`Mathematical Problems in EngineeringVolume 2007, Article ID 65636, 14 pageshttp://dx.doi.org/10.1155/2007/65636`
Research Article

## A Stochastic Model for the HIV/AIDS Dynamic Evolution

1Department of Science, University G. D'Annunzio of Chieti-Pescara, viale Pindaro 42, Pescara 65127, Italy
2Department of Drug Sciences, University G. D'Annunzio of Chieti-Pescara, via dei Vestini, Chieti 66100, Italy
3Division of Infectious Diseases, Chieti Hospital, via dei Vestini, Chieti 66100, Italy
4CESIAF, EURIA, Universite de Bretagne Occidentale, 6 avenue le Gorgeu, CS 93837, Brest, Cedex 3 29238, France
5Department of Medical Oncology, University G. D'Annunzio of Chieti-Pescara, via dei Vestini 66, Chieti 66100, Italy
6Department of Mathematics for the Economics, Financial and Insurance Decisions, University La Sapienza of Rome, via del Castro Laurenziano 9, Rome 00161, Italy

Received 28 September 2006; Revised 28 February 2007; Accepted 3 June 2007

Copyright © 2007 Giuseppe Di Biase et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 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 state j after a time t given that she/he entered at time 0 (starting time) in state i; that she/he will survive up to a time t, given the starting state; that she/he will continue to remain in the starting state up to time t; that she/he reach stage j of the disease in the next transition, if the previous state was i and no state change occurred up to time t. 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.