Open Access
2012 Chaos in a Tumor Growth Model with Delayed Responses of the Immune System
M. Saleem, Tanuja Agrawal
J. Appl. Math. 2012: 1-16 (2012). DOI: 10.1155/2012/891095


A simple prey-predator-type model for the growth of tumor with discrete time delay in the immune system is considered. It is assumed that the resting and hunting cells make the immune system. The present model modifies the model of El-Gohary (2008) in that it allows delay effects in the growth process of the hunting cells. Qualitative and numerical analyses for the stability of equilibriums of the model are presented. Length of the time delay that preserves stability is given. It is found that small delays guarantee stability at the equilibrium level (stable focus) but the delays greater than a critical value may produce periodic solutions through Hopf bifurcation and larger delays may even lead to chaotic attractors. Implications of these results are discussed.


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M. Saleem. Tanuja Agrawal. "Chaos in a Tumor Growth Model with Delayed Responses of the Immune System." J. Appl. Math. 2012 1 - 16, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1244.37049
MathSciNet: MR2910923
Digital Object Identifier: 10.1155/2012/891095

Rights: Copyright © 2012 Hindawi

Vol.2012 • 2012
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