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Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy

Author

Listed:
  • Ebraheem Alzahrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • M. M. El-Dessoky

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Muhammad Altaf Khan

    (Institute for Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa)

Abstract

In the present study, we formulate a mathematical model to understand breast cancer in the population of Saudi Arabia. We consider a mathematical model and study its mathematical results. We show that the breast cancer model possesses a unique system of solutions. The stability results are shown for the model. We consider the reported cases in Saudi Arabia for the period 2004–2016. The data are given for the female population in Saudi Arabia that is suffering from breast cancer. The data are used to obtain the values of the parameters, and then we predict the long-term behavior with the obtained numerical results. The numerical results are obtained using the proposed parameterized approach. We present graphical results for the breast cancer model under effective parameters such as τ 1 , τ 2 , and τ 3 that cause decreasing future cases in the population of stages 3 and 4, and the disease-free condition. Chemotherapy generally increases the risk of cardiotoxicity, and, hence, our model result shows this fact. The combination of chemotherapy stages 3 and 4 and the parameters τ 1 and τ 2 together at a low-level rate and also treating the patients before the chemotherapy will decrease the population of cardiotoxicity. The findings of this study are intended to reduce the number of cardiotoxic patients and raise the number of patients who recover following chemotherapy, which will aid in public health decision making.

Suggested Citation

  • Ebraheem Alzahrani & M. M. El-Dessoky & Muhammad Altaf Khan, 2023. "Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy," Mathematics, MDPI, vol. 11(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:1975-:d:1129871
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    References listed on IDEAS

    as
    1. A. M. Elaiw & E. Kh. Elnahary, 2019. "Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays," Mathematics, MDPI, vol. 7(2), pages 1-35, February.
    2. Liu, Zijian & Yang, Chenxue, 2016. "A mathematical model of cancer treatment by radiotherapy followed by chemotherapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 1-15.
    3. Fidele Hategekimana & Snehanshu Saha & Anita Chaturvedi, 2017. "Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis," Mathematics, MDPI, vol. 5(4), pages 1-23, November.
    4. Khajanchi, Subhas & Nieto, Juan J., 2019. "Mathematical modeling of tumor-immune competitive system, considering the role of time delay," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 180-205.
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