Angiogenesis model with Erlang distributed delays
We consider the model of angiogenesis process proposed by Bodnar and Foryś (2009) with time delays included into the vessels formation and tumour growth processes. Originally, discrete delays were considered, while in the present paper we focus on distributed delays and discuss specific results for...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017001 |
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| _version_ | 1832590069885566976 |
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| author | Emad Attia Marek Bodnar Urszula Foryś |
| author_facet | Emad Attia Marek Bodnar Urszula Foryś |
| author_sort | Emad Attia |
| collection | DOAJ |
| description | We consider the model of angiogenesis process proposed by Bodnar and Foryś (2009) with time delays included into the vessels formation and tumour growth processes. Originally, discrete delays were considered, while in the present paper we focus on distributed delays and discuss specific results for the Erlang distributions. Analytical results concerning stability of positive steady states are illustrated by numerical results in which we also compare these results with those for discrete delays. |
| format | Article |
| id | doaj-art-a1d8706d36024fa4a5aa5343494a5930 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a1d8706d36024fa4a5aa5343494a59302025-01-24T02:39:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114111510.3934/mbe.2017001Angiogenesis model with Erlang distributed delaysEmad Attia0Marek Bodnar1Urszula Foryś2Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, EgyptInstitute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw Banacha 2, 02-097 Warsaw, PolandInstitute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw Banacha 2, 02-097 Warsaw, PolandWe consider the model of angiogenesis process proposed by Bodnar and Foryś (2009) with time delays included into the vessels formation and tumour growth processes. Originally, discrete delays were considered, while in the present paper we focus on distributed delays and discuss specific results for the Erlang distributions. Analytical results concerning stability of positive steady states are illustrated by numerical results in which we also compare these results with those for discrete delays.https://www.aimspress.com/article/doi/10.3934/mbe.2017001delay differential equationsstability analysishopf bifurcationangiogenesistumour growth |
| spellingShingle | Emad Attia Marek Bodnar Urszula Foryś Angiogenesis model with Erlang distributed delays Mathematical Biosciences and Engineering delay differential equations stability analysis hopf bifurcation angiogenesis tumour growth |
| title | Angiogenesis model with Erlang distributed delays |
| title_full | Angiogenesis model with Erlang distributed delays |
| title_fullStr | Angiogenesis model with Erlang distributed delays |
| title_full_unstemmed | Angiogenesis model with Erlang distributed delays |
| title_short | Angiogenesis model with Erlang distributed delays |
| title_sort | angiogenesis model with erlang distributed delays |
| topic | delay differential equations stability analysis hopf bifurcation angiogenesis tumour growth |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017001 |
| work_keys_str_mv | AT emadattia angiogenesismodelwitherlangdistributeddelays AT marekbodnar angiogenesismodelwitherlangdistributeddelays AT urszulaforys angiogenesismodelwitherlangdistributeddelays |