Control by Viability in a Chemotherapy Cancer Model

被引:0
|
作者
M. Serhani
H. Essaadi
K. Kassara
A. Boutoulout
机构
[1] University Moulay Ismail,TSI Team, FSJES
[2] University Moulay Ismail,TSI Team, Faculty of Sciences
[3] University Hassan II,MACS
来源
Acta Biotheoretica | 2019年 / 67卷
关键词
Cancer model; Feedback control; Viability; Set-valued analysis; 34H05; 34A60; 49 J52; 49K15; 92C50; 9C60;
D O I
暂无
中图分类号
学科分类号
摘要
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” Lc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_c$$\end{document}, while retaining the density of normal cells above a “healthy level” Nc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_c$$\end{document}. 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.
引用
收藏
页码:177 / 200
页数:23
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