Analysis of a differential equation model of HIV infection of CD4+ T -cells with saturated reverse function

In this paper, an ordinary differential equation model of HIV infection of CD4 + T-cells with saturated reverse function is studied. We prove that if the basic reproduction number R0 1, the virus-free equilibrium is locally asymptotically stable. And there will exhibit backward bifurcation when R0 1. If R0 1, some feasibly sufficient conditions are obtained for the global asymptotic stability of a positive equilibrium of the model by using the theory of competitive systems, compound matrices and stability of periodic orbits. Furthermore, we also obtain the conditions for which the model exists an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.