Search Advanced

Mathematical Biosciences and Engineering

2013, Volume 10, Issue 1: 263-278. doi: 10.3934/mbe.2013.10.263
Previous Article Next Article
Special Issues

On a mathematical model of tumor growth based on cancer stem cells

  • 1.
    Departamento de Matemática Aplicada, EUI Informática, Universidad Politécnica de Madrid, 28031 Madrid
  • Received: 01 July 2012 Accepted: 29 June 2018 Published: 01 December 2012

  • MSC : Primary: 35R35, 35Q92; Secondary: 92C37.

  • 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 ofdifferent 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 thatthere exists a unique homogeneous steady state which is stable.

    Citation: J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 263-278. doi: 10.3934/mbe.2013.10.263

    Related Papers:

  • 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 ofdifferent 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 thatthere exists a unique homogeneous steady state which is stable.


    加载中
    [1] Cell, 124 (2006), 1111-1115.
    [2] Cancer Res, 65 (2005), 10946-10951.
    [3] Blood, 112 (2008), 4793-4807.
    [4] Tutorials in mathematical biosciences. III, 223-246, Lecture Notes in Math., 1872, Springer, Berlin, 2006.
    [5] J. Math. Biol., 47 (2003), 391-423.
    [6] Proceedings of the CS2Bio 2nd International Workshop on Interactions between Computer Science and Biology, 2011.
    [7] PLoS ONE, 7 (2012), e26233.
    [8] Journal of Theoretical Biology, 250 (2008), 606-620.
    [9] Willey Edt. New Jersey, 2009.
    [10] Mathematical Models and Methods in Applied Sciences, 19 (2009), 257-281.
    [11] Discrete and Continuous Dynamical Systems - Serie A., 25 (2009), 343-361.
    [12] in "Modern Mathematical Tools and Techniques in Capturing Complexity Series: Understanding Complex Systems" (Eds. L. Pardo, N. Balakrishnan and M. A. Gil), Springer 2011.
  • Reader Comments
  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(2711) PDF downloads(549) Cited by(10)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog