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A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network

Zeshan Faiz1, Iftikhar Ahmed1, Dumitru Baleanu2,3,4, Shumaila Javeed1,5,6,*

1 Department of Mathematics, COMSATS University Islamabad, Islamabad, 45550, Pakistan
2 Department of Mathematics, Cankaya University, Ankara, 06790, Turkey
3 Institute of Space Sciences, Magurele-Bucharest, 077125, Romania
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
5 Department of Computer Science and Mathematics, Lebanese American University, Beirut, 135053, Lebanon
6 Department of Mathematics, Mathematics Research Center, Near East University, Nicosia/Mersin, 99138, Turkey

* Corresponding Author: Shumaila Javeed. Email: email

Computer Modeling in Engineering & Sciences 2024, 139(2), 1217-1238. https://doi.org/10.32604/cmes.2023.029879

Abstract

The purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model (FDTM) in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network (LM-NN) technique. The fractional dengue transmission model (FDTM) consists of 12 compartments. The human population is divided into four compartments; susceptible humans (Sh), exposed humans (Eh), infectious humans (Ih), and recovered humans (Rh). Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments: aquatic (eggs, larvae, pupae), susceptible, exposed, and infectious. We investigated three different cases of vertical transmission probability (η), namely when Wolbachia-free mosquitoes persist only (η = 0.6), when both types of mosquitoes persist (η = 0.8), and when Wolbachia-carrying mosquitoes persist only (η = 1). The objective of this study is to investigate the effectiveness ofWolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives (α = 0.4, 0.6, 0.8). LM-NN approach includes a training, validation, and testing procedure to minimize the mean square error (MSE) values using the reference dataset (obtained by solving the model using the Adams-Bashforth-Moulton method (ABM). The distribution of data is 80% data for training, 10% for validation, and, 10% for testing purpose) results. A comprehensive investigation is accessible to observe the competence, precision, capacity, and efficiency of the suggested LM-NN approach by executing the MSE, state transitions findings, and regression analysis. The effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures, which achieves a precision of up to 10−4.

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Faiz, Z., Ahmed, I., Baleanu, D., Javeed, S. (2024). A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network. CMES-Computer Modeling in Engineering & Sciences, 139(2), 1217–1238.



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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