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2003 | 13 | 3 | 395-406
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
13
Numer
3
Strony
395-406
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-03-01
poprawiono
2003-06-01
Twórcy
autor
  • Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, ul. Trojdena 4, 02-109 Warsaw, Poland
Bibliografia
  • Bodnar M. (2000): The nonnegativity of solutions of delay differential equations. - Appl. Math. Lett., Vol. 13, No. 6, pp. 91-95.
  • Bodnar M. and Foryś U. (2000a): Behaviour of solutions to Marchuk's model depending on a time delay. - Int. J. Appl. Math. Comput.Sci., Vol. 10, No. 1, pp. 97-112.
  • Bodnar M. and Foryś U. (2000b): Periodic dynamics in the model of immune system. - Appl. Math., Vol. 27, No. 1, pp. 113-126.
  • Byrne H.M. (1997): The effect of time delay on the dynamics of avascular tumour growth. - Math. Biosci., Vol. 144, No. 2, pp. 83-117.
  • Foryś U. (2002): Marchuk's model of immune system dynamics with application to tumour growth. - J. Theor. Med., Vol. 4, No. 1, pp. 85-93.
  • Foryś U. and Kolev M. (2002): Time delays in proliferation and apoptosis for solid avascular tumour. - Prep. Institute of Applied Mathematics and Mechanics, No. RW 02-10 (110), Warsaw University.
  • Foryś U. and Marciniak-Czochra A. (2002): Delay logistic equation with diffusion. - Proc. 8-th Nat. Conf.s Application of Mathematics in Biology and Medicine, Lajs, pp. 37-42.
  • Hale J.K. (1997): Theory of functional differential equations - New York: Springer.
  • Kirschner D. and Panetta J.C. (1998): Modeling immunotherapy of the tumor-immune interaction - J. Math. Biol., Vol. 37, No. 3, pp. 235-252.
  • Kuang Y. (1993): Delay Differerntial Equations with Applications in Population Dynamics - London: Academic Press.
  • 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.
  • 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.
  • Perko L. (1991): Differential Equations and Dynamical Systems - New York: Springer.
  • 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.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i3p395bwm
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