A steady-state model for the spread of HIV among drug users

This paper proposes a new approach to model the spread of HIV/AIDS among in travenous drug users (IVDUs). The focus is on a group of n IVDUs within whi ch infective contacts occur, and which evolves in discrete time, subject to group splitting, immigration, and emigration. We are interested in finding the probability distribution of the ultimate number Y-n of HIV infectives produced by the group as time tends to infinity, and obtain a stochastic re cursive equation for it. Although, or the surface, the process resembles a branching process, our results cannot be obtained using techniques from the theory of branching processes. We use the probability metrics approach to obtain limit theorems for the normalized sequence L-n = (Y-n - EYn)n(-1/2). Finally, we consider the behavior of L-n under different sets of regularit y conditions, when for example L-n = (Y-n - EYn)n(-1/alpha) tends to an alp ha-stable distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.