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

Abstract A differential equation model of HIV infection of CD4+ T-cells with cure rate is studied. We prove that if the basic reproduction number R 0 1 , the HIV infection is cleared from the T-cell population and the disease dies out; if R 0 > 1 , the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if R 0 > 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.

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