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2003 | 13 | 3 | 317-325
Tytuł artykułu

Logistic equations in tumour growth modelling

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.
Rocznik
Tom
13
Numer
3
Strony
317-325
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-03-01
poprawiono
2003-06-01
Twórcy
  • Faculty of Mathematics, Informatics and Mechanics,Institute of Applied Mathematics and Mechanics Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
  • Institute of Applied Mathematics, University of Heidelberg, INF 294, 69120 Heidelberg, Germany
Bibliografia
  • Bodnar M. (2000): The nonnegativity of solutions of delay differential equations. - Appl. Math. Let., Vol. 13, No. 6, pp. 91-95.
  • Britton N.F. (1986): Reaction-Diffusion Equations and Their Applicationsto Biology. - New York: Academic-Press.
  • Cook K. and Driessche P. (1986): On zeros of some transcendental equations. - Funkcialaj Ekvacioj, Vol. 29, pp. 77-90.
  • Cook K. and Grosmann Z. (1982): Discrete delay, distributed delay and stability switches. - J. Math. Anal. Appl., Vol. 86, pp. 592-627.
  • Drasdo D. and Home S. (2003): Individual based approaches to birth and death in avascular tumours. - Math. Comp. Modell., (to appear).
  • Fisher R.A. (1937): The wave of advance of adventage genes. - Ann.Eugenics, Vol. 7, pp. 353-369.
  • Foryś U. (2001): On the Mikhailov criterion and stability of delay differential equations. - Prep. Warsaw University, No. RW 01-14 (97).
  • Foryś U. and Marciniak-Czochra A. (2002): Delay logistic equation with diffusion. - Proc. 8-th Nat. Conf. Mathematics Applied to Biology and Medicine, Łajs, Warsaw, Poland, pp. 37-42.
  • Gopalsamy K. (1992): Stability and Oscillations in Delay Differential Equations of Population Dynamics. - Dordrecht: Kluwer.
  • Gourley S.A. and So J.W.-H. (2002): Dynamics of a food limited population model incorporating nonlocal delays on a finite domain. - J. Math.Biol., Vol. 44, No. 1, pp. 49-78.
  • Hale J. (1997): Theory of Functional Differential Equations. - New York: Springer.
  • Henry D. (1981): Geometric Theory of Semilinear Parabolic Equations. - Berlin: Springer.
  • Hutchinson G.E. (1948): Circular casual systems in ecology. - Ann.N.Y. Acad. Sci., Vol. 50, pp. 221-246.
  • Kolmanovskii V. and Nosov V. (1986): Stability of Functional DifferentialEquations. - London: Academic Press.
  • Kowalczyk R. and Foryś U. (2002): Qualitative analysis on the initial value problem to the logistic equation with delay. - Math. Comp. Model., Vol. 35, No. 1-2, pp. 1-13.
  • Krug H. and Taubert G. (1985): Zur praxis der anpassung derlogistischen function an das wachstum experimenteller tumoren. - Arch.Geschwulstforsch., Vol. 55, pp. 235-244.
  • Kuang Y. (1993): Delay Differential Equations with Applicationsin Population Dynamics. - Boston: Academic Press, 1993.
  • Lauter H. and Pincus R. (1989): Mathematisch-Statistische Datenanalyse. - Berlin: Akademie-Verlag.
  • Murray J.D. (1993): Mathematical Biology. - Berlin: Springer.
  • Schuster R. and Schuster H. (1995): Reconstruction models for the Ehrlich Ascites Tumor of the mouse, In: Mathematical Population Dynamics, Vol. 2, (O. Arino, D. Axelrod, M. Kimmel, Eds.). - Wuertz: Winnipeg, Canada, pp. 335-348.
  • Smoller J. (1994): Shock Waves and Reaction-Diffusion Equations. - New York: Springer.
  • Taira K. (1995): Analytic Semigroups and Semilinear Initial Boundary Value Problems. - Cambridge: University Press.
  • Verhulst P.F. (1838): Notice sur la loi que la population suit dansson accroissement. - Corr. Math. Phys., Vol. 10, pp. 113-121.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i3p317bwm
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