The idea is put forward and analysed numerically, that within an infec
ted person HIV evolves to increase its reproductivity within the popul
ation of CD4(+) cells. A mathematical model predicts initial viremia a
nd CD4(+) cell drop after HIV infection and thereafter a slow progress
ive decline in the number of CD4(+) cells, although for an extended pe
riod HIV is kept at a relatively low level by an active immune respons
e. The time span T until the number of CD4(+) cells falls below 20 per
cent of its normal value depends on several model parameters. Assumin
g Gaussian distributions for these parameters, the model predicts a di
stribution function for T which resembles the observed distribution fu
nction for the incubation period to AIDS.