The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease

被引:22
|
作者
Rehman, Muhammad Abaid Ur [1 ]
Ahmad, Jamshad [1 ]
Hassan, Ali [1 ]
Awrejcewicz, Jan [2 ]
Pawlowski, Witold [3 ]
Karamti, Hanen [4 ]
Alharbi, Fahad M. [5 ]
机构
[1] Univ Gujrat, Dept Math, Gujrat 50700, Pakistan
[2] Lodz Univ Technol, Dept Automat Biomech & Mechatron, PL-90924 Lodz, Poland
[3] Lodz Univ Technol, Inst Machine Tools & Prod Engn, PL-90924 Lodz, Poland
[4] Princess Nourah bint Abdulrahman Univ, Coll Comp & Informat Sci, Dept Comp Sci, POB 84428, Riyadh 11671, Saudi Arabia
[5] Umm Al Qura Univ, Al Qunfudah Univ Coll, Dept Math, Mecca 24382, Saudi Arabia
来源
SYMMETRY-BASEL | 2022年 / 14卷 / 08期
关键词
cancer tumor models; Caputo-fractional time derivative; nonlinear PDEs; chemotherapy drugs; tumor cells; immune cells; normal cells; reduced differential transform method (RDTM); series form solutions; DIFFERENTIAL-EQUATIONS; GROWTH; SYSTEM; CELLS;
D O I
10.3390/sym14081694
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
This article explores the application of the reduced differential transform method (RDTM) for the computational solutions of two fractional-order cancer tumor models in the Caputo sense: the model based on cancer chemotherapeutic effects which explain the relation between chemotherapeutic drugs, tumor cells, normal cells, and immune cells using a fractional partial differential equations, and the model that describes the different cases of killing rate K of cancer cells (the killing percentage of cancer cells K (I) is dependent on the number of cells, (II) is a function of time only, and (III) is a function of space only). The solutions are presented using Mathematica software as a convergent power series with elegantly computed terms using the suggested technique. The proposed method gives new series form results for various values of gamma. To clarify the complexity of the models, we plot the two- and three-dimensional and contour graphics of the obtained solutions at varied values of fractional-order gamma and the selected system parameters. The solutions are analyzed with fractional and reduced differential transform methods to obtain an idea of invariance regarding the computed solution of the designed mathematical model. The obtained results demonstrate the efficiency and preciseness of the proposed method to achieve a better understanding of chemotherapy effects. It is observed that chemotherapy drugs boost immunity against the specific cancer by decreasing the number of tumor cells, and the killing rate K of cancerous cells depend on the cells concentration.
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页数:28
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