Stable periodic oscillations in a two-stage cancer model of tumor and immune system interactions
This paper presents qualitative and bifurcation analysis near the degenerate equilibrium in a two-stage cancer model of interactions betweenlymphocyte cells and solid tumor and contributes to a better understanding of the dynamics of tumor and immune system interactions.We first establish the existe...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.347 |
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| Summary: | This paper presents qualitative and bifurcation analysis near the degenerate equilibrium in a two-stage cancer model of interactions betweenlymphocyte cells and solid tumor and contributes to a better understanding of the dynamics of tumor and immune system interactions.We first establish the existence of Hopf bifurcation in the 3-dimensional cancer model and rule out the occurrence of the degenerateHopf bifurcation. Then a general Hopf bifurcation formula is applied to determine the stability of the limit cycle bifurcated fromthe interior equilibrium. Sufficient conditions on the existence of stable periodic oscillations of tumor levels are obtained forthe two-stage cancer model. Numerical simulations are presented to illustrate the existence of stable periodic oscillations with reasonable parametersand demonstrate the phenomenon of long-term tumor relapse in the model. |
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| ISSN: | 1551-0018 |