Analysis of the family of angiogenesis models with distributed time delays

Abstract

In the presented paper a family of angiogenesis models, that is a generalisation of Hahnfeldt et al. model is proposed. Considered family of models is a system of two differential equations with distributed time delays. The global existence and the uniqueness of the solutions are proved. Moreover, the stability of the unique positive steady state is examined in the case when delay distributions are Erlang or piecewise linear distributions. Theorems guaranteeing the existence of stability switches and occurrence of the Hopf bifurcation are proved. Theoretical results are illustrated by numerical analysis performed for parameters estimated by Hahnfeldt et al. (Cancer Res., 1999).