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Antiviral combination therapies consisting of reverse transcriptase inhibitors, protease inhibitors and an integrase inhibitor, have been developed to suppress HIV below the limit of detection. We introduce a mathematical model for the effect of different combination treatment regimens on the dynamics of HIV RNA and CD4 T-cell counts. We will especially focus on modelling the treatment effect of the integrase inhibitor-Raltegravir. The model consists of a system of ordinary differential equations and the parameters were chosen or estimated in order to agree with clinical data of a recent clinical trial. All the numerical simulations were calculated with Matlab.