Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach

In this article, we develop and analyze a non-linear mathematical model of tumor-immune interactions with combined therapeutic drug and treatment controls. To understand under what circumstances the cancerous cells can be destroyed, an optimal control problem is formulated with treatments as control parameters. By designing a quadratic control based functional, we establish the optimal treatment strategies that maximize the number of immune-effector cells, minimize the number of cancer cells, and detrimental effects caused by the amount of drugs. The necessary and sufficient conditions for optimal control are established. We prove the existence and uniqueness of an optimal control problem. To recognize significant system's parameters, sensitivity analysis are performed for the drug administration and cost functional respectively. We also carry out a cost-effectiveness analysis to determine the most cost-effective therapeutic strategy. The numerical results validate analytical findings and also elucidates that the combinatorial drug therapy can alleviate the cancerous cells under different scenarios.