Journal of Applied Mathematics

Chaos in a Tumor Growth Model with Delayed Responses of the Immune System

M. Saleem and Tanuja Agrawal

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 891095, 16 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495111

Digital Object Identifier
doi:10.1155/2012/891095

Mathematical Reviews number (MathSciNet)
MR2910923

Zentralblatt MATH identifier
1244.37049

Citation

Saleem, M.; Agrawal, Tanuja. Chaos in a Tumor Growth Model with Delayed Responses of the Immune System. J. Appl. Math. 2012 (2012), Article ID 891095, 16 pages. doi:10.1155/2012/891095. https://projecteuclid.org/euclid.jam/1355495111


Export citation