Model of tumour angiogenesis -- analysis of stability with respect to delays

doi:10.3934/mbe.2013.10.19

Mathematical Biosciences and Engineering, 2013, 10(1): 19-35. doi: 10.3934/mbe.2013.10.19. Primary: 34K11, 34K13, 34K18, 34K20, 49K25; Secondary: 92B05, 93C23.

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Model of tumour angiogenesis -- analysis of stability with respect to delays

1. Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw

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In the paper we consider the model of tumour angiogenesis process proposed by Bodnar&Foryś (2009). The model combines ideas of Hahnfeldt et al. (1999) and Agur et al. (2004) describing the dynamics of tumour, angiogenic proteins and effective vessels density. Presented analysis is focused on the dependance of the model dynamics on delays introduced to the system. These delays reflect time lags in the proliferation/death term and the vessel formation/regression response to stimuli.It occurs that the dynamics strongly depends on the model parameters and the behaviour independent of the delays magnitude as well as multiple stability switches with increasing delay can be obtained.

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Keywords: angiogenesis; stability analysis; tumour growth.; Hopf bifurcation; Delay differential equations

Citation: Marek Bodnar, Monika Joanna Piotrowska, Urszula Foryś, Ewa Nizińska. Model of tumour angiogenesis -- analysis of stability with respect to delays. Mathematical Biosciences and Engineering, 2013, 10(1): 19-35. doi: 10.3934/mbe.2013.10.19

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