An Optimal Control Problem of Chemotherapy In Presence of Gene and Immunotherapy

Abstract

In this study, a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy has been proposed. Boundedness and positiveness of the solutions in the respective feasible domains of the proposed model are verified. Conditions for which the equilibrium points of the system are stable have been derived. Amounts of immunotherapy to be injected to a patient for eradication of cancerous tumor cells have been found. To minimize the chemotherapy drug-induced toxicity to the patient, an optimal control problem for the system has been constructed and solved. Numerical and graphical results have been presented. Through the investigation, it was seen that tumor cells can be eliminated in a specific time interval with the control of chemotherapeutic drug concentration.