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Alharbi2020 - An ODE-based model of the dynamics of tumor cell progression and its effects on normal cell growth and immune system functionality

ABSTRACT: This ordinary differential equation model of tumor cell growth, called the normal-tumor-immune-unhealthy diet model (NTIUNHDM), is described by the publication: Alharbi, S.A.; Rambely, A.S. "A New ODE-Based Model for Tumor Cells and Immune System Competition" Mathematics 2020, 8, 1285. doi:10.3390/math8081285 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.

DISEASE(S): Cancer

SUBMITTER: Emilia Chen

PROVIDER: BIOMD0000001023 | BioModels | 2021-07-29

REPOSITORIES: BioModels

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Project description:This ordinary differential equation model of the interactions between tumor and normal cells is based on the publication: S. A. Alharbi and A. S. Rambely, "Dynamic Simulation for Analyzing the Effects of the Intervention of Vitamins on Delaying the Growth of Tumor Cells," in IEEE Access, vol. 7, pp. 128816-128827, 2019 doi: 10.1109/ACCESS.2019.2940060. Comment: This TNM model is described by the system of equations presented in (2), in the publication manuscript. Abstract: The natural sources of the vitamins, which come from a balanced diet (as recommended by the World Cancer Research Fund and the American Institute for Cancer Research) contribute to protecting the body from advancing progressive of cancer stages. Thus, in this study, we analyze the effect of the intervention of vitamins on delaying the growth of cancer cells based on the dynamics of a normal cell cycle when the tumor cells appear in a tissue as a resulting for progressing abnormal cells due to the weak response of the immune system. We developed a mathematical model, called tumor-normal-vitamins model (TNVM), which is governed by a system of ordinary differential equations and refers to two main populations normal cells and tumor cells. This model considers the intervention of vitamins as a moderating factor within thirty days. The models are discussed analytically and numerically by utilizing the Runge-Kutta method to simulate them. The results of the analysis and simulation of free model illustrate that the model will be stable if the tumor cells succeed in eliminating normal cells in the tissue. Whereas, the analysis and simulation of the TNVM showed a case of coexistence between normal cells and tumor cells occur if an individual consumes a regular rate of vitamins that have been simulated to be 87% per day from a natural food source. Even though the response of the immune system is weak, the daily consumption of enough vitamins can play an essential role in delaying the development of an early stage of cancer. This study contributes to the increasing awareness regarding a healthy diet to reduce the risk of some deadly diseases, especially cancer.

Project description:This ordinary differential equation model of the interactions between tumor and normal cells, in the presence of a regular rate of vitamins, is based on the publication: S. A. Alharbi and A. S. Rambely, "Dynamic Simulation for Analyzing the Effects of the Intervention of Vitamins on Delaying the Growth of Tumor Cells," in IEEE Access, vol. 7, pp. 128816-128827, 2019 doi: 10.1109/ACCESS.2019.2940060. Comment: This TNVM model is described by the system of equations presented in (10), in the publication manuscript. Reproduction of Fig. 11 was achieved by swapping the values of gamma and beta2 stated in the manuscript, i.e. gamma = 0.9817 and beta2 = 0.2291. Abstract: The natural sources of the vitamins, which come from a balanced diet (as recommended by the World Cancer Research Fund and the American Institute for Cancer Research) contribute to protecting the body from advancing progressive of cancer stages. Thus, in this study, we analyze the effect of the intervention of vitamins on delaying the growth of cancer cells based on the dynamics of a normal cell cycle when the tumor cells appear in a tissue as a resulting for progressing abnormal cells due to the weak response of the immune system. We developed a mathematical model, called tumor-normal-vitamins model (TNVM), which is governed by a system of ordinary differential equations and refers to two main populations normal cells and tumor cells. This model considers the intervention of vitamins as a moderating factor within thirty days. The models are discussed analytically and numerically by utilizing the Runge-Kutta method to simulate them. The results of the analysis and simulation of free model illustrate that the model will be stable if the tumor cells succeed in eliminating normal cells in the tissue. Whereas, the analysis and simulation of the TNVM showed a case of coexistence between normal cells and tumor cells occur if an individual consumes a regular rate of vitamins that have been simulated to be 87% per day from a natural food source. Even though the response of the immune system is weak, the daily consumption of enough vitamins can play an essential role in delaying the development of an early stage of cancer. This study contributes to the increasing awareness regarding a healthy diet to reduce the risk of some deadly diseases, especially cancer.

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Alharbi2020 - An ODE-based model of the dynamics of tumor cell progression and its effects on normal cell growth and immune system functionality

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