On the AIDS incubation distribution (Q2573986)

A Markov chain model is proposed for the description of the latent period between the HIV infection and AIDS development. \(k\) latent sub-stages \(S_1\),\dots, \(S_k\) are assumed with possible transitions \(S_1\leftrightarrows S_2\leftrightarrows\dots\leftrightarrows S_k\) and there also can be a transition from \(S_i\) to the AIDS stage for any \(i\). In the second version of the model there exists some intermediate (also latent) stage \(B\) between \(S_i\) and AIDS (common for all \(S_i\)). The authors describe the distribution of the incubation period (from \(S_1\) to AIDS) which is a mixture of Gamma distributions and derive its mean. The methods of Ten and Bayers and Longini et al. are considered as examples.