The cubic growth of AIDS cases: general dependence on early infection rates and distribution of times to appearance of clinical symptoms.

An observed cubic dependence on time of the cumulative growth in numbers of AIDS patients is shown to be the leading term of a power series in general. The cubic leading term follows from a nearly model-independent description of the rate of HIV infection, provided only that there is a distribution of incubation times to the appearance of clinically diagnosed AIDS symptoms with a finite initial derivative, that none of those infected exhibit immediate indications of illness, and that the epidemic begins with a finite initial rate of infection.