Dynamics of Cancer-Immune System with External Treatment and Optimal Control

Herein, we present a mathematical model of tumour-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. A discrete time-delay is considered to justify the time-needed for the effector cells to develop a suitable response to the tumour cells. The control variables are included to justify the best treatment strategy with minimum side effects by reducing the production of new tumour cells and keeping the number of normal cells above the average of its carrying capacity. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells increases the effector cells after few days of therapy.