Open Access

ARTICLE

A Neural Study of the Fractional Heroin Epidemic Model

by Wajaree Weera¹, Thongchai Botmart^1,*, Samina Zuhra², Zulqurnain Sabir³, Muhammad Asif Zahoor Raja⁴, Salem Ben Said⁵

1 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
2 Department of Computing and Engineering, Abasyn University Peshawar, Pakistan
3 Department of Mathematics and Statistics, Hazara University, Mansehra, 21120, Pakistan
4 Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan
5 Department of Mathematical Science College of Science United Arab Emirates University Al Ain, Abu Dhabi, UAE

* Corresponding Author: Thongchai Botmart. Email:

Computers, Materials & Continua 2023, 74(2), 4453-4467. https://doi.org/10.32604/cmc.2023.033232

Received 11 June 2022; Accepted 09 September 2022; Issue published 31 October 2022

Abstract

This works intends to provide numerical solutions based on the nonlinear fractional order derivatives of the classical White and Comiskey model (NFD-WCM). The fractional order derivatives have provided authentic and accurate solutions for the NDF-WCM. The solutions of the fractional NFD-WCM are provided using the stochastic computing supervised algorithm named Levenberg-Marquard Backpropagation (LMB) based on neural networks (NNs). This regression approach combines gradient descent and Gauss-Newton iterative methods, which means finding a solution through the sequences of different calculations. WCM is used to demonstrate the heroin epidemics. Heroin has been on-growth world wide, mainly in Asia, Europe, and the USA. It is the fourth foremost cause of death due to taking an overdose in the USA. The nonlinear mathematical system NFD-WCM discusses the overall circumstance of different drug users, such as suspected groups, drug users without treatment, and drug users with treatment. The numerical results of NFD-WCM via LMB-NNs have been substantiated through training, testing, and validation measures. The stability and accuracy are then checked through the statistical tool, such as mean square error (MSE), error histogram, and fitness curves. The suggested methodology’s strength is demonstrated by the high convergence between the reference solutions and the solutions generated by adding the efficacy of a constructed solver LMB-NNs, with accuracy levels ranging from 10⁻⁹ to 10⁻¹⁰.

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Keywords

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