A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer
Abstract The main objective of this work is to study the mathematical model that combines stem cell therapy and chemotherapy for cancer cells. We study the model using the fractal fractional derivative with the Mittag-Leffler kernel. In the analytical part, we study the existence of the solution and...
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| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-87308-w |
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| author | Esam Y. Salah Bhausaheb Sontakke Ahmed A. Hamoud Homan. Emadifar Atul Kumar |
| author_facet | Esam Y. Salah Bhausaheb Sontakke Ahmed A. Hamoud Homan. Emadifar Atul Kumar |
| author_sort | Esam Y. Salah |
| collection | DOAJ |
| description | Abstract The main objective of this work is to study the mathematical model that combines stem cell therapy and chemotherapy for cancer cells. We study the model using the fractal fractional derivative with the Mittag-Leffler kernel. In the analytical part, we study the existence of the solution and its uniqueness, which was studied based on the fixed point theory. The equilibrium points were also studied and discussed after stem cell therapy, and the approximate solutions for the given model were obtained using the Adam Bashford method, which depends on interpolation with Lagrange polynomials. Finally, the model was simulated using the Mathematica software, and through the figures, we found that the components of the model approach the equilibrium point, which indicates the stability of the model at the equilibrium point. Also, the result of the numerical simulation and graphic for the concentration of cells over time indicate the effects of the therapies on the decay rate of tumor cells and the growth rate of effector cells to modify the cancer patient’s immune system. It is worth noting that we simulated all the model components with different fractional orders, confirming the effect of stem cell therapy and chemotherapy on the cells and the decay of cancer cells. |
| format | Article |
| id | doaj-art-c590b8b38190489686dce9947ee4e45e |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-c590b8b38190489686dce9947ee4e45e2025-02-02T12:18:24ZengNature PortfolioScientific Reports2045-23222025-01-0115111610.1038/s41598-025-87308-wA fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancerEsam Y. Salah0Bhausaheb Sontakke1Ahmed A. Hamoud2Homan. Emadifar3Atul Kumar4Department of Mathematics, Pratishthan College, Dr. Babasaheb Ambedkar Marathwada UniversityDepartment of Mathematics, Pratishthan College, Dr. Babasaheb Ambedkar Marathwada UniversityDepartment of Mathematics, Taiz UniversityDepartment of Mathematics, Hamedan Branch, Islamic Azad UniversityDepartment of Mathematics, Dayalbagh Educational InstituteAbstract The main objective of this work is to study the mathematical model that combines stem cell therapy and chemotherapy for cancer cells. We study the model using the fractal fractional derivative with the Mittag-Leffler kernel. In the analytical part, we study the existence of the solution and its uniqueness, which was studied based on the fixed point theory. The equilibrium points were also studied and discussed after stem cell therapy, and the approximate solutions for the given model were obtained using the Adam Bashford method, which depends on interpolation with Lagrange polynomials. Finally, the model was simulated using the Mathematica software, and through the figures, we found that the components of the model approach the equilibrium point, which indicates the stability of the model at the equilibrium point. Also, the result of the numerical simulation and graphic for the concentration of cells over time indicate the effects of the therapies on the decay rate of tumor cells and the growth rate of effector cells to modify the cancer patient’s immune system. It is worth noting that we simulated all the model components with different fractional orders, confirming the effect of stem cell therapy and chemotherapy on the cells and the decay of cancer cells.https://doi.org/10.1038/s41598-025-87308-wMathematical modelFractional derivativeMatignon criterionAdams-Bashforth method |
| spellingShingle | Esam Y. Salah Bhausaheb Sontakke Ahmed A. Hamoud Homan. Emadifar Atul Kumar A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer Scientific Reports Mathematical model Fractional derivative Matignon criterion Adams-Bashforth method |
| title | A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer |
| title_full | A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer |
| title_fullStr | A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer |
| title_full_unstemmed | A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer |
| title_short | A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer |
| title_sort | fractal fractional order modeling approach to understanding stem cell chemotherapy combinations for cancer |
| topic | Mathematical model Fractional derivative Matignon criterion Adams-Bashforth method |
| url | https://doi.org/10.1038/s41598-025-87308-w |
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