IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i9p1975-d1129871.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/9/1975/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/9/1975/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Zhong & Pang, Liuyong & Li, Qiuying, 2021. "Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. A. M. Elaiw & N. H. AlShamrani & E. Dahy & A. A. Abdellatif & Aeshah A. Raezah, 2023. "Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection," Mathematics, MDPI, vol. 11(3), pages 1-26, January.
    3. Khajanchi, Subhas, 2021. "The impact of immunotherapy on a glioma immune interaction model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Ahmed M. Elaiw & Aeshah A. Raezah & Matuka A. Alshaikh, 2023. "Global Dynamics of Viral Infection with Two Distinct Populations of Antibodies," Mathematics, MDPI, vol. 11(14), pages 1-26, July.
    5. Yousefpour, Amin & Jahanshahi, Hadi & Bekiros, Stelios, 2020. "Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. Ahmed Elaiw & Afnan Al Agha, 2020. "Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response," Mathematics, MDPI, vol. 8(4), pages 1-32, April.
    7. Deng, Shuning & Ji, Jinchen & Wen, Guilin & Xu, Huidong, 2021. "A comparative study of the dynamics of a three-disk dynamo system with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    8. Sardar, Mrinmoy & Biswas, Santosh & Khajanchi, Subhas, 2021. "The impact of distributed time delay in a tumor-immune interaction system," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Jing Li & Yuying Chen & Shaotao Zhu, 2022. "Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules," Mathematics, MDPI, vol. 10(11), pages 1-24, June.
    10. Han, Haoming & Zhang, Jing & Liu, Yan, 2023. "Stability analysis of hybrid high-order nonlinear multiple time-delayed coupled systems via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    11. Dalal Yahya Alzahrani & Fuaada Mohd Siam & Farah A. Abdullah, 2023. "Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives," Mathematics, MDPI, vol. 11(7), pages 1-21, April.
    12. Li, Jianquan & Xie, Xin & Chen, Yuming & Zhang, Dian, 2021. "Complex dynamics of a tumor-immune system with antigenicity," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    13. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:1975-:d:1129871. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.