The effects of drugs in chemotherapy as optimal control of tumor growth dynamical model

Abstract

Cancer is the disease caused by disordered hormone so that it causes the lumps to grow abnormally on body tissue, and it is known as a malignant tumor. Some mortalities in the world are caused by cancer, while in Indonesia, cancer contributes to the third-largest death. This research will explain about stability and optimal control of tumor growth dynamical model by drugs in chemotherapy. In the tumor growth dynamical model, there are normal cells, tumor cells, and immune cells. From the mathematical model of tumor growth, some equilibrium points will be analyzed for their stability using eigenvalue. In this research, from the mathematical model of tumor growth, it will be added control, such as drugs in chemotherapy. The method used for solving optimal control problems and resulting numerical solutions is Forward Backward Sweep Method. Based on simulation results, drugs in chemotherapy give effects in a normal cell, tumor cell, and immune cell.