Geodesic
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics
Marek Bodnar1 ; Urszula Foryś2
1 Institute of Applied Mathematics & Mechanics Faculty of Mathematics, Informatics & Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2 Faculty of Mathematics, Informatics & Mechanics Institute of Applied Mathematics & Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 251-262.

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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 $\alpha $ 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.
DOI : 10.4064/am36-3-1
Keywords: study influence time delays dynamics general hahnfeldt model angiogenesis process analyse dynamics system different values parameter alpha which reflects strength stimulation vessel formation process time delays introduced three subprocesses tumour growth stimulation inhibition vessel formation represented endothelial cell dynamics focus possible destabilisation positive steady state due delay results illustrated numerical simulations performed parameter values estimated hahnfeldt tumour volume lewis lung carcinoma implanted mice

Marek Bodnar 1 ; Urszula Foryś 2

1 Institute of Applied Mathematics & Mechanics Faculty of Mathematics, Informatics & Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2 Faculty of Mathematics, Informatics & Mechanics Institute of Applied Mathematics & Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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Marek Bodnar; Urszula Foryś. Influence of time delays on the
 Hahnfeldt et al. angiogenesis model dynamics. Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 251-262. doi : 10.4064/am36-3-1. http://geodesic.mathdoc.fr/articles/10.4064/am36-3-1/

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