ON FRACTAL-FRACTIONAL WATERBORNE DISEASE MODEL: A STUDY ON THEORETICAL AND NUMERICAL ASPECTS OF SOLUTIONS VIA SIMULATIONS

Hasib Khan, Jehad Alzabut, Anwar Shah, Zai-Yin He, Sina Etemad, Shahram Rezapour and Akbar Zada
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Hasib Khan: Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia*Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan
Jehad Alzabut: Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia‡Department of Industrial Engineering, OSTIM Technical University, Ankara 06374, Turkey
Anwar Shah: �Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
Zai-Yin He: �Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China∥Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China
Sina Etemad: *Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Shahram Rezapour: *Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran††Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
Akbar Zada: ��‡Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-16

Abstract: Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution’s existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional integral form and study its qualitative analysis using an iterative convergent sequence and fixed-point technique to see whether there is a solution. We use Lagrange’s interpolation to construct numerical algorithms for the fractal-fractional waterborne disease model in terms of computations. The approach is then put to the test in a case study, yielding some interesting outcomes.

Keywords: Fractal-fractional Differential Operator; Waterborne Model; Existence of Solution; Stability; Numerical Simulations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400558

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