The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as...
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...
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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