The dynamics of an optimally controlled tumor model: A case study
The dynamics of an optimally controlled tumor model: A case study
复制标题
DOI：
10.1016/s0895-7177(03)00133-x
复制
发表时间：
2003-06-01
影响因子：
--
通讯作者：
Radunskaya, A
中科院分区：
文献类型：
--
作者：
De Pillis, LG;Radunskaya, A
我们提出了一个具有免疫反应和化疗的肿瘤生长数学模型的相空间分析。我们证明了所有的轨道都是有界的，并且一定收敛到几个可能的平衡点之一。因此，轨道的长期行为是根据它开始时所处的引力盆地进行分类的。在系统中增加一个药物术语可以将溶液轨迹移动到一个理想的吸引盆中。我们证明了具有时变药物项的模型的解在治疗停止时逼近于没有药物的系统的解。我们提出了数字实验，其中最优控制疗法能够将系统驱动到理想的吸引盆中，而传统的脉冲化疗则不能。(C)2003爱思唯尔科学有限公司。保留所有权利。
We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. We show that the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once treatment has stopped. We present numerical experiments in which optimal control therapy is able to drive the system into a desirable basin of attraction, whereas traditional pulsed chemotherapy is not. (C) 2003 Elsevier Science Ltd. All rights reserved.