Time Delay In Necrotic Core Formation - Marek Bodnar; Urszula Foryś (Mathematical Biosciences and Engineering)
A simple model of avascular solid tumor dynamics is studied inthe paper. The model is derived on the basis of reaction-diffusion dynamicsand mass conservation law. We introduce time delay in a cell proliferationprocess. In the case studied in this paper, the model reduces to one ordinaryfunctional-differential equation of the form that depends on the existence ofnecrotic core. We focus on the process of this necrotic core formation andthe possible influence of delay on it. Basic mathematical properties of themodel are studied. The existence, uniqueness and stability of steady state arediscussed. Results of numerical simulations are presented.