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

Volume 36 / 2009

Marek Bodnar, Urszula Foryś Applicationes Mathematicae 36 (2009), 251-262 MSC: 92C60, 37G15, 34K20, 34K60. DOI: 10.4064/am36-3-1

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 $\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.

Authors

  • Marek BodnarInstitute of Applied Mathematics & Mechanics
    Faculty of Mathematics, Informatics & Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Urszula ForyśFaculty of Mathematics, Informatics & Mechanics
    Institute of Applied Mathematics & Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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