Research Article Open Access

Dynamical Analysis of Chemotherapy Optimal Control using Mathematical Model Presented by Fractional Differential Equations, Describing Effector Immune and Cancer Cells Interactions

Abstract

Evaluation of chemotherapy treatment in cancer cells is important because of its damaging side effects. For controlling chemotherapy treatment in cancer cells an accurate and comprehensive mathematical model could be useful. Many mathematical models have been used to show the benefits of immune system on controlling the growth of a tumor and the detrimental effects of chemotherapy on both the tumor cell and the immune cell populations. In this article, we offer a novel mathematical model presented by fractional differential equations. This model will then be used to analyze the bifurcation and stability of the complex dynamics which occur in the local interaction of effector-immune cell and tumor cells in a solid tumor. We will also investigate the optimal control of combined chemo-immunotherapy. We argue that our fractional differential equations model will be superior to its ordinary differential equations counterpart in facilitating understanding of the natural immune interactions to tumor and of the detrimental side-effects which chemotherapy may have on a patient’s immune system.

Mehdi Shahbazi, G Hussian Erjaee, and Hoda Erjaee

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