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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
  • 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

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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.


    A correction on

    Deaths in Immigration and Customs Enforcement (ICE) detention: FY2018–2020

    By Sophie Terp, Sameer Ahmed, Elizabeth Burner, Madeline Ross, Molly Grassini, Briah Fischer, Parveen Parmar. Deaths in Immigration and Customs Enforcement (ICE) detention: FY2018–2020[J]. AIMS Public Health, 2021, 8(1): 81–89. doi: 10.3934/publichealth.2021006.

    We would like to submit the following correction to our recently published paper due to the wrong of reference 8. The details as the following.

    8. Congress.gov (2018) H. Rept. 115–239—Department OF Homeland Security Appropriations Bill, 2018. Available from: https://www.congress.gov/congressional-report/115th-congress/house-report/239.

    [1] Cell, 124 (2006), 1111-1115.
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    [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.
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