Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks
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.
Share and Cite
ISRP Style
M. A. El-Shorbagy, S. Tabussam, M. u. Rahman, Waseem, Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks, Journal of Mathematics and Computer Science, 36 (2025), no. 2, 185--206
AMA Style
El-Shorbagy M. A. , Tabussam S., Rahman M. u., Waseem, Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks. J Math Comput SCI-JM. (2025); 36(2):185--206
Chicago/Turabian Style
El-Shorbagy, M. A. , Tabussam, S., Rahman, M. u., Waseem,. "Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks." Journal of Mathematics and Computer Science, 36, no. 2 (2025): 185--206
Keywords
- Giardiasis duodenalis
- existence result
- fractal-fractional ABC operator
- deep neural network
- numerical results
MSC
References
-
[1]
T. Abdeljawad, D. Baleanu, Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels, Adv. Difference Equ., 2016 (2016), 18 pages
-
[2]
N. Ali, R. Khan, Existence of positive solution to a class of fractional differential equations with three point boundary conditions, Math. Sci. Lett., 5 (2016), 291–296
-
[3]
B. Ahmad, S. Sivasundaram, On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order, Appl. Math. Comput., 217 (2010), 480–487
-
[4]
A. Atangana, Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system, Chaos Solitons Fractals, 102 (2017), 396–406
-
[5]
A. Atangana, Modelling the spread of COVID-19 with new fractal-fractional operators: can the lockdown save mankind before vaccination?, Chaos Solitons Fractals, 136 (2020), 38 pages
-
[6]
A. Atangana, S. ˙I ˘gret Araz, Mathematical model of COVID-19 spread in Turkey and South Africa: theory, methods, and applications, Adv. Difference Equ., 200 (2020), 89 pages
-
[7]
˙I. Avcı, H. Lort, B. E. Tatlıcıo ˘ glu, Numerical investigation and deep learning approach for fractal-fractional order dynamics of Hopfield neural network model, Chaos Solitons Fractals, 177 (2023), 14 pages
-
[8]
Z. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal., 72 (2010), 916–924
-
[9]
S. R. Birkeland, S. P. Preheim, B. J. Davids, M. J. Cipriano, D. Palm, D. S. Reiner, S. G. Sv¨ard, F. D. Gillin, A. G. McArthur, Transcriptome analyses of the giardia lamblia life cycle, Mol. Biochem. Parasitol., 174 (2010), 62–65
-
[10]
R. T. Chen, Y. Rubanova, J. Bettencourt, D. K. Duvenaud, Neural ordinary differential equations, Adv. Neural Inf. Process. Syst., 31 (2018),
-
[11]
M. Di Giovanni, D. Sondak, P. Protopapas, M. Brambilla, Finding multiple solutions of odes with neural networks, In: Combining Artificial Intelligence and Machine Learning with Physical Sciences 2020, CEUR-WS, 2587 (2020), 1–7
-
[12]
S. Etemad, A. Shikongo, K. M. Owolabi, B. Tellab, ˙I. Avcı, S. Rezapour, R. P. Agarwal, A new fractal-fractional version of giving up smoking model: Application of lagrangian piece-wise interpolation along with asymptotical stability, Mathematics, 10 (2022), 1–31
-
[13]
C. L. Fischer Walker, M. J. Aryee, C. Boschi-Pinto, R. E. Black, Estimating diarrhea mortality among young children in low and middle income countries, PLOS ONE, 7 (2012), 1–7
-
[14]
W. Gao, H. M. Baskonus, L. Shi, New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system, Adv. Difference Equ., 2020 (2020), 11 pages
-
[15]
Deep learning, I. Goodfellow, Y. Bengio, A. Courville, MIT Press, Cambridge, MA (2016)
-
[16]
M. S. Hashemi, M. Inc, A. Yusuf, On three-dimensional variable order time fractional chaotic system with nonsingular kernel, Chaos Solitons Fractals, 133 (2020), 8 pages
-
[17]
R. Hilfer, Applications of fractional calculus in physics, World Scientific Publishing Co., River Edge, NJ (2000)
-
[18]
R. A. Khan, K. Shah, Existence and uniqueness of solutions to fractional order multi-point boundary value problems, Commun. Appl. Anal., 19 (2015), 515–525
-
[19]
V. Lakshmikantham, S. Leela, Nagumo-type uniqueness result for fractional differential equations, Nonlinear Anal., 71 (2009), 2886–2889
-
[20]
S. Lane, D. Lloyd, Current trends in research into the waterborne parasite giardia, Crit. Rev. Microbiol., 28 (2022), 123–147
