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**Dynamical behavior of a delay virus dynamics model with CTL immune response.**
*(English)*
Zbl 1204.34110

From the abstract: The dynamical behaviour of a virus dynamics model with CTL immune response and time delay is studied. Time delay is used to describe the time between the infected cell and the emission of viral particles on a cellular level. The effect of time delay on the stability of the equilibria of the CTL immune response model is studied and sufficient criteria for local asymptotic stability of the disease-free equilibrium, immune-free equilibrium and endemic equilibrium and global asymptotic stability of the disease-free equilibrium are given. Some conditions for Hopf bifurcation at the immune-free equilibrium and the endemic equilibrium are also obtained by using the time delay as a bifurcation parameter. Numerical simulation with some hypothetical sets of data is carried out to support the analytical findings.

Reviewer: Eva Sanchez (Madrid)

### MSC:

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K18 | Bifurcation theory of functional-differential equations |

34K20 | Stability theory of functional-differential equations |

92C60 | Medical epidemiology |

### Keywords:

virus dynamics; CTL immune response; delay; asymptotic stability of equilibria; Hopf bifurcation
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\textit{X. Shi} et al., Nonlinear Anal., Real World Appl. 11, No. 3, 1795--1809 (2010; Zbl 1204.34110)

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