Open Access

ARTICLE

Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

by Sakda Noinang¹, Zulqurnain Sabir², Muhammad Asif Zahoor Raja³, Soheil Salahshour⁴, Wajaree Weera^5,*, Thongchai Botmart⁵

1 Department of Mathematics Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani, 34190, Thailand
2 Department of Mathematics and Statistics, Hazara University, Mansehra, 21120, Pakistan
3 Future Technology Research Center, National Yunlin University of Science and Technology, Douliou, Yunlin, 64002, Taiwan
4 Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, 34494, Turkey
5 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

* Corresponding Author: Wajaree Weera. Email:

Computers, Materials & Continua 2023, 74(2), 2575-2588. https://doi.org/10.32604/cmc.2023.029046

Received 23 February 2022; Accepted 28 April 2022; Issue published 31 October 2022

Abstract

The current investigations are presented to solve the fractional order HBV differential infection system (FO-HBV-DIS) with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMBNNs. The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics, healthy hepatocytes (H), capsids (D), infected hepatocytes (I), free virus (V) and antibodies (W). The investigations for three different FO variants have been tested numerically to solve the nonlinear FO-HBV-DIS. The data magnitudes are implemented 75% for training, 10% for certification and 15% for testing to solve the FO-HBV-DIS with the response of antibody immune. The numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton approach. To authenticate the validity, competence, consistency, capability and exactness of the LMBNNs, the numerical presentations using the mean square error (MSE), error histograms (EHs), state transitions (STs), correlation and regression are accomplished.

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Keywords

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