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Analysis of stability and Hopf bifurcation for an HIV infection model with time delay. (English) Zbl 1136.92027

Summary: A class of more general HIV infection models with time delay is proposed based on some important biological meanings. The effect of time delays on the stability of the equilibria of the infection model has been studied. Sufficient criteria for stability switch of the infected equilibrium and the local and global asymptotic stability of the viral-free equilibrium are given. Using the normal form theory and center manifold arguments, explicit formulae which determine the stability, the direction and the period of bifurcating periodic solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.

MSC:

92C60 Medical epidemiology
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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