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A new high-precision numerical method for solving the HIV infection model of CD4(+) cells

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  • He, Jilong

Abstract

This paper proposes a new method called the “Special Neural Network” to solve the HIV infection model of CD4(+) cells using a novel approximation approach. Unlike traditional methods that involve constructing loss functions and performing inverse matrix operations, our method discretizes the differential equations at configuration points, combines them, and transforms the system into a set of nonlinear equations. Parameters in the neural network are then iteratively solved using optimization to obtain an approximate solution. Additionally, when using the neural network as an approximate solution to the differential equations, we provide a form that satisfies the initial conditions through construction, eliminating the need to handle initial conditions during the solving process and thus streamlining the method. Finally, by comparing with other numerical methods using two sets of models and parameters, the Special Neural Network achieves high precision results and further demonstrates the advantages of our approach.

Suggested Citation

  • He, Jilong, 2024. "A new high-precision numerical method for solving the HIV infection model of CD4(+) cells," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 653(C).
  • Handle: RePEc:eee:phsmap:v:653:y:2024:i:c:s0378437124005995
    DOI: 10.1016/j.physa.2024.130090
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    References listed on IDEAS

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    1. Beler, Ayşe & Özaltun Şimşek, Gökçe & Gümgüm, Sevin, 2023. "Numerical solutions of the HIV infection model of CD4(+) cells by Laguerre wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 205-219.
    2. Umar, Muhammad & Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Aguilar, J.F. Gómez & Amin, Fazli & Shoaib, Muhammad, 2021. "Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 241-253.
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