https://doi.org/10.1140/epjp/s13360-025-06940-7
Regular Article
Solutions of the fractional-order HIV infection system of T-cells by exploiting a radial basis neural network procedure
1
Department of Mathematics, Firat University, Elazig, Turkey
2
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3
Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
4
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
a
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Received:
10
September
2025
Accepted:
6
October
2025
Published online:
21
October
2025
Abstract
Motivation: The present research is investigating the numerical performances of the fractional-order nonlinear model of the human immunodeficiency virus (HIV) infection system of T-cells or CD4+ T-cells by implementing a computational stochastic scheme. The mathematical fractional-order HIV model is presented in concentration of susceptible cells, septic T-cells-based HIV, and free HIV virus elements in the blood. Method: The structure of the solver is designed by the Levenberg–Marquardt backpropagation neural network (LMBNN), activation radial basis (RB) function in the single hidden layer with fifteen number of neurons. A reference data are obtained through the improved Euler method, which is tested through the proposed solver by taking the statistics 80% for training, 10% for testing, and 10% for authentication. Results: The approximate outcomes obtained through the designed solver are compared with the reference outcomes, which perform the correctness of the scheme. Moreover, the negligible absolute error measures together with different tests including state transition, error histogram, and correlation validate the correctness of the proposed procedure. Novelty: The designed neural network process using the LMBNN together with the RB activation function has never been implemented before to present the results of the fractional-order HIV model.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
