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Logistic equations in tumour growth modelling

Urszula Foryś;  Anna Marciniak-Czochra — 2003

International Journal of Applied Mathematics and Computer Science

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...

Reaction-Difusion Model of Early Carcinogenesis: The Effects of Influx of Mutated Cells

Anna Marciniak-Czochra;  Marek Kimmel — 2008

Mathematical Modelling of Natural Phenomena

In this paper we explore a new model of field carcinogenesis, inspired by lung cancer precursor lesions, which includes dynamics of a spatially distributed population of pre-cancerous cells , constantly supplied by an influx of mutated normal cells. Cell proliferation is controlled by growth factor molecules bound to cells, . Free growth factor molecules are produced by precancerous cells and may diffuse before they become bound to other cells. The purpose of modelling is to investigate the existence...

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