Mathematical Model for Cancer Treatment by Chemotherapy With Healthy Food Intake

Cancer is one of the leading causes of death in the world, and its treatment by chemotherapy has been extensively researched using mathematical models. This paper constructs a nonlinear system of ordinary differential equations to model the dynamics of tumor cells, effector immune cells, chemotherapy drug concentration, and healthy food consumption. The model is new due to the inclusion of healthy food intake as a new parameter affecting immune response and tumor dynamics. The model is examined by finding the equilibrium points and examining the local stability of the equilibrium points by the Jacobian matrix and the eigenvalue method. Moreover, Scilab is used to conduct numerical simulations to demonstrate how the system behaves dynamically with different amounts of chemotherapy and dietary intake. The findings reveal that a higher consumption of healthy food contributes greatly to the population of effector cells and speeds up the elimination of tumor cells when used together with chemotherapy. Chemotherapy alone is not very effective in decreasing tumor burden in the absence of proper nutrition. The results indicate that increased healthy food intake from 1000 g to 1500 g per day enhanced the population of the effector cells from 150,000 to 220,000 and, at the same time, accelerated the reduction of tumor cells at the rate from 400 per day to 50 per day. These results demonstrate the importance of nutrition in enhancing the outcome of cancer treatment and present fresh information on the synergistic effect of diet and chemotherapy through a mathematical modeling approach. The increase in percentage of healthy food intake has shown an increase in the number of effector cells with a higher amount of healthy food intake, with a relatively decreasing pattern.