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Logistic equations in tumour growth modelling

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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.








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  • 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


  • 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.

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