A three-stage real diffusion process is used as a model of the T-cell count of an HIV-positive individual who is to receive antiviral therapy such as AZT. The ‘quality of life' of such a person is identified as the sojourn time of the diffusion process above a certain critical T-cell level c. The time of introducing therapy is defined as the first-passage time of the diffusion to a prescribed level z > c. The distribution of the sojourn time of the diffusion above the level c depends on the level z at which therapy is initiated. The expected sojourn time is explicitly computed as a function of z for the particular diffusion process defining the model. There is a simple criterion for determining when to start therapy as early as possible.