The general mixing of addicts and needles in a variable-infectivity needle-sharing environment

D. Greenhalgh, F. Lewis

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. The model we discuss focuses on the transmission of HIV through the sharing of contaminated drug injection equipment and in particular we examine the mixing of addicts and needles when the AIDS incubation period is divided into three distinct infectious stages. The impact of this assumption is to greatly increase the complexity of the HIV transmission mechanism. We begin the paper with a brief literature review followed by the derivation of a model which incorporates three classes of infectious addicts and three classes of infectious needles and where a general probability structure is used to represent the interaction of addicts and needles of varying levels of infectivity. We find that if the basic reproductive number is less than or equal to unity then there exists a globally stable disease free equilibrium. The model possesses an endemic equilibrium solution if the basic reproductive number exceeds unity. We then conduct a brief simulation study of our model. We find that the spread of disease is heavily influenced by the way addicts and needles of different levels of infectivity interact.
LanguageEnglish
Pages561-598
Number of pages37
JournalJournal of Mathematical Biology
Volume44
Issue number6
DOIs
Publication statusPublished - 2002

Fingerprint

Needle Sharing
Needles
Sharing
pathogenicity
Basic Reproductive number
HIV
Acquired Immunodeficiency Syndrome
Drugs
drug injection
Drug Users
Model
Endemic Equilibrium
Literature Review
Equilibrium Solution
Less than or equal to
Injection
Exceed
Equipment and Supplies
Injections
Simulation Study

Keywords

  • HIV
  • AIDS
  • dug use
  • needle exchange
  • simulation
  • stability analysis
  • mathematical biology

Cite this

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The general mixing of addicts and needles in a variable-infectivity needle-sharing environment. / Greenhalgh, D.; Lewis, F.

In: Journal of Mathematical Biology, Vol. 44, No. 6, 2002, p. 561-598.

Research output: Contribution to journalArticle

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KW - HIV

KW - AIDS

KW - dug use

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KW - simulation

KW - stability analysis

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