Stability properties and Hopf bifurcation of a delayed viral infection model with lytic immune response

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Abstract

A class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings. The effect of time delay on stabilities of the equilibria is given. The sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no-immune response equilibrium are given. We also get the sufficient criteria for stability switch of the positive equilibrium. Numerical simulations are carried out to explain the mathematical conclusions.

Keywords

Viral infection
Lytic immune response
Center manifold
Hopf bifurcation

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This work is supported by the National Natural Science Foundation of China (10771179), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (2010IRTSTHN006) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province (104200510011).