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

Gleb Haynatzki, J. M. Gani, S. T. Rache V

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)181-195
Number of pages15
JournalMathematical and Computer Modelling
Volume32
Issue number1-2
DOIs
StatePublished - Jul 1 2000

Fingerprint

Probability distributions
Drugs
Branching process
Probability Metrics
Tend
Stable Distribution
Immigration
Regularity Conditions
Limit Theorems
Discrete-time
Probability Distribution
Infinity
Model
Contact
Stable distribution
Emigration
Limit theorems
Probability distribution
Regularity

Keywords

  • Limit theorems
  • Probability metrics
  • Spread of HIV/AIDS
  • Stable distributions.

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications

Cite this

A steady-state model for the spread of HIV among drug users. / Haynatzki, Gleb; Gani, J. M.; Rache V, S. T.

In: Mathematical and Computer Modelling, Vol. 32, No. 1-2, 01.07.2000, p. 181-195.

Research output: Contribution to journalArticle

Haynatzki, Gleb ; Gani, J. M. ; Rache V, S. T. / A steady-state model for the spread of HIV among drug users. In: Mathematical and Computer Modelling. 2000 ; Vol. 32, No. 1-2. pp. 181-195.
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