Mathematical modeling for solving fractional model cancer bosom malignant growth

Shaimaa A. M. Abdelmohsen; D. Sh. Mohamed; Haifa A. Alyousef; M. R. Gorji; Amr M. S. Mahdy; Shaimaa A. M. Abdelmohsen; D. Sh. Mohamed; Haifa A. Alyousef; M. R. Gorji; Amr M. S. Mahdy

doi:10.3934/biophy.2023018

AIMS Biophysics

2023, Volume 10, Issue 3: 263-280. doi: 10.3934/biophy.2023018

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Mathematical modeling for solving fractional model cancer bosom malignant growth

1.
Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
3.
Faculty of Medicine and Health Sciences, Ghent University, Ghent 9000, Belgium
4.
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 29 June 2023 Revised: 25 August 2023 Accepted: 03 September 2023 Published: 15 September 2023

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.
- Cancer bosom malignant growth,
- Caputo sense,
- graph of a signal,
- optimal control,
- predictor-corrector method
Citation: 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[J]. AIMS Biophysics, 2023, 10(3): 263-280. doi: 10.3934/biophy.2023018

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Abstract

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.

Acknowledgments

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number WE-44-0043.

Fundings

The authors state that there are no competing interests.

Author contributions

For the lettering of this paper, all authors evenly shared, also read, and agree on the firm copy of the manuscript.

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