Open Access

ARTICLE

Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

by Ghaliah Alhamzi¹, Badr Saad T. Alkahtani², Ravi Shanker Dubey³, Mati ur Rahman^4,5,*

1 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 13318, Saudi Arabia
2 Department of Mathematics, College of Science, King Saud University, Riyadh, 11989, Saudi Arabia
3 Department of Mathematics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur, 302002, India
4 School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, China
5 Department of Computer Science and Mathematics, Lebanese American University, Beirut, 13-5053, Lebanon

* Corresponding Author: Mati ur Rahman. Email:

(This article belongs to the Special Issue: Innovative Applications of Fractional Modeling and AI for Real-World Problems)

Computer Modeling in Engineering & Sciences 2025, 142(1), 609-633. https://doi.org/10.32604/cmes.2024.056604

Received 25 July 2024; Accepted 17 October 2024; Issue published 17 December 2024

Abstract

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu (AB) derivatives having arbitrary order. The HIV infection model has a susceptible class, a recovered class, along with a case of infection divided into three sub-different levels or categories and the recovered class. The total time interval is converted into two, which are further investigated for ordinary and fractional order operators of the AB derivative, respectively. The proposed model is tested separately for unique solutions and existence on bi intervals. The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial. The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law. The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease. This study uses the neural network (NN) technique to obtain a better set of weights with low residual errors, and the epochs number is considered 1000. The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

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Keywords

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