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

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.