COMPUTATIONAL STUDY OF FRACTIONAL-ORDER VECTOR BORNE DISEASES MODEL

Pallavi Bedi (), Aziz Khan (), Anoop Kumar and Thabet Abdeljawad
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Pallavi Bedi: Department of Mathematics and Statistics, Central University of Punjab, Bathinda 151001, Punjab, India
Aziz Khan: ��Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
Anoop Kumar: Department of Mathematics and Statistics, Central University of Punjab, Bathinda 151001, Punjab, India
Thabet Abdeljawad: ��Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia‡Department of Medical Research, China Medical University, 40402 Taichung, Taiwan

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-12

Abstract: In this paper, we solve a nonlinear fractional-order model for analyzing the dynamical behavior of vector-borne diseases within the frame of Caputo-fractional derivative. The proposed mathematical model advances the existing integer-order model on transmission and cure of vector-borne diseases. The existence and uniqueness of the solutions of the fractional-order model are proved using the Banach contraction principle. We investigate the local asymptomatic stability for the obtained disease-free equilibrium point and global stability for the proposed model in the sense of Ulam–Hyers stability criteria, respectively. Besides that, we obtain a numerical solution for the projected model using the Corrector-Predictor algorithm. Finally, to illustrate the obtained theoretical results, we perform numerical simulations for different values of fractional-order derivative and make a comparison with the results of the integer-order derivative.

Keywords: Vector-Borne Diseases; Caputo-Fractional Derivative; Basic Reproduction Number; Fixed Point Technique; Ulam–Hyers Stability (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401491

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