A differential equation model of HIV infection of CD4+T-cells with cure rate

A differential equation model of HIV infection of CD4+T-cells with cure rate is studied. We prove that if the basic reproduction number R0<1, the HIV infection is cleared from the T-cell population and the disease dies out; if R0>1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if R0>1. Furthermore, we also obtain the conditions for which the system exists an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.