# Logistic equations in tumour growth modelling

Urszula Foryś; Anna Marciniak-Czochra

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 3, page 317-325
- ISSN: 1641-876X

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topForyś, Urszula, and Marciniak-Czochra, Anna. "Logistic equations in tumour growth modelling." International Journal of Applied Mathematics and Computer Science 13.3 (2003): 317-325. <http://eudml.org/doc/207646>.

@article{Foryś2003,

abstract = {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.},

author = {Foryś, Urszula, Marciniak-Czochra, Anna},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {global stability; Ehrlich ascities tumour; reaction-diffusion equation; logistic equation; Hopf bifurcation; delay differential equation; spatial pattern; stability},

language = {eng},

number = {3},

pages = {317-325},

title = {Logistic equations in tumour growth modelling},

url = {http://eudml.org/doc/207646},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Foryś, Urszula

AU - Marciniak-Czochra, Anna

TI - Logistic equations in tumour growth modelling

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 3

SP - 317

EP - 325

AB - 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.

LA - eng

KW - global stability; Ehrlich ascities tumour; reaction-diffusion equation; logistic equation; Hopf bifurcation; delay differential equation; spatial pattern; stability

UR - http://eudml.org/doc/207646

ER -

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