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

• Autorzy: Marek Bodnar , Urszula Foryś
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37G15: Bifurcations of limit cycles and periodic orbits
• 34K20: Stability theory
• 34K60: Qualitative investigation and simulation of models
• 92C60: Medical epidemiology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2009
• Tom: 36
• Numer: 3
• Strony: 251-262

Daty

wydano

2009

Twórcy

autor

Marek Bodnar

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

autor

Urszula Foryś

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

Identyfikatory

DOI

10.4064/am36-3-1