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Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis

Author

Listed:
  • Abayneh Kebede Fantaye
  • Zerihun Kinfe Birhanu

Abstract

In this study, the authors proposed a nonlinear deterministic model and stability analysis for the transmission dynamics of chewing khat. The model’s solution is proved to be positive and bounded, and the basic reproduction number (R0) is calculated using the next‐generation matrix method. Following that, the authors have looked at the local and global stability of the model’s khat‐free and endemic equilibrium points. When R0 1, the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.

Suggested Citation

  • Abayneh Kebede Fantaye & Zerihun Kinfe Birhanu, 2022. "Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:3844885
    DOI: 10.1155/2022/3844885
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    References listed on IDEAS

    as
    1. Abayneh Kebede Fantaye & Zerihun Kinfe Birhanu & Bruno Carpentieri, 2022. "Mathematical Model and Analysis of Corruption Dynamics with Optimal Control," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-16, January.
    2. Havlicek, Judy R. & Garcia, Antonio R. & Smith, Douglas C., 2013. "Mental health and substance use disorders among foster youth transitioning to adulthood: Past research and future directions," Children and Youth Services Review, Elsevier, vol. 35(1), pages 194-203.
    3. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. Abayneh Kebede Fantaye, 2022. "Modelling and Stability Analysis of Cotton Leaf Curl Virus (CLCuV) Transmission Dynamics in Cotton Plant," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    5. Kahsay Godifey Wubneh & Fitsum Mulaw Desta & Hafte Amsalu Kahsay & Basil Papadopoulos, 2021. "Mathematical Modeling and Analysis of Khat-Chewing Dynamics," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, February.
    6. Abayneh Kebede Fantaye & Zerihun Kinfe Birhanu, 2022. "Mathematical Model and Analysis of Corruption Dynamics with Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    7. Abayneh Kebede Fantaye & Qiankun Song, 2022. "Modelling and Stability Analysis of Cotton Leaf Curl Virus (CLCuV) Transmission Dynamics in Cotton Plant," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-12, August.
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