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8. , Part 8. Mathematical methods in biology, ecology and chemistry

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n t m t h t S t r = Bn - P( S )n - .(nV - Dnn), r = P( S )n - .(nV ), r =-.(hV ), =- kS S + S* n + DS S .

n m , h -- . , (), (). Dn -- , V(x,y) -- . , , . , : n + m + h = 1. , [8], , :
r V = + Dnn.

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, (1) :
n = Bn(1 - n) - P( S )n + .( Dn (1 - n)n) - (n, ), t m = P( S )n - mBn - .( Dn mn) - (m, ), t S kS =- n + DS S , t S + S*

= Bn.

[9]. (2) 400x400, :
n E = m E = 0, S = = 0, n I = m I = S I = I = 0,

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8. , Part 8. Mathematical methods in biology, ecology and chemistry

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8. , Part 8. Mathematical methods in biology, ecology and chemistry
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DIRECTED TUMOUR GROWTH AND INVASION IN ABSENCE OF CHEMOTACTIC CELL MOTILITY Kolobov A.V., Polezhaev A. A.

(Russia, Moscow) Chemotaxis plays an important role in morphogenesis and processes of structure formation in nature. Both unicellular organisms and single cells in tissue demonstrate this property. In vitro experiments show that many types of transformed cell, especially metastatic competent, are capable for directed motion in response usually to chemical signal. There is a number of theoretical papers on mathematical modeling of tumour growth and invasion using Keller-Segel model for the chemotactic motility of cancer cells. One of the crucial questions for using the chemotactic term in modelling of tumour growth is a lack of reliable quantitative estimation of its parameters. The 2D mathematical model of tumour growth and invasion, which takes into account only random cell motility and convective fluxes in compact tissue, has showed that due to competitive mechanism tumour can grow toward sources of nutrients in absence of chemotactic cell motility.

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