-
[21]
Y. A. Liana, F. M. Chuma, Mathematical modeling of giardiasis transmission dynamics with control strategies in the presence of carriers, J. Appl. Math., 2023 (2023), 14 pages
-
[22]
T. Mahmood, M. ur Rahman, M. Arfan, S.-I. Kayani, M. Sun, Mathematical study of algae as a bio-fertilizer using fractal–fractional dynamic model, Math. Comput. Simulation, 203 (2023), 207–222
-
[23]
W. S. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys, 5 (1943), 115–133
-
[24]
S. C. Mpeshe, N. Nyerere, A human-animal model of giardiasis infection in contaminated environment, Int. J. Adv. Appl. Math. Mech., 8 (2021), 37–47
-
[25]
T. Nabil, Krasnoselskii N-tupled fixed point theorem with applications to fractional nonlinear dynamical system, Adv. Math. Phys., 2019 (2019), 9 pages
-
[26]
S. Osman, H. A. Togbenon, D. Otoo, Modelling the dynamics of campylobacteriosis using nonstandard finite difference approach with optimal control, Comput. Math. Methods Med., 2020 (2020), 12 pages
-
[27]
I. Podlubny, Fractional differential equations, mathematics in science and engineering, Academic Press, New York (1999)
-
[28]
H. Qu, M. Ur Rahman, M. Arfan, G. Laouini, A. Ahmadian, N. Senu, S. Salahshour, Investigating fractal-fractional mathematical model of Tuberculosis (TB) under fractal-fractional Caputo operator, Fractals, 30 (2022), 14 pages
-
[29]
S. Qureshi, A. Atangana, Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data, Chaos Solitons Fractals, 136 (2020), 14 pages
-
[30]
S. Qureshi, A. Yusuf, A. A. Shaikh, M. Inc, D. Baleanu, Mathematical modeling for adsorption process of dye removal nonlinear equation using power law and exponentially decaying kernels, Chaos, 30 (2020), 9 pages
-
[31]
H.-O. Rashid, R. K. Yadav, H.-R. Kim, H.-J. Chae, Er stress: Autophagy induction, inhibition and selection, Autophagy, 11 (2015), 1956–1977
-
[32]
S. Rezapour, J. K. K. Asamoah, S. Etemad, A. Akg¨ ul, ˙I. Avcı, S. M. El Din, On the fractal-fractional mittag-leffler model of a covid-19 and zika co-infection, Results Phys., 55 (2023), 1–21
-
[33]
S. Rezapour, S. Etemad, ˙I. Avcı, H. Ahmad, A. Hussain, A study on the fractal-fractional epidemic probability-based model of SARS-CoV-2 virus along with the Taylor operational matrix method for its Caputo version, J. Funct. Spaces, 2022 (2022), 33 pages
-
[34]
K. Shah, M. A. Alqudah, F. Jarad, T. Abdeljawad, Semi-analytical study of Pine Wilt disease model with convex rate under Caputo-Febrizio fractional order derivative, Chaos Solitons Fractals, 135 (2020), 9 pages
-
[35]
G. Spiga, M. Spiga, Two-dimensional transient solutions for crossflow heat exchangers with neither gas mixed, J. Heat Transfer., 109 (1987), 281–286
-
[36]
S. A. Squire, U. Ryan, Cryptosporidium and giardia in africa: current and future challenges, Parasites Vectors, 10 (2017), 1–32
-
[37]
A. Sulemana, T. A. Paget, E. L. Jarroll, Commitment to cyst formation in giardia, Microbiology, 160 (2014), 330–339
-
[38]
M. ur Rahman, Generalized fractal–fractional order problems under non-singular Mittag-Leffler kernel, Results Phys., 35 (2022), 15 pages
-
[39]
M. ur Rahman, A. Althobaiti, M. B. Riaz, F. S. Al-Duais, A theoretical and numerical study on fractional order biological models with caputo fabrizio derivative, Fractal Fract., 6 (2022), 1–15
-
[40]
A. Waldram, R. Vivancos, C. Hartley, K. Lamden, Prevalence of giardia infection in households of giardia cases and risk factors for household transmission, BMC Infect. Dis., 17 (2017), 1–7
-
[41]
World Health Organization, Organization, Global diffusion of eHealth: making universal health coverage achievable: report of the third global survey on eHealth, World Health Organization, (2017),
-
[42]
C. Yildiz, M. Heinonen, H. Lahdesmaki, ODE2VAE: Deep generative second order ODEs with Bayesian neural networks, Adv. Neural Inf. Process. Syst., 32 (2019),
-
[43]
Y.-Z. Zhang, A.-M. Yang, Y. Long, Initial boundary value problem for fractal heat equation in the semi-infinite region by yang-laplace transform, Therm. Sci., 18 (2014), 677–681