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A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases

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  • Mohamed M. Mousa

    (Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia
    Department of Basic Engineering Sciences, Faculty of Engineering at Benha, Benha University, Benha 13512, Egypt)

  • Fahad Alsharari

    (Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia
    Department of Mathematics, College of Science and Arts, Jouf University, Gurayat 77455, Saudi Arabia)

Abstract

The objective of this work is to examine the dynamics of a fractional-order susceptible-infectious-recovered (SIR) model that simulate epidemiological diseases such as childhood diseases. An effective numerical scheme based on Grünwald–Letnikov fractional derivative is suggested to solve the considered model. A stability analysis is performed to qualitatively examine the dynamics of the SIR model. The reliability and robustness of the proposed scheme is demonstrated by comparing obtained results with results obtained from a fourth order Runge–Kutta built-in Maple syntax when considering derivatives of integer order. Graphical illustrations of the numerical results are given. The inaccuracy of some results presented in two studies exist in the literature have been clearly explained. Generalizing of the cases examined in another study, by considering a model with fraction-order derivatives, is another objective of this work as well.

Suggested Citation

  • Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2847-:d:675794
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    References listed on IDEAS

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    1. Amira Rachah & Delfim F. M. Torres, 2015. "Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-9, May.
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    4. Hamed Al-Sulami & Moustafa El-Shahed & Juan J. Nieto & Wafa Shammakh, 2014. "On Fractional Order Dengue Epidemic Model," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, August.
    5. Okuonghae, D. & Omame, A., 2020. "Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Fazal Haq & Muhammad Shahzad & Shakoor Muhammad & Hafiz Abdul Wahab & Ghaus ur Rahman, 2017. "Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, December.
    7. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Silva, Cristiana J. & Torres, Delfim F.M., 2021. "Fractional model of COVID-19 applied to Galicia, Spain and Portugal," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    1. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.

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