Analysis of stability and Hopf bifurcation for an HIV infection model with time delay

A class of more general HIV infection models with time delay is proposed based on some important biological meanings. The effect of time delay on stability of the equilibria of the infection model has been studied. And the 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 argument, the explicit formulaes which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.