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A mathematical model of tumor growth. II. Effects of geometry and spatial nonuniformity on stability. (English) Zbl 0634.92002
Summary: A theoretical account of mitotic inhibition in one-, two-, and three- dimensional configurations is presented. Based on part I, ibid. 81, 229- 244 (1986; Zbl 0601.92007), the inhibitor production rate is taken to be nonuniform throughout the tissue, resulting in significant deviations from the prediction of uniform models. Geometry affects the stability of growth also. The analysis presented here represents a detailed study of the properties of highly nonuniform inhibition, from which information on intermediate inhibition models can be readily deduced. This information is used to compare such a model with experimental results in part III, see the following entry, Zbl 0634.92003.

MSC:
92C50Medical applications of mathematical biology
92D25Population dynamics (general)