American Institute of Mathematical Sciences

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2013, 10(1): 263-278. doi: 10.3934/mbe.2013.10.263

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

J. Ignacio Tello 1,

1. 

Departamento de Matemática Aplicada, EUI Informática, Universidad Politécnica de Madrid, 28031 Madrid, Spain

Received  July 2012 Revised  September 2012 Published  December 2012

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.
Keywords: free boundary problems, stability., Cancer steam cells.
Mathematics Subject Classification: Primary: 35R35, 35Q92; Secondary: 92C3.
Citation: J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263
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show all references

References:
[1]

Cell, 124 (2006), 1111-1115. Google Scholar

[2]

Cancer Res, 65 (2005), 10946-10951. Google Scholar

[3]

Blood, 112 (2008), 4793-4807. Google Scholar

[4]

Tutorials in mathematical biosciences. III, 223-246, Lecture Notes in Math., 1872, Springer, Berlin, 2006.  Google Scholar

[5]

J. Math. Biol., 47 (2003), 391-423. doi: 10.1007/s00285-003-0199-5.  Google Scholar

[6]

Proceedings of the CS2Bio 2nd International Workshop on Interactions between Computer Science and Biology, 2011. Google Scholar

[7]

PLoS ONE, 7 (2012), e26233. Google Scholar

[8]

Journal of Theoretical Biology, 250 (2008), 606-620. Google Scholar

[9]

Willey Edt. New Jersey, 2009. Google Scholar

[10]

Mathematical Models and Methods in Applied Sciences, 19 (2009), 257-281.  Google Scholar

[11]

Discrete and Continuous Dynamical Systems - Serie A., 25 (2009), 343-361.  Google Scholar

[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. Google Scholar

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