  Mathematical models of angiogenesis, pioneered by P. Hahnfeldt, are under
study. To enrich the dynamics of three models, we introduced biologically
motivated time-varying delays. All models under study belong to a special class
of nonlinear nonautonomous systems with delays. Explicit conditions for the
existence of positive global solutions and the equilibria solutions were
obtained. Based on a notion of an M-matrix, new results are presented for the
global stability of the system and were used to prove local stability of one
model. For a local stability of a second model, the recent result for a
Lienard-type second-order differential equation with delays was used. It was
shown that models with delays produce a complex and nontrivial dynamics. Some
open problems are presented for further studies.
