On the AIDS incubation distribution

This paper derives the distribution of the AIDS incubation period, by considering two models which are more complicated than the ones usually studied. Model 1 is a multistate Markovian model with probabilities of moving back and forth from one state to the next, with the possible onset of AIDS at any stage. Model 2, of a similar kind, has an added state B for the onset of AIDS-related illnesses, which may also lead to AIDS. There follows a good deal of matrix algebra, ending with distributions of the AIDS incubation period which are (different) weighted sums of Gamma distributions for both Models.