A study on fractional tumor-immune interaction model related to lung cancer via generalized Laguerre polynomials

BMC Medical Research Methodology

Research

Samrad Mehrabi¹  Zakieh Avazzadeh²  Hossein Hassani³  Praveen Agarwal³  M. J. Ebadi⁴  Eskandar Naraghirad⁵  Mohammad Shafi Dahaghin⁶ 

[1] Department of Internal Medicine, Shiraz University of Medical Sciences, Shiraz, Iran;Department of Mathematical Sciences, University of South Africa, Florida, South Africa;Department of Mathematics, Anand International College of Engineering, 303012, Jaipur, India;Department of Mathematics, Chabahar Maritime University, Chabahar, Iran;Department of Mathematics, Yasouj University, Yasouj, Iran;Faculty of Mathematics, Shahrekord University, Shahrekord, Iran;

关键词: Fractional Tumor-Immune Interaction Model;    Tumor Cells;    Lung Cancer;    Generalized Laguerre Polynomials;    Macrophages Cells;    92C42;    41A58;    97M60;   

DOI  :  10.1186/s12874-023-02006-3

 received in 2022-10-30, accepted in 2023-08-02,  发布年份 2023

来源: Springer

【 摘 要 】

BackgroundCancer, a complex and deadly health concern today, is characterized by forming potentially malignant tumors or cancer cells. The dynamic interaction between these cells and their environment is crucial to the disease. Mathematical models can enhance our understanding of these interactions, helping us predict disease progression and treatment strategies.MethodsIn this study, we develop a fractional tumor-immune interaction model specifically for lung cancer (FTIIM-LC). We present some definitions and significant results related to the Caputo operator. We employ the generalized Laguerre polynomials (GLPs) method to find the optimal solution for the FTIIM-LC model. We then conduct a numerical simulation and compare the results of our method with other techniques and real-world data.ResultsWe propose a FTIIM-LC model in this paper. The approximate solution for the proposed model is derived using a series of expansions in a new set of polynomials, the GLPs. To streamline the process, we integrate Lagrange multipliers, GLPs, and operational matrices of fractional and ordinary derivatives. We conduct a numerical simulation to study the effects of varying fractional orders and achieve the expected theoretical results.ConclusionThe findings of this study demonstrate that the optimization methods used can effectively predict and analyze complex phenomena. This innovative approach can also be applied to other nonlinear differential equations, such as the fractional Klein–Gordon equation, fractional diffusion-wave equation, breast cancer model, and fractional optimal control problems.

【 授权许可】

CC BY   
© BioMed Central Ltd., part of Springer Nature 2023

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