

Abstract

In this article, a fractal-fractional order tuberculosis mathematical model is presented for the existence results, numerical simulations and stability analysis. The model has six classes S1,S2,S3,E,I,R. The first three classes S1, S2, S3 represent the population of susceptible children, middle-aged, and senior adults, respectively. While I is the class of active infected individuals who can transmit the tuberculosis, E stands for non-active infected class. The population of recovered individuals is represented by R. For the existence criterion of the given model, successive iterative sequences are defined whose limit points are the solutions of our proposed tuberculosis model. After investigation of uniqueness property, the Hyers–Ulam (HU)-stability is established in the sequel. With the help of two-step Lagrange polynomials, we provide numerical solutions and we give a comparative numerical analysis for different values of the fractional order and fractal order based on the obtained algorithms. The numerical simulations show the applicability of the schemes and the future prediction.

Suggested Citation

  • Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:455-473
    DOI: 10.1016/j.matcom.2022.03.009
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    References listed on IDEAS

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    1. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Khan, Aziz & Khan, Hasib & Gómez-Aguilar, J.F. & Abdeljawad, Thabet, 2019. "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 422-427.
    3. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    4. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Djilali, Salih & Ghanbari, Behzad, 2020. "Coronavirus pandemic: A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Smith, James P. & Strauss, John & Zhao, Yaohui, 2014. "Healthy aging in China," The Journal of the Economics of Ageing, Elsevier, vol. 4(C), pages 37-43.
    9. Khan, Aziz & Gómez-Aguilar, J.F. & Saeed Khan, Tahir & Khan, Hasib, 2019. "Stability analysis and numerical solutions of fractional order HIV/AIDS model," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 119-128.
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    2. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.

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