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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 1: 263-278. doi: 10.3934/mbe.2013.10.263
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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
  • 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

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  • 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.


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  • © 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)
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