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

Date

2000

Authors

Gani, Joseph
Racherla, Deepti

Journal Title

Journal ISSN

Volume Title

Publisher

Pergamon-Elsevier Ltd

Abstract

This paper proposes a new approach to model the spread of HIV/AIDS among intravenous drug users (IVDUs). The focus is on a group of n IVDUs within which 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 recursive equation for it. Although, on 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) - EY(n))n(-1/2). Finally, we consider the behavior of L(n) under different sets of regularity conditions, when for example L(n) = (Y(n) - EY(n))n(-1/α) tends to an α-stable distribution. (C) 2000 Elsevier Science Ltd.

Description

Keywords

Keywords: Limit theorems; Probability metrics; Spread of HIV/AIDS; Stable distributions.

Citation

Source

Mathematical and Computer Modelling

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1016/S0895-7177(00)00128-X

Restricted until

2037-12-31