Optimal Control Applied In Mathematical Cancer Treatment Model

Abstract

Cancer is lethal disease, growing rapidly in most parts of the world. Treatments for cancer includes chemotherapy, radiotherapy, immunotherapy etc. The side effects of these treatments impact negatively on patient’s health. Side effects can be reduced if proper control of the treatments is employed while keeping the tumor cells at low level. In this work, optimum solution to the cancer treatment is determined while side effects are minimised. Existing simple mathematical model is used to describe a hypothetical cancer patient. The selected model in this work is based on a combination of immunotherapy and anti-angiogenic treatment to a general cancer model. Two optimal control solutions based on Pontryagin’s Maximum Principle are determined using different objective functions. The optimal control strategy applied is bang-bang control. Multi-objective Evolutionary Algorithms such as MODE, MOEAD, and MOPSO, are combined with the optimal control to adjust the weights in the objective functions in order to balance the cancer cells and drugs dosage minimization. The results showed that the use of anti-angiogenic is unnecessary as it was not useful in reducing the level of cancer cells. Inspired of that, the optimization lead to cancer cells minimization by using lesser amount of immunotherapy drug. Based on the results, it can be concluded that continuous administration of immunotherapy can reduce the cancer cells level.