Time Delay In Necrotic Core Formation

Marek Bodnar; Urszula Foryś

doi:10.3934/mbe.2005.2.461

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2005, Volume 2, Issue 3: 461-472. Doi: 10.3934/mbe.2005.2.461

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Time Delay In Necrotic Core Formation

Marek Bodnar^1, and
Urszula Foryś^1,

1.
University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 Warsaw

Received: January 2005

Revised: July 2005

Published: July 2005

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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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Mathematics Subject Classification: 34D05, 34K20, 34K60.

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