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Dynamical Analysis of the Interaction between Effector Immune and Cancer Cells and Optimal Control of Chemotherapy

机译：效应物免疫与癌细胞相互作用的动力学分析及化学疗法的最佳控制

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It is well known that the tumor chemotherapy treatment has damaging side effects and hence, optimal control of this treatment is extremely important. With this in mind an accurate and comprehensive mathematical model could be useful. Various mathematical models have been derived to describe not only the beneficial effects of the immune system on controlling the growing tumor, but also to track, directly, 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.
机译：众所周知，肿瘤化学疗法具有有害的副作用，因此，对该疗法的最佳控制极为重要。考虑到这一点，准确而全面的数学模型可能会有用。已经获得了各种数学模型，不仅描述了免疫系统对控制生长中的肿瘤的有益作用，而且还直接追踪了化学疗法对肿瘤细胞和免疫细胞群体的有害作用。在本文中，我们提供了由分数阶微分方程表示的新颖数学模型。然后，该模型将用于分析实体实体中效应免疫细胞和肿瘤细胞局部相互作用中发生的复杂动力学的分叉和稳定性。我们还将研究联合化学免疫疗法的最佳控制。我们认为，分数分数微分方程模型在促进对肿瘤的天然免疫相互作用以及化学疗法可能对患者免疫系统产生的有害副作用的理解上将优于其普通微分方程模型。

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