A Stochastic Model for the HIV/AIDS Dynamic Evolution

Abstract

This paper analyses the HIV/AIDS dynamic evolution as defined by CD4 levels, from a macroscopic point of view, by means of homogeneous semi-Markov stochastic processes. A large number of results have been obtained including the following conditional probabilities: an infected patient will be in statejafter a timetgiven that she/he entered at time 0 (starting time) in statei; that she/he will survive up to a timet, given the starting state; that she/he will continue to remain in the starting state up to timet; that she/he reach stagejof the disease in the next transition, if the previous state wasiand no state change occurred up to timet. The immunological states considered are based on CD4 counts and our data refer to patients selected from a series of 766 HIV-positive intravenous drug users.