Mathematical modeling for solving fractional model cancer bosom malignant growth
In this essay, we have presented a fractional numerical model of breast cancer stages with cardiac outcomes. Five compartments were used to build the model, each of which represented a subpopulation of breast cancer patients. Variables A, B, C, D, and E each represent a certain subpopulation. They a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Biophysics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/biophy.2023018?viewType=HTML |
| _version_ | 1797657807374254080 |
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| author | Shaimaa A. M. Abdelmohsen D. Sh. Mohamed Haifa A. Alyousef M. R. Gorji Amr M. S. Mahdy |
| author_facet | Shaimaa A. M. Abdelmohsen D. Sh. Mohamed Haifa A. Alyousef M. R. Gorji Amr M. S. Mahdy |
| author_sort | Shaimaa A. M. Abdelmohsen |
| collection | DOAJ |
| description | In this essay, we have presented a fractional numerical model of breast cancer stages with cardiac outcomes. Five compartments were used to build the model, each of which represented a subpopulation of breast cancer patients. Variables A, B, C, D, and E each represent a certain subpopulation. They are levels 1 and 2 (A), level 3 (B), level 4 (C), disease-free (D) and cardiotoxic (E). We have demonstrated that the fractional model has a stable solution. We also discuss how to optimally control this model and numerically simulate the control problem. Using numerical simulations, we computed the results of the dissection. The model's compartment diagram has been completed. A predictor-corrector method has been used to manage the fractional derivatives and produce numerical solutions. The Caputo sense has been used to describe fractional derivatives. The results have been illustrated through numerical simulations. Furthermore, the numerical simulations show that the cancer breast malignant growth fractional order model is easier to model than the traditional integer-order model. To compute the results, we have used mathematical programming. We have made it clear that the numerical method that was applied in this publication to solve this model was not utilized by any other author before that, nor has this method been investigated in the past. Our investigation established this approach. |
| first_indexed | 2024-03-11T17:50:03Z |
| format | Article |
| id | doaj.art-6a7d3d8e053147068e025081f6e15672 |
| institution | Directory Open Access Journal |
| issn | 2377-9098 |
| language | English |
| last_indexed | 2024-03-11T17:50:03Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Biophysics |
| spelling | doaj.art-6a7d3d8e053147068e025081f6e156722023-10-18T06:36:12ZengAIMS PressAIMS Biophysics2377-90982023-09-0110326328010.3934/biophy.2023018Mathematical modeling for solving fractional model cancer bosom malignant growthShaimaa A. M. Abdelmohsen0 D. Sh. Mohamed 1Haifa A. Alyousef2M. R. Gorji3Amr M. S. Mahdy41. Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt1. Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia3. Faculty of Medicine and Health Sciences, Ghent University, Ghent 9000, Belgium2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt4. Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this essay, we have presented a fractional numerical model of breast cancer stages with cardiac outcomes. Five compartments were used to build the model, each of which represented a subpopulation of breast cancer patients. Variables A, B, C, D, and E each represent a certain subpopulation. They are levels 1 and 2 (A), level 3 (B), level 4 (C), disease-free (D) and cardiotoxic (E). We have demonstrated that the fractional model has a stable solution. We also discuss how to optimally control this model and numerically simulate the control problem. Using numerical simulations, we computed the results of the dissection. The model's compartment diagram has been completed. A predictor-corrector method has been used to manage the fractional derivatives and produce numerical solutions. The Caputo sense has been used to describe fractional derivatives. The results have been illustrated through numerical simulations. Furthermore, the numerical simulations show that the cancer breast malignant growth fractional order model is easier to model than the traditional integer-order model. To compute the results, we have used mathematical programming. We have made it clear that the numerical method that was applied in this publication to solve this model was not utilized by any other author before that, nor has this method been investigated in the past. Our investigation established this approach.https://www.aimspress.com/article/doi/10.3934/biophy.2023018?viewType=HTMLcancer bosom malignant growthcaputo sensegraph of a signaloptimal controlpredictor-corrector method |
| spellingShingle | Shaimaa A. M. Abdelmohsen D. Sh. Mohamed Haifa A. Alyousef M. R. Gorji Amr M. S. Mahdy Mathematical modeling for solving fractional model cancer bosom malignant growth AIMS Biophysics cancer bosom malignant growth caputo sense graph of a signal optimal control predictor-corrector method |
| title | Mathematical modeling for solving fractional model cancer bosom malignant growth |
| title_full | Mathematical modeling for solving fractional model cancer bosom malignant growth |
| title_fullStr | Mathematical modeling for solving fractional model cancer bosom malignant growth |
| title_full_unstemmed | Mathematical modeling for solving fractional model cancer bosom malignant growth |
| title_short | Mathematical modeling for solving fractional model cancer bosom malignant growth |
| title_sort | mathematical modeling for solving fractional model cancer bosom malignant growth |
| topic | cancer bosom malignant growth caputo sense graph of a signal optimal control predictor-corrector method |
| url | https://www.aimspress.com/article/doi/10.3934/biophy.2023018?viewType=HTML |
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