Dynamics Analysis and Limit Cycle in a Delayed Model for Tumor Growth with Quiescence

The model analyzed in this paper is based on the unstructured model set forth by Gyllenberg and Webb (1989) without delay, which describes an interaction between the proliferating and quiescent cells tumor. In the present paper we consider the model with one delay and a unique positive equilibrium E∗ and the other is trivial. Their dynamics are studied in terms of the local stability of the two equilibrium points and of the description of the Hopf bifurcation at E∗ , that is proven to exists as the delay (taken as a parameter) crosses some critical value. We suggest to examine in laboratory experiments how to employ these results for containing tumor growth.