We construct a model based on biological principles of the interaction of HIV-1 with the CD4+ T cells at primary infection. Most of the parameters are obtained from the literature, the remainder from fitting the output of the model to data from seven patients. On the basis of the model we find that initial viral containment is due to an effective immune response. The viral level after the initial peak, a surrogate marker of disease progression, was determined by the rate of reactivation of memory cells. Differences in this rate may occur because of inter- or intra-individual differences in the capability of memory cells to recognise and dispose of variants of HIV, either due to immune escape mutations within the virus or because the virus directly inhibits reactivation. With no choice of parameters could direct and indirect killing produce the gradual loss in CD4+ T cells with the observed viral behaviour. The loss of CD4+ T cells is perhaps due to defective expansion of activated cells of both HIV specific and nonspecific cells. As less memory cells are produced as a result then this compartment decreases and hence so do naive numbers through less reversion of memory cells to the naive phenotype.