Time delays in proliferation and apoptosis for solid avascular tumour

• Autorzy: Urszula Foryś , Mikhail Kolev
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 62P10: Applications to biology and medical sciences
• 35K57: Reaction-diffusion equations
• 93A30: Mathematical modeling (models of systems, model-matching, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 63
• Numer: 1
• Strony: 187-196

Daty

wydano

2003

Twórcy

autor

Urszula Foryś

• Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics & Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Mikhail Kolev

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
• South-West University, Blagoevgrad, Bulgaria

Identyfikatory

DOI

10.4064/bc63-0-7