Open Access

ARTICLE

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

by Zeshan Faiz¹, Iftikhar Ahmed¹, Dumitru Baleanu^2,3,4, Shumaila Javeed^1,5,6,*

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:

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

Received 12 March 2023; Accepted 02 August 2023; Issue published 29 January 2024

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 (S_h), exposed humans (E_h), infectious humans (I_h), and recovered humans (R_h). 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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Keywords

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