Summary: We consider the mathematical model for the viral dynamics of HIV-1 introduced by L. Rong
et al. [J. Theor. Biol. 247, 804–818 (2007); see also Bull. Math. Biol. 69, No. 6, 2027–2060 (2007; Zbl 05265722
)]. One main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class. The viral dynamics is described by four nonlinear ordinary differential equations. Rong et al. have analyzed the stability of the infected equilibrium locally. We perform a global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on a higher-order generalization of Bendixson’s criterion. We obtain sufficient conditions in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.