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Stochastic models of tumour development andrelated mesoscopic equations

Dmitri Finkelshtein Orcid Logo, Martin Friesen, Haralampos Hatzikirou, Yuri Kondratiev, Tyll Krueger, Oleksandr Kutoviy

Interdisciplinary Studies of Complex Systems, Volume: 7, Pages: 5 - 85

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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Abstract

We consider different mathematical models inspired by the problems of medicine, in particular, the tumour growth and the related topics. We demonstrate how to starting from an individual-based (microscopic) description, which characterizes cells’ behaviour, derive the so-called kinetic (mesoscopic)...

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Published in: Interdisciplinary Studies of Complex Systems
ISSN: 2307-4515 2307-4515
Published: 2015
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa31246
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Abstract: We consider different mathematical models inspired by the problems of medicine, in particular, the tumour growth and the related topics. We demonstrate how to starting from an individual-based (microscopic) description, which characterizes cells’ behaviour, derive the so-called kinetic (mesoscopic) equations, which describe the approximate system density. Properties of the solutions to the mesoscopic equations (in particular, their long-time behaviour) reflect statistical characteristics of the whole system and demonstrate the corresponding dependence on the system parameters.
College: Faculty of Science and Engineering
Start Page: 5
End Page: 85