Constrained optimal control problem of oncolytic viruses in cancer treatment

Oncolytic viruses are genetically modified viruses that selectively infect and destroy cancer cells while leaving normal and healthy cells intact. Most previous studies did not consider realistic constraints such as daily or total injection amount of oncolytic viruses; consequently, a gap exists between the research results and the real-world setting. This study aimed to investigate a constrained optimal control problem in tumor treatment utilizing oncolytic viruses, based on a mathematical model. This constraint reflects the practical scenario where the total dosage of oncolytic viruses that can be administered is limited. We introduced auxiliary state variables to address these limitations and employed the penalty function method. Furthermore, we established the existence of an optimal solution for the optimal control problem and derived the corresponding optimality system. Numerical simulations demonstrate the effectiveness of an approach that involves initiating treatment with a high dosage and gradually reducing it over time. Additionally, we confirmed that applying the optimal control strategy leads to a significant reduction in the number of cancer cells compared with uniform dosing, even when the same quantity of virus is administered.