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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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    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).
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    Cited by:

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    2. Kanwal, Tanzeela & Hussain, Azhar & Avcı, İbrahim & Etemad, Sina & Rezapour, Shahram & Torres, Delfim F.M., 2024. "Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Avcı, İbrahim & Lort, Hüseyin & Tatlıcıoğlu, Buğce E., 2023. "Numerical investigation and deep learning approach for fractal–fractional order dynamics of Hopfield neural network model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. 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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