Advanced Search
Article Contents
Article Contents

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

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: Primary: 35R35, 35Q92; Secondary: 92C37.


    \begin{equation} \\ \end{equation}
  • [1]

    M. F. Clarke and M. Fuller, Stem cells and cancer: Two faces of eve, Cell, 124 (2006), 1111-1115.


    A. T. Collins, P. A. Berry, C. Hyde, M. J. Stower and N. J. Maitland, Prospective identification of tumorigenic prostate cancer stem cells, Cancer Res, 65 (2005), 10946-10951.


    J. E. Dick, Stem cell concepts renew cancer research, Blood, 112 (2008), 4793-4807.


    A. Friedman, Cancer models and their mathematical analysis, Tutorials in mathematical biosciences. III, 223-246, Lecture Notes in Math., 1872, Springer, Berlin, 2006.


    A. Friedman and Y. Tao, Analysis of a model of a virus that replicates selectively in tumor cells, J. Math. Biol., 47 (2003), 391-423.doi: 10.1007/s00285-003-0199-5.


    C. Fornari, F. Cordero, D. Manini, R. A. Calogero and G. Balbo, Mathematical approach to predict the drug effects on cancer stem cell models, Proceedings of the CS2Bio 2nd International Workshop on Interactions between Computer Science and Biology, 2011.


    R. Molina-Peña and M. M. Álvarez, A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth, PLoS ONE, 7 (2012), e26233.


    K. Qu and P. Ortoleva, Understanding stem cell differentiation through self-organization theory, Journal of Theoretical Biology, 250 (2008), 606-620.


    S. Bapat, "Cancer Steam Cells, Identification and Targets," Willey Edt. New Jersey, 2009.


    Z. Szymánska, C. Morales Rodrigo, M. Lachowicz and M. A. J. Chaplain, Mathematical modelling of cancer invasion of tissue: The role and effect of nonlocal interaction, Mathematical Models and Methods in Applied Sciences, 19 (2009), 257-281.


    J. I. Tello, Mathematical analysis of a model of Morphogenesis, Discrete and Continuous Dynamical Systems - Serie A., 25 (2009), 343-361.


    J. I. Tello, On the existence of solutions of a mathematical model of morphogens, in "Modern Mathematical Tools and Techniques in Capturing Complexity Series: Understanding Complex Systems" (Eds. L. Pardo, N. Balakrishnan and M. A. Gil), Springer 2011.

  • 加载中

Article Metrics

HTML views() PDF downloads(46) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint