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Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases

Author

Listed:
  • Suganya Subramanian

    (Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600 127, India)

  • Agilan Kumaran

    (Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600 127, India)

  • Srilekha Ravichandran

    (Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600 127, India)

  • Parthiban Venugopal

    (Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600 127, India)

  • Slim Dhahri

    (Department of Computer Engineering and Networks, College of Computer and Information Sciences, Jouf University, Sakaka 72388, Saudi Arabia)

  • Kavikumar Ramasamy

    (School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea)

Abstract

In this work, the susceptible-infectious-removed (SIR) dynamics are considered in relation to the effects on the health system. With the help of the Caputo derivative fractional-order method, the SIR epidemic model for childhood diseases is designed. Subsequenly, a set of sufficient conditions ensuring the existence and uniqueness of the addressed model by choosing proper fuzzy approximation methods. In particular, the fuzzy Laplace method along with the Adomian decomposition transform were employed to better understand the dynamical structures of childhood diseases. This leads to the development of an efficient methodology for solving fuzzy fractional differential equations using Laplace transforms and their inverses, specifically with the Caputo sense derivative. This innovative approach facilitates the numerical resolution of the problem and numerical simulations are executed for considering parameter values.

Suggested Citation

  • Suganya Subramanian & Agilan Kumaran & Srilekha Ravichandran & Parthiban Venugopal & Slim Dhahri & Kavikumar Ramasamy, 2024. "Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases," Mathematics, MDPI, vol. 12(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:466-:d:1330781
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    References listed on IDEAS

    as
    1. 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.
    2. Gao, Wei & Veeresha, P. & Prakasha, D.G. & Baskonus, Haci Mehmet & Yel, Gulnur, 2020. "New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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