A simple model of avascular solid tumor dynamics is studied in
the paper. The model is derived on the basis of reaction-diffusion dynamics
and mass conservation law. We introduce time delay in a cell proliferation
process. In the case studied in this paper, the model reduces to one ordinary
functional-differential equation of the form that depends on the existence of
necrotic core. We focus on the process of this necrotic core formation and
the possible influence of delay on it. Basic mathematical properties of the
model are studied. The existence, uniqueness and stability of steady state are
discussed. Results of numerical simulations are presented.
Citation: Marek Bodnar, Urszula Foryś. Time Delay In Necrotic Core Formation[J]. Mathematical Biosciences and Engineering, 2005, 2(3): 461-472. doi: 10.3934/mbe.2005.2.461
Abstract
A simple model of avascular solid tumor dynamics is studied in
the paper. The model is derived on the basis of reaction-diffusion dynamics
and mass conservation law. We introduce time delay in a cell proliferation
process. In the case studied in this paper, the model reduces to one ordinary
functional-differential equation of the form that depends on the existence of
necrotic core. We focus on the process of this necrotic core formation and
the possible influence of delay on it. Basic mathematical properties of the
model are studied. The existence, uniqueness and stability of steady state are
discussed. Results of numerical simulations are presented.
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