Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/1671
Title: Bifurcation Analysis of a Modified Tumor-immune System Interaction Model Involving Time Delay
Authors: Kayan, S.
Merdan, Hüseyin
Yafia, R.
Göktepe, S.
125872
Keywords: Hopf bifurcation
tumor immune system competition
reaction-diffusion system
delay differential equations
stability
periodic solutions
Issue Date: 2017
Publisher: EDP Sciences
Source: Kayan, Ş., Merdan, H., Yafia, R., & Goktepe, S. (2017). Bifurcation analysis of a modified tumor-immune system interaction model involving time delay. Mathematical Modelling of Natural Phenomena, 12(5), 120-145.
Abstract: We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.
URI: https://doi.org/10.1051/mmnp/201712508
https://hdl.handle.net/20.500.11851/1671
ISSN: 0973-5348
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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