The aim of this study is to provide a feedback control, called the Chemotherapy Protocol Law, with the purpose to keep the density of tumor cells that are treated by chemotherapy below a “tolerance level” $$L_c$$Lc, while retaining the density of normal cells above a “healthy level” $$N_c$$Nc. The mathematical model is a controlled dynamical system involving three nonlinear differential equations, based on a Gompertzian law of cell growth. By evoking viability and set-valued theories, we derive sufficient conditions for the existence of a Chemotherapy Protocol Law. Thereafter, on a suitable viability domain, we build a multifunction whose selections are the required Chemotherapy Protocol Laws. Finally, we propose a design of selection that generates a Chemotherapy Protocol Law.

中文翻译：

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化疗癌症模型中的活力控制

本研究的目的是提供一种反馈控制，称为化疗方案法，目的是将接受化疗的肿瘤细胞的密度保持在“耐受水平”以下，同时保持密度正常细胞高于“健康水平”$$N_c$$Nc。数学模型是基于 Gompertzian 细胞生长定律的包含三个非线性微分方程的受控动力系统。通过唤起可行性和集值理论，我们推导出存在化疗方案法的充分条件。此后，在合适的生存能力域上，我们构建了一个多功能，其选择是所需的化疗方案法律。最后，我们提出了一种选择设计，以生成化疗方案法。