  A mathematical model of infiltrative tumour growth taking into account cell
proliferation, death and motility is considered. The model is formulated in
terms of local cell density and nutrient (oxygen) concentration. In the model
the rate of cell death depends on the local nutrient level. Thus heterogeneous
nutrient distribution in tissue affects tumour structure and development. The
existence of automodel solutions is demonstrated and their properties are
investigated. The results are compared to the properties of the
Kolmogorov-Petrovskii-Piskunov and Fisher equations. Influence of the nutrient
distribution on the autowave speed selection as well as on the relaxation to
automodel solution is demonstrated. The model adequately describes the data,
observed in experiments.
