Dynamical Analysis and Optimal Control of Breast Cancer Patient Model

This research studied the dynamics model of breast cancer patients that was built as a dynamical system. The model had five compartments, including the subpopulations of stage 1 and 2 breast cancer patients, stage 3 cancer patients, stage 4 cancer patients, recovered individuals due to chemotherapy treatment, and patients who suffered cardiotoxicity. Equilibrium points and local stability were determined. The dynamical analysis resulted in one equilibrium point that exists and is stable under certain conditions. The model was constructed with the assumption that all patients undergo intensive chemotherapy treatment. This treatment caused side effects in the form of cardiotoxicity. Therefore, optimal control of additional treatment and ketogenic diet was applied. Additional treatment control is applied to prevent cardiotoxicity, while ketogenic diet control is used to reduce tumor cell growth. The aim of optimal control was to find out the treatment strategy that is effective in reducing cardiotoxicity and treatment costs. Numerical simulations were conducted to support the analysis results.