Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics

Marek Bodnar, and Urszula Foryś. "Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics." Applicationes Mathematicae 36.3 (2009): 251-262. <http://eudml.org/doc/279882>.

@article{MarekBodnar2009,
abstract = {We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due to the delay. Results are illustrated by numerical simulations performed for parameter values estimated by Hahnfeldt et al. for tumour volume data of Lewis lung carcinoma implanted in mice.},
author = {Marek Bodnar, Urszula Foryś},
journal = {Applicationes Mathematicae},
language = {eng},
number = {3},
pages = {251-262},
title = {Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics},
url = {http://eudml.org/doc/279882},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Marek Bodnar
AU - Urszula Foryś
TI - Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 3
SP - 251
EP - 262
AB - We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due to the delay. Results are illustrated by numerical simulations performed for parameter values estimated by Hahnfeldt et al. for tumour volume data of Lewis lung carcinoma implanted in mice.
LA - eng
UR - http://eudml.org/doc/279882
ER -