Angiogenesis model with Erlang distributed delays

Emad Attia; Marek Bodnar; Urszula Foryś

doi:10.3934/mbe.2017001

Angiogenesis model with Erlang distributed delays

Emad Attia, Marek Bodnar, Urszula Foryś

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Mathematical Biosciences and Engineering
Volume	14
Issue number	1
DOIs	https://doi.org/10.3934/mbe.2017001
State	Published - Feb 2017
Externally published	Yes

Keywords

Angiogenesis
Delay differential equations
Hopf bifurcation
Stability analysis
Tumour growth

Access to Document

10.3934/mbe.2017001

Cite this

@article{21465d7eaf304ad5a42fa05c1081467f,

title = "Angiogenesis model with Erlang distributed delays",

abstract = "We consider the model of angiogenesis process proposed by Bodnar and Fory{\'s} (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.",

keywords = "Angiogenesis, Delay differential equations, Hopf bifurcation, Stability analysis, Tumour growth",

author = "Emad Attia and Marek Bodnar and Urszula Fory{\'s}",

year = "2017",

month = feb,

doi = "10.3934/mbe.2017001",

language = "English",

volume = "14",

pages = "1--15",

journal = "Mathematical Biosciences and Engineering",

issn = "1547-1063",

publisher = "American Institute of Mathematical Sciences",

number = "1",

}

TY - JOUR

T1 - Angiogenesis model with Erlang distributed delays

AU - Attia, Emad

AU - Bodnar, Marek

AU - Foryś, Urszula

PY - 2017/2

Y1 - 2017/2

N2 - 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.

AB - 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.

KW - Angiogenesis

KW - Delay differential equations

KW - Hopf bifurcation

KW - Stability analysis

KW - Tumour growth

UR - http://www.scopus.com/inward/record.url?scp=85002534670&partnerID=8YFLogxK

U2 - 10.3934/mbe.2017001

DO - 10.3934/mbe.2017001

M3 - Article

C2 - 27879116

AN - SCOPUS:85002534670

SN - 1547-1063

VL - 14

SP - 1

EP - 15

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

IS - 1

ER -

Angiogenesis model with Erlang distributed delays

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this