Qualitative analysis of a free boundary problem for tumor growth under the action of periodic external inhibitors

In this paper, a free boundary problem for a solid avascular tumor growth under the action of periodic external inhibitors with time delays in proliferation is studied. Sufficient conditions for the global stability of tumor-free equilibrium are given. Moreover, if external concentration of nutrients is large, we also prove that the tumor will not disappear and determine the conditions under which there exist periodic solutions to the model. The results show that the periodicity of the inhibitor may imply periodicity of the size of the tumor. More precisely, if sigma(infinity) (the concentration of external nutrients) is greater than mu beta* + v, where mu,v are two constants; beta* = max(0 <= t <=omega) phi(t); phi(t) is a periodic function which can be interpreted as a treatment and omega is the period of phi(t). Results are illustrated by computer simulations.