Departamento de Matematica Aplicada, EUI Informatica, Universidad Politecnica de Madrid, 28031 Madrid, Spain.
Math Biosci Eng. 2013 Feb;10(1):263-78. doi: 10.3934/mbe.2013.10.263.
We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show that there exists a unique homogeneous steady state which is stable.
我们考虑了一个基于癌症干细胞的简单肿瘤生长数学模型。该模型由四个一阶双曲型方程组成，用于描述不同细胞亚群（癌症干细胞、祖细胞、分化细胞和死亡细胞）的演化。引入了一个第五个方程来模拟移动边界的演化。该系统在系数中包含积分型的非局部项。在参数的一些限制下，我们证明了存在唯一的齐次稳定状态，且该状态是稳定的。
