American Institute of Mathematical Sciences

Advanced
2005, 2(3): 461-472. doi: 10.3934/mbe.2005.2.461

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, Poland, Poland

Received  January 2005 Revised  July 2005 Published  August 2005

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.
Keywords: delay differential equation, stability., necrotic core, avascular tumor growth, steady state, asymptotic behavior.
Mathematics Subject Classification: 34D05, 34K20, 34K6.
Citation: Marek Bodnar, Urszula Foryś. Time Delay In Necrotic Core Formation. Mathematical Biosciences & Engineering, 2005, 2 (3) : 461-472. doi: 10.3934/mbe.2005.2.461
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