FRACTIONAL-ORDER MEASLES INFECTION MODEL WITH VACCINATION EFFECTS

Shaher Momani, R. P. Chauhan (), Sunil Kumar and Samir Hadid
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Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE2Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
R. P. Chauhan: Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
Sunil Kumar: Department of Mathematics, National Institute of Technology, Jamshedpur, Jamshedpur 831014, Jharkhand, India1Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Samir Hadid: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE5Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-32

Abstract: The purpose of this work is to investigate the dynamical behavior of a measles disease model adopting fractional and fractal–fractional operators with Mittag-Leffler kernel using two distinct numerical algorithms. First, we discuss the measles model in a fractional framework with Atangana–Baleanu–Caputo derivative and examine some fundamental mathematical assumptions of the considered model. We implement fixed-point theory to explore the existence and uniqueness of model solutions. Next, we apply the novel fractal–fractional concept with Atangana–Baleanu derivative to the measles model and reveal that the model has unique solution. We present the approximate results for the proposed models with graphical illustrations. The results are presented with various choices of fractal and fractional orders. The system behavior to various biological parameters is also investigated. In addition, we compare the considered operators using novel numerical schemes that take into account different ϱ values.

Keywords: Mittag-Leffler Kernel; Fractional and Fractal–Fractional Derivatives; Measles Model; Existence and Uniqueness; Numerical Results (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400947

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