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Model of tumour angiogenesis -- analysis of stability with respect to delays.
MedLine Citation:
PMID:  23311360     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
In the paper we consider the model of tumour angiogenesis process proposed by Bodnar and Fory (2009). The model combines ideas of Hahnfeldt et al. (1999) and Agur et al. (2004) describing the dynamics of tumour, angiogenic proteins and effective vessels density. Presented analysis is focused on the dependance of the model dynamics on delays introduced to the system. These delays reflect time lags in the proliferation/death term and the vessel formation/regression response to stimuli. It occurs that the dynamics strongly depends on the model parameters and the behaviour independent of the delays magnitude as well as multiple stability switches with increasing delay can be obtained.
Authors:
Marek Bodnar; Monika Joanna Piotrowska; Urszula Fory; Ewa Nizinska
Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Mathematical biosciences and engineering : MBE     Volume:  10     ISSN:  1551-0018     ISO Abbreviation:  Math Biosci Eng     Publication Date:  2013 Feb 
Date Detail:
Created Date:  2013-01-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101197794     Medline TA:  Math Biosci Eng     Country:  United States    
Other Details:
Languages:  eng     Pagination:  19-35     Citation Subset:  IM    
Affiliation:
Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland. mbodnar@mimuw.edu.pl.
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