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Abstract

This paper discusses the influence of a Reserve Transcriptase Inhibitor (RT Inhibitor or simply RTI) therapy to HIV infection of healthy CD4^+ Tcells. The model is constructed with four variables, namely susceptibleCD4^+ T cells, pre-RT infected CD4^+ Tcells, post-RT infected CD4^+ Tcells, and the HIV viruses. Since the CD4^+ TCells which are produced by the body are affected by the limited density of CD4^+ T cells, the growth of CD4^+ T cells is assumed to be logistic. We investigate the basic reproductive ratio and a critical therapeutic level , together with two points of equilibrium, namely the infection-free equilibrium point and the endemic equilibrium point. In general, the critical therapeutic level critis influenced by the amount of virus produced by the infected CD4^+ Tcells and the magnitude of the efficacy of RTI. Furthermore, the therapeutic effect was analyzed by comparing two different conditions of the endemic equilibrium, when there is no RTI and when the RT inhibitor exists. The stability analysis of the equilibrium point is done through the Routh - Hurwitz criteria.