The idea is put forward and analysed numerically, that within an infected person HIV evolves to increase its reproductivity within the population of CD4+ cells. A mathematical model predicts initial viremia and CD4+ cell drop after HIV infection and thereafter a slow progressive decline in the number of CD4+ cells, although for an extended period HIV is kept at a relatively low level by an active immune response. The time span T until the number of CD4+ cells falls below 20 per cent of its normal value depends on several model parameters. Assuming Gaussian distributions for these parameters, the model predicts a distribution function for T which resembles the observed distribution function for the incubation period to AIDS.