Cost-effectiveness analysis of optimal strategy for tumor treatment

We propose and analyze an antitumor model with combined immunotherapy and chemotherapy. Firstly, we explore the treatment effects of single immunotherapy and single chemotherapy, respectively. Results indicate that neither immunotherapy nor chemotherapy alone are adequate to cure a tumor. Hence, we apply optimal theory to investigate how the combination of immunotherapy and chemotherapy should be implemented, for a certain time period, in order to reduce the number of tumor cells, while minimizing the implementation cost of the treatment strategy. Secondly, we establish the existence of the optimality system and use Pontryagin’s Maximum Principle to characterize the optimal levels of the two treatment measures. Furthermore, we calculate the incremental cost-effectiveness ratios to analyze the cost-effectiveness of all possible combinations of the two treatment measures. Finally, numerical results show that the combination of immunotherapy and chemotherapy is the most cost-effective strategy for tumor treatment, and able to eliminate the entire tumor with size 4.470 × 108 in a year.