Dynamics of the tumor-immune system competition - the effect of time delay

Magda Galach

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 3, page 395-406
  • ISSN: 1641-876X

Abstract

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The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve a better compatibility with reality.

How to cite

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Galach, Magda. "Dynamics of the tumor-immune system competition - the effect of time delay." International Journal of Applied Mathematics and Computer Science 13.3 (2003): 395-406. <http://eudml.org/doc/207653>.

@article{Galach2003,
abstract = {The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve a better compatibility with reality.},
author = {Galach, Magda},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {mathematical model; differential equation; time delay; tumor growth},
language = {eng},
number = {3},
pages = {395-406},
title = {Dynamics of the tumor-immune system competition - the effect of time delay},
url = {http://eudml.org/doc/207653},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Galach, Magda
TI - Dynamics of the tumor-immune system competition - the effect of time delay
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 3
SP - 395
EP - 406
AB - The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve a better compatibility with reality.
LA - eng
KW - mathematical model; differential equation; time delay; tumor growth
UR - http://eudml.org/doc/207653
ER -

References

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  10. Kuang Y. (1993): Delay Differerntial Equations with Applications in Population Dynamics - London: Academic Press. 
  11. Kuznetsov V.A. and Taylor M.A. (1994): Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. - Bull. Math. Biol., Vol. 56, No. 2, pp. 295-321. Zbl0789.92019
  12. Mayer H., Zänker K.S. and der Heiden U. (1995) A basic mathematical model of the immune response. - Chaos, Vol. 5, No. 1, pp. 155-161. 
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  14. Waniewski J. and Zhivkov P. (2002): A simple mathematical model for tumour-immune system interactions. - Proc. 8-th Nat. Conf. Application of Mathematics in Biology and Medicine, LAjs, pp. 149-154. 

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