摘要

In this paper we continue the analysis of a family of models with delays describing the process of angiogenesis, that is a physiological process involving the growth of new blood vessels from pre-existing ones. This family of models depends on two time delays and a parameter alpha is an element of [0, 1] which reflects how strongly the vessels dynamics depends on the ratio between tumour and vessels volume. Previously, in Piotrowska and Forys (2011) [11] we have considered three cases with either one of the delays equals to 0 or both delays equal to each other. Here, we focus on the case with two unequal and non-zero delays present in the model, and study the dynamics depending on the parameter alpha, including stability switches, Hopf bifurcation and stability of arising periodic orbits for different alpha is an element of [0, 1], especially for alpha = 1 and alpha = 0 which reflects the Hahnfeldt et al. model and d%26apos;Onofrio %26 Gandolfi model, respectively. Moreover, we consider the influence of constant treatment on the model dynamics. It occurs that the treatment not only decreases the tumour size at a steady state but also enlarges the region of stability.

  • 出版日期2013-9-1