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

• Published in: Physica A 2024-11, Vol.653, p.130090, Article 130090
• Main Author: He, Jilong
• Format: Article
• Language: English
• Subjects: HIV infection modeling; Iterative optimization; Numerical simulation; Special neural network; System of nonlinear differential equations; Trial function
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2024.130090

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. •We apply the differential equation transformation method for the first time to solve the HIV infection model of CD4(+) cells.•We construct an approximate solution structure that satisfies the initial conditions, eliminating the need to handle the initial conditions directly.•We transformed and solved the differential equation system.•We present numerical experiments and compare the results of different methods to validate the accuracy of our approach..