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Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

Author

Listed:
  • Jorge E. Macías-Díaz

    (Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico)

  • Nauman Ahmed

    (Department of Mathematics and Statistics, University of the Lahore, Lahore 54590, Pakistan)

  • Muhammad Rafiq

    (Faculty of Engineering, University of Central Punjab, Lahore 54590, Pakistan)

Abstract

In this work, we numerically investigate a three-dimensional nonlinear reaction-diffusion susceptible-infected-recovered hepatitis B epidemic model. To that end, the stability and bifurcation analyses of the mathematical model are rigorously discussed using the Routh–Hurwitz condition. Numerically, an efficient structure-preserving nonstandard finite-difference time-splitting method is proposed to approximate the solutions of the hepatitis B model. The dynamical consistency of the splitting method is verified mathematically and graphically. Moreover, we perform a mathematical study of the stability of the proposed scheme. The properties of consistency, stability and convergence of our technique are thoroughly analyzed in this work. Some comparisons are provided against existing standard techniques in order to validate the efficacy of our scheme. Our computational results show a superior performance of the present approach when compared against existing methods available in the literature.

Suggested Citation

  • Jorge E. Macías-Díaz & Nauman Ahmed & Muhammad Rafiq, 2019. "Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1157-:d:292842
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    References listed on IDEAS

    as
    1. Xi-Lan Liu & Shuxia Pan, 2019. "Spreading Speed in A Nonmonotone Equation with Dispersal and Delay," Mathematics, MDPI, vol. 7(3), pages 1-9, March.
    2. Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    3. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    4. Tilahun, Getachew Teshome & Makinde, Oluwole Daniel & Malonza, David, 2018. "Co-dynamics of Pneumonia and Typhoid fever diseases with cost effective optimal control analysis," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 438-459.
    Full references (including those not matched with items on IDEAS)

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