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In this talk.I will present some analytic results on an ordinary differential equation system that models fighting the HIV-1 virus with a genetically modified virus.We show that when the basic reproduction ratio $-nathcal R_0<1 $.then the infection-free equilibrium $E_0$ is globally asymptotically stable: when $mathcal R_0>1$.$E_0$ loses its stability and there is the single infection-equilibrium $E_s$.If $mathcal R_0 in (1.1+delta)$ where $delta$ is a positive constant explicitly depending on system parameters.then the single infection-equilibrium $E_s$ that is globally asymptotically stable.