Time delays in proliferation process for solid avascular tumour

In the paper, a simple model of solid avascular tumour growth is studied. The model is based on the reaction-diffusion dynamics and mass conservation law and is considered with delay in cell proliferation process. In the case considered in this paper, the model reduces to one ordinary differential equation with time delay which describes the evolution of tumour radius. properties of the model are studied in the paper. Steady-state analysis is presented with respect to the magnitude of delay. Existence of periodic solutions is proved for some parameter values. Global stability is proved for other ones. Results are illustrated by computer simulations.