Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response

Yafia, Radouane

doi:https://doi.org/10.1155/DDNS/2006/95296

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Volume 2006 | Article ID 095296 | https://doi.org/10.1155/DDNS/2006/95296

Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response

Radouane Yafia¹

Received26 Aug 2005

Accepted28 Nov 2005

Published26 Jun 2006

Abstract

The dynamics of the model for tumor-immune system competition with negative immune response and with one delay investigated. We show that the asymptotic behavior depends crucially on the time delay parameter. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state, by using the delay as a parameter of bifurcation. The obtained results provide the oscillations given by the numerical study in M. Gałach (2003), which are observed in reality by Kirschner and Panetta (1998).

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Copyright

Copyright © 2006 Radouane Yafia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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