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A New ODE-Based Model for Tumor Cells and Immune System Competition

Author

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  • Sana Abdulkream Alharbi

    (Department of Mathematics & Statistics, College of Science, Taibah University, Yanbu 41911, Almadinah Almunawarah, Saudi Arabia)

  • Azmin Sham Rambely

    (Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia)

Abstract

Changes in diet are heavily associated with high mortality rates in several types of cancer. In this paper, a new mathematical model of tumor cells growth is established to dynamically demonstrate the effects of abnormal cell progression on the cells affected by the tumor in terms of the immune system’s functionality and normal cells’ dynamic growth. This model is called the normal-tumor-immune-unhealthy diet model (NTIUNHDM) and governed by a system of ordinary differential equations. In the NTIUNHDM, there are three main populations normal cells, tumor cell and immune cells. The model is discussed analytically and numerically by utilizing a fourth-order Runge–Kutta method. The dynamic behavior of the NTIUNHDM is discussed by analyzing the stability of the system at various equilibrium points and the Mathematica software is used to simulate the model. From analysis and simulation of the NTIUNHDM, it can be deduced that instability of the response stage, due to a weak immune system, is classified as one of the main reasons for the coexistence of abnormal cells and normal cells. Additionally, it is obvious that the NTIUNHDM has only one stable case when abnormal cells begin progressing into early stages of tumor cells such that the immune cells are generated once. Thus, early boosting of the immune system might contribute to reducing the risk of cancer.

Suggested Citation

  • Sana Abdulkream Alharbi & Azmin Sham Rambely, 2020. "A New ODE-Based Model for Tumor Cells and Immune System Competition," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1285-:d:394216
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    References listed on IDEAS

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    1. Masurel, Léon & Bianca, Carlo & Lemarchand, Annie, 2018. "On the learning control effects in the cancer-immune system competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 462-475.
    2. Mingliang Zheng, 2020. "Quantitative Analysis for the Spread Range of Malignant Tumor Based on Lie Symmetry," Complexity, Hindawi, vol. 2020, pages 1-6, April.
    3. Witten, Matthew, 1982. "Modeling cellular agign and tumorigenic transformation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(6), pages 572-584.
    4. Carlo Bianca & Caterina Mogno, 2018. "Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 24(2), pages 207-235, March.
    5. Adam E. Glick & Antonio Mastroberardino, 2017. "An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors," Mathematics, MDPI, vol. 5(4), pages 1-14, October.
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    Cited by:

    1. Kaushik Dehingia & Ahmed A. Mohsen & Sana Abdulkream Alharbi & Reima Daher Alsemiry & Shahram Rezapour, 2022. "Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    2. Dehingia, Kaushik & Das, Parthasakha & Upadhyay, Ranjit Kumar & Misra, Arvind Kumar & Rihan, Fathalla A. & Hosseini, Kamyar, 2023. "Modelling and analysis of delayed tumour–immune system with hunting T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 669-684.

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