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Research Article | Open Access

Existence theory and numerical solution of leptospirosis disease model via exponential decay law

Amir Khan1,5, Abdur Raouf1, Rahat Zarin2, Abdullahi Yusuf3,4, Usa Wannasingha Humphries5( )
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
Department of Basic Sciences, University of Engineering and Technology Peshawar, Khyber Pakhtunkhwa, Pakistan
Department of Computer Engineering, Biruni University, Istanbul, Turkey
Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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Abstract

We investigated the leptospirosis epidemic model by using Caputo and Fabrizio fractional derivatives. Picard's successive iterative method and Sumudu transform are taken into consideration for developing the iterative solutions for the leptospirosis disease. Employing nonlinear functional analysis, the stability and uniqueness of the proposed model are established. Sensitivity analysis is taken into account to highlight the most sensitive parameters corresponding to the basic reproductive number. Various solutions to the proposed system have been interpolated by graphs with the application of Matlab software.

Keywords

mathematical modelexponential decay lawSumudu transformexistence and uniqueness
CLC number: 92B05, 37G05, 37G15, 39A28

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8822-8846
DOI: 10.3934/math.2022492

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Cite this article:
Khan A, Raouf A, Zarin R, et al. Existence theory and numerical solution of leptospirosis disease model via exponential decay law. AIMS Mathematics, 2022, 7(5): 8822-8846. https://doi.org/10.3934/math.2022492

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Received: 26 November 2021
Revised: 23 January 2022
Accepted: 28 January 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)