title: On a mathematical model of tumor growth based on cancer stem cells.
abstract: 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.
authors: Departamento de Matematica Aplicada, EUI Informatica, Universidad Politecnica de Madrid, 28031 Madrid, Spain. jtello@eui.upm.es
authors: J Ignacio
authors: JI
authors: Tello
mesh_terms: D000465:Algorithms; D002454:Cell Differentiation; D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009362:Neoplasm Metastasis; D009369:Neoplasms / Q000378:metabolism / Q000473:pathology*; D014411:Neoplastic Stem Cells / Q000166:cytology*