Angiogenesis model with Erlang distributed delays

  • Received: 23 November 2015 Accepted: 06 April 2016 Published: 01 February 2017
  • MSC : Primary: 34K11, 34K13, 34K18, 37N25; Secondary: 92B05

  • 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.

    Citation: Emad Attia, Marek Bodnar, Urszula Foryś. Angiogenesis model with Erlang distributed delays[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 1-15. doi: 10.3934/mbe.2017001

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  • 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.
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    © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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