Asymptotic properties of a HIV-1 infection model with time delay

Based on some important biological meanings, a class of more general HIV-1 infection models with time delay is proposed in the paper. In the HIV-1 infection model, time delay is used to describe the time between infection of uninfected target cells and the emission of viral particles on a cellular level as proposed by Herz et al. [A.V.M. Herz, S. Bonhoeffer, R.M. Anderson, R.M. May, M.A. Nowak, Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay, Proc. Natl. Acad. Sci. USA 93 (1996) 7247–7251]. Then, the effect of time delay on stability of the equilibria of the HIV-1 infection model has been studied and sufficient criteria for local asymptotic stability of the infected equilibrium and global asymptotic stability of the viral free equilibrium are given.