A study on ODE-based model of risk breast cancer with body mass

Abstract

In this study, we propose a fat-estrogen-breast cancer mathematical model to discuss the effect of body mass, estrogen, and the immune system on the evolution of cancer cells. To do this, stability analysis has been performed at each of the biologically feasible equilibria of the model. It is found that the tumor-free equilibrium exists if the estrogen level is normal and is asymptotically stable if the growth of tumor cells in the presence of fat cells is less than the response rate of immune cells against the tumor; otherwise, it is unstable. However, the co-existing equilibrium exists for excess estrogen levels and it is stable, provided certain conditions hold. It is observed that the eradication or proliferation of tumor cells directly depends on the growth of fat cells, the response of the immune system against the tumor, and the estrogen level. Numerical simulations have been performed to verify the theoretical results.