Open AccessAngiogenesis model with Erlang distributed delays
Author(s) -
Emad R. Attia,
Marek Bodnar,
Urszula Foryś
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017001
Subject(s) - erlang (programming language) , erlang distribution , computer science , focus (optics) , stability (learning theory) , discrete time and continuous time , mathematics , distributed computing , theoretical computer science , physics , statistics , exponential distribution , functional programming , machine learning , optics
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.