An optimal control problem of immuno-chemotherapy in presence of gene therapy

Abstract

This study addresses a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy. The main objective of this study is to understand the optimal effect of immuno-chemotherpay in the presence of gene therapy. The 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 exist and are stable have been derived. An optimal control problem for the system has been constructed and solved to minimize the immuno-chemotherapy drug-induced toxicity to the patient. Amounts of immunotherapy to be injected into a patient for eradication of cancerous tumor cells have been found. Numerical and graphical results have been presented. From the results, it is seen that tumor cells can be eliminated in a specific time interval with the control of immuno-chemotherapeutic drug concentration.

Keywords

• cancer
• gene therapy
• chemotherapy
• immunotherapy
• stability
• optimal control