Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
Math Biosci Eng. 2013 Feb;10(1):19-35. doi: 10.3934/mbe.2013.10.19.
In the paper we consider the model of tumour angiogenesis process proposed by Bodnar and Fory (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.
在本文中，我们考虑了 Bodnar 和 Fory（2009）提出的肿瘤血管生成过程模型。该模型结合了 Hahnfeldt 等人（1999 年）和 Agur 等人（2004 年）的思想，描述了肿瘤、血管生成蛋白和有效血管密度的动力学。目前的分析集中在模型动力学对系统中引入的时滞的依赖性上。这些时滞反映了增殖/死亡项和血管形成/退化对刺激的反应中的时间滞后。结果表明，动力学强烈依赖于模型参数，并且行为独立于延迟的大小，以及随着延迟的增加可以获得多个稳定性开关。
