Dynamic Simulation for Analyzing the Effects of the Intervention of Vitamins on Delaying the Growth of Tumor Cells

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.

Keywords

• Dynamic system
• numerical simulation
• tumor-normal model
• healthy diet