Giardiasis transmission dynamics‎: ‎insights from fractal-fractional modeling and deep neural networks

Volume 36, Issue 2, pp 185--206 https://dx.doi.org/10.22436/jmcs.036.02.04

Publication Date: July 15, 2024 Submission Date: February 20, 2024 Revision Date: May 14, 2024 Accteptance Date: May 29, 2024

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Authors

M‎. ‎A‎. ‎ El-Shorbagy - Department of Mathematics‎, ‎College of Science and Humanities in Al-Kharj, ‎Prince Sattam bin Abdulaziz University, ‎Al-Kharj 11942, Saudi Arabia. - Department of Basic Engineering Science‎, ‎Faculty of Engineering, ‎Menoufia University, ‎Shebin El-Kom 32511, ‎Egypt. S. Tabussam - Department of Applied Sciences‎, National Textile University‎, Faisalabad 37610, Pakistan. M. u. Rahman - School of Mathematical Sciences‎, ‎Jiangsu University, Zhenjiang 212013, Jiangsu, P.R‎. ‎China. - Department of computer science and mathematics‎ , Lebanese American University, Beirut, ‎Lebanon. Waseem - School of Mechnical Engineering‎, Jiangsu University‎, ‎Zhenjiang 212013, Jiangsu, ‎P.R‎. ‎China.

Abstract

‎The World Health Organization highlights Giardias as a neglected zoonotic disease caused by Giardia duodenalis‎. ‎The disease often goes overlooked despite the significant harm it causes humans and animals‎. ‎We present a mathematical model for transmitting Giardiasis incorporating various preventative measures‎, ‎including screening‎, ‎treatment‎, ‎and environmental sanitation‎. ‎Among the factors influencing Giardiasis transmission within a community is the interaction parameter between humans and the environment‎. ‎In this manuscript‎, ‎Atangana-Baleanu Caputo (ABC) derivatives of fractional order \(v\) and fractal dimension \(q\) are utilized to explore a modified model with a fractal-fractional approach‎. ‎The study qualitatively analyses the model using functional non-linearity and population-based fixed-point theory‎. ‎The fractional Adams-Bashforth iterative method is used to obtain numerical solutions‎. ‎Ulam-Hyers (UH) stability techniques are used to analyze stability in this study‎. ‎A comparison is made between simulation results for all compartments and Giardia duodenalis data already available‎. ‎To manage Giardiasis duodenalis effectively‎, ‎societal behavioral changes and adherence to preventive measures are essential to controlling the effective transmission rate‎. ‎Additionally‎, ‎a deep neural network (DNN) approach is used to analyze the given disease condition with excellent accuracy in training‎, ‎testing‎, ‎and validation data‎.

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Keywords

• Giardiasis duodenalis
• existence result‎
• fractal-fractional ABC operator‎
• deep neural network
• numerical results

MSC

•  34K37
•  92D30
•  65L05
•  34A08

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