Dynamic behaviour and stabilisation to boost the immune system by complex interaction between tumour cells and vitamins intervention

Abstract

Abstract In this paper, we establish and examine a mathematical model that combines the effects of vitamins intervention on strengthening the immune system and its role in suppressing and delaying the growth and division of tumour cells. In order to accomplish this, we propose a tumour–immune–vitamins model (TIVM) governed by ordinary differential equations and comprised of two populations, namely tumour and immune cells. It is presumed that the source of vitamins in TIVM originates from organic foods and beverages, based on the food pyramid. The simulation of TIVM employs the fourth order Runge–Kutta method. It is found from the analysis and simulation results that one of the side effects of weakening the immune system is the possibility of transforming immune cells into immune cancer cells to prevent or delay the growth and division of tumour cells. Evidently, for regular intakes of vitamins, which is projected at 55% of vitamins per day, the immune system is strengthened, preventing the production of tumour cells.

Keywords

• Dynamic model
• Nonlinear ordinary differential equations
• Stability
• Numerical simulation
• Immune cells
• Tumour cells