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

Suganya Subramanian, Agilan Kumaran, Srilekha Ravichandran, Parthiban Venugopal (), Slim Dhahri () and Kavikumar Ramasamy ()
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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

Mathematics, 2024, vol. 12, issue 3, 1-12

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.

Keywords: susceptible-infectious-removed dynamics; fractional-order model; fuzzy systems; Caputo derivative; existence and uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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