Optimal control design for drug delivery of immunotherapy in chemoimmunotherapy treatment.

• The importance of drug delivery timing and dosage in chemoimmunotherapy has been studied on a new model proposed in the paper. • The optimal controller is designed to reduce cancer cells for a lower dosage of immunotherapy and a fixed dosage of chemotherapy. • The suggested optimal timing and dosage of immunotherapy is able to reduce cancer cells, with less amount of drug injection compared to a fixed protocol. • The achievement of this paper could be the basis for designing new clinical trials. There are various approaches to control a mathematical dynamic of cancer, each of which is suitable for a special goal. Optimal control is considered as an applicable method to calculate the minimum necessary drug delivery in such systems. In this paper, a mathematical dynamic of cancer is proposed considering tumor cells, natural killer cells, CD8+ T cells, circulating lymphocytes, IL-2 cytokine and Regulatory T cells as the system states, and chemotherapy, IL-2 and activated CD8+ T cells injection rate as the control signals. After verifying the proposed mathematical model, the importance of the drug delivery timing and the effect of cancer cells initial condition are discussed. Afterwards, an optimal control is designed by defining a proper cost function with the goal of minimizing the number of tumor cells, and two immunotherapy drug amounts during treatment Results show that inappropriate injection of immunotherapy time schedule and the number of initial conditions of cancer cells might result in chemoimmunotherapy failure and auxiliary treatment must be prescribed to decrease tumor size before any treatment takes place. The obtained optimal control signals show that with lower amount of drug delivery and a suitable drug injection time schedule, tumor cells can be eliminated while a fixed immunotherapy time schedule protocol fails with larger amount of drug injection. This conclusion can be utilized with the aim of personalizing drug delivery and designing more accurate clinical trials based on the improved model simulations in order to save cost and time. [ABSTRACT FROM AUTHOR]