Mathematical model analysis of breast cancer stages with side effects on heart in chemotherapy patients

Breast cancer is the second largest cause of death for women in the world. Cancer treatment is used to kill cancer cells, remove cancer cells through surgery, or prevent cancer from getting the signal needed for cell division. Cancer treatment does not necessarily have a good effect on patients. Breast cancer treatment with chemotherapy can effect heart health. Side effects of chemotherapy on the heart is called cardiotoxicity. Therefore, we have constructed a mathematical model from the breast cancer patient population in the hospital. A population is divided into five sub-populations. They are stage 1 and 2 (A), stage 3 (B), stage 4 (C), disease-free (D), and cardiotoxic (E). The model is constructed by using a differential equation system. The equilibrium point and stability analysis are used to study the dynamics associated with time. Analysis of equilibrium point stability using Routh Hurwitz criteria. Based on the analysis obtained an asymptotic stable equilibrium point. We verified the results of analysis with numerical simulations. Numerical simulations have a result that an equilibrium point is always stable without conditions using a variety of initial conditions. It is evident that the five sub-populations of patients will be stable when they reach the equilibrium point.