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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa31246
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first_indexed 2016-11-25T20:13:38Z
last_indexed 2018-02-09T05:17:57Z
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spelling 2016-11-25T13:31:28.7311523 v2 31246 2016-11-25 Stochastic models of tumour development andrelated mesoscopic equations 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2016-11-25 SMA 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. Journal Article Interdisciplinary Studies of Complex Systems 7 5 85 2307-4515 2307-4515 31 12 2015 2015-12-31 http://iscs-journal.npu.edu.ua/article/view/56266/52444 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2016-11-25T13:31:28.7311523 2016-11-25T13:25:51.8588646 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Martin Friesen 2 Haralampos Hatzikirou 3 Yuri Kondratiev 4 Tyll Krueger 5 Oleksandr Kutoviy 6
title Stochastic models of tumour development andrelated mesoscopic equations
spellingShingle Stochastic models of tumour development andrelated mesoscopic equations
Dmitri Finkelshtein
title_short Stochastic models of tumour development andrelated mesoscopic equations
title_full Stochastic models of tumour development andrelated mesoscopic equations
title_fullStr Stochastic models of tumour development andrelated mesoscopic equations
title_full_unstemmed Stochastic models of tumour development andrelated mesoscopic equations
title_sort Stochastic models of tumour development andrelated mesoscopic equations
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Dmitri Finkelshtein
Martin Friesen
Haralampos Hatzikirou
Yuri Kondratiev
Tyll Krueger
Oleksandr Kutoviy
format Journal article
container_title Interdisciplinary Studies of Complex Systems
container_volume 7
container_start_page 5
publishDate 2015
institution Swansea University
issn 2307-4515
2307-4515
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://iscs-journal.npu.edu.ua/article/view/56266/52444
document_store_str 0
active_str 0
description 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.
published_date 2015-12-31T03:38:09Z
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score 10.997956