Theoretical study and numerical simulation for a mathematical model of diffusive cancer with effect of stem cell therapy and chemotherapy

Abstract

Cancer is the most dangerous disease in the world. Therefore, this paper is devoted to studying a mathematical model of diffusive cancer and the effect of its treatments. One of the cancer treatments currently being explored is stem cell transplant, which works to stimulate and strengthen the immune system while the patient receives chemotherapy. This work introduces a mathematical system for the temporal and spatial interactions between the tumor, stem cells and effector cells during chemotherapy and the extent of the spread of these interactions within the tissue. Also, we study the stability of the system through the equilibrium points of the reaction-diffusion model. In addition, the existence, uniqueness, positivity, and boundedness are proven. We found a numerical simulation by the finite difference method and observed a dynamic of the solutions. Also, we described the tumor behaviour before and after the treatments and the effect of its diffusion.