Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, and Mikhail Kolev. "Time delays in proliferation and apoptosis for solid avascular tumour." Banach Center Publications 63.1 (2003): 187-196. <http://eudml.org/doc/282087>.

@article{UrszulaForyś2003,
abstract = {The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the model depending on the magnitude of delay are studied. Nonnegativity of solutions is investigated. Steady state and the Hopf bifurcation analysis are presented. The results are illustrated by computer simulations.},
author = {Urszula Foryś, Mikhail Kolev},
journal = {Banach Center Publications},
keywords = {delay-differential equation; stability; Hopf bifurcation; changes of tumour radius},
language = {eng},
number = {1},
pages = {187-196},
title = {Time delays in proliferation and apoptosis for solid avascular tumour},
url = {http://eudml.org/doc/282087},
volume = {63},
year = {2003},
}

TY - JOUR
AU - Urszula Foryś
AU - Mikhail Kolev
TI - Time delays in proliferation and apoptosis for solid avascular tumour
JO - Banach Center Publications
PY - 2003
VL - 63
IS - 1
SP - 187
EP - 196
AB - The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the model depending on the magnitude of delay are studied. Nonnegativity of solutions is investigated. Steady state and the Hopf bifurcation analysis are presented. The results are illustrated by computer simulations.
LA - eng
KW - delay-differential equation; stability; Hopf bifurcation; changes of tumour radius
UR - http://eudml.org/doc/282087
ER -