Analysing the effect of trastuzumab treatment on breast cancer stages and cardiac function: A mathematical modeling and numerical simulation

. Breast cancer is the second most common cause of death among women worldwide. Trastuzumab is the first humanised monoclonal antibody against HER2-positive metastatic breast cancer. However, the most serious side effect of trastuzumab is cardiotoxicity, which has become a limiting factor in the drug’s safe use. In this study, we investigated the effect of trastuzumab treatment on breast cancer stages and cardiac function. Therefore, we constructed a mathematical model based on breast cancer patients. The model was created using a differential equation system, and equilibrium point and stability analysis were employed to study the associated temporal dynamics. The stability of the equilibrium point was analysed using the Routh-Hurwitz criteria, which identified an asymptotically stable equilibrium point. To valudate these findings, numerical simulations were performed, which demonstrated that the equilibrium point is always stable regardless of the initial conditions. Finally, our results suggest that the five sub-populations of patients will reach a stable state upon reaching the equilibrium point.