Model of tumour angiogenesis -- analysis of stability with respect to delays
In the paper we consider the model of tumour angiogenesis process proposed by Bodnar&Foryś (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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.19 |
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| author | Marek Bodnar Monika Joanna Piotrowska Urszula Foryś Ewa Nizińska |
| author_facet | Marek Bodnar Monika Joanna Piotrowska Urszula Foryś Ewa Nizińska |
| author_sort | Marek Bodnar |
| collection | DOAJ |
| description | In the paper we consider the model of tumour angiogenesis process proposed by Bodnar&Foryś (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. |
| format | Article |
| id | doaj-art-d70267e60db34e3f848c374fdd8fddb7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d70267e60db34e3f848c374fdd8fddb72025-01-24T02:25:25ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-11-01101193510.3934/mbe.2013.10.19Model of tumour angiogenesis -- analysis of stability with respect to delaysMarek Bodnar0Monika Joanna Piotrowska1Urszula Foryś2Ewa Nizińska3Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 WarsawInstitute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 WarsawInstitute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 WarsawInstitute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 WarsawIn the paper we consider the model of tumour angiogenesis process proposed by Bodnar&Foryś (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.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.19angiogenesisstability analysistumour growth.hopf bifurcationdelay differential equations |
| spellingShingle | Marek Bodnar Monika Joanna Piotrowska Urszula Foryś Ewa Nizińska Model of tumour angiogenesis -- analysis of stability with respect to delays Mathematical Biosciences and Engineering angiogenesis stability analysis tumour growth. hopf bifurcation delay differential equations |
| title | Model of tumour angiogenesis -- analysis of stability with respect to delays |
| title_full | Model of tumour angiogenesis -- analysis of stability with respect to delays |
| title_fullStr | Model of tumour angiogenesis -- analysis of stability with respect to delays |
| title_full_unstemmed | Model of tumour angiogenesis -- analysis of stability with respect to delays |
| title_short | Model of tumour angiogenesis -- analysis of stability with respect to delays |
| title_sort | model of tumour angiogenesis analysis of stability with respect to delays |
| topic | angiogenesis stability analysis tumour growth. hopf bifurcation delay differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.19 |
| work_keys_str_mv | AT marekbodnar modeloftumourangiogenesisanalysisofstabilitywithrespecttodelays AT monikajoannapiotrowska modeloftumourangiogenesisanalysisofstabilitywithrespecttodelays AT urszulaforys modeloftumourangiogenesisanalysisofstabilitywithrespecttodelays AT ewanizinska modeloftumourangiogenesisanalysisofstabilitywithrespecttodelays |