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Dynamical Behavior of a Cancer Growth Model with Chemotherapy and Boosting of the Immune System

Author

Listed:
  • Shireen Jawad

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

  • Matthias Winter

    (Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, UK)

  • Zain-Aldeen S. A. Rahman

    (Department of Electrical Techniques, Technical Institute/Qurna, Southern Technical University, Basra 33511, Iraq)

  • Yasir I. A. Al-Yasir

    (Faculty of Engineering and Informatics, School of Electrical Engineering and Computer Science, University of Bradford, Bradford BD7 1DP, UK)

  • Anwar Zeb

    (Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan)

Abstract

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are examined. The equilibrium points’ asymptotic stability is analyzed using linear stability. Then, global stability and persistence are investigated using the Lyapunov strategy. The occurrence of bifurcations of the model, such as of trans-critical or Hopf type, is also explored. Numerical simulations are used to verify the theoretical analysis. The Runge–Kutta method of fourth order is used in the simulation of the model. The analytical study and simulation findings show that the immune system is boosted by regular vitamin consumption, inhibiting the growth of tumor cells. Further, the chemotherapy drug contributes to the control of tumor cell progression. Vitamin intake and chemotherapy are treated both individually and in combination, and in all situations, the minimal level required to eliminate the cancer is determined.

Suggested Citation

  • Shireen Jawad & Matthias Winter & Zain-Aldeen S. A. Rahman & Yasir I. A. Al-Yasir & Anwar Zeb, 2023. "Dynamical Behavior of a Cancer Growth Model with Chemotherapy and Boosting of the Immune System," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:406-:d:1033848
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    References listed on IDEAS

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    1. Yang, Huan & Tan, Yuanshun & Yang, Jin & Liu, Zijian, 2021. "Extinction and persistence of a tumor-immune model with white noise and pulsed comprehensive therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 456-470.
    2. Junyuan Yang & Xiaoyan Wang & Fengqin Zhang, 2008. "A Differential Equation Model of HIV Infection of CD T-Cells with Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-16, February.
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