### Abstract

Language | English |
---|---|

Pages | 561-598 |

Number of pages | 37 |

Journal | Journal of Mathematical Biology |

Volume | 44 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

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

### Cite this

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*Journal of Mathematical Biology*, vol. 44, no. 6, pp. 561-598. https://doi.org/10.1007/s002850200140

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - The general mixing of addicts and needles in a variable-infectivity needle-sharing environment

AU - Greenhalgh, D.

AU - Lewis, F.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - HIV

KW - AIDS

KW - dug use

KW - needle exchange

KW - simulation

KW - stability analysis

KW - mathematical biology

UR - http://dx.doi.org/10.1007/s002850200140

U2 - 10.1007/s002850200140

DO - 10.1007/s002850200140

M3 - Article

VL - 44

SP - 561

EP - 598

JO - Journal of Mathematical Biology

T2 - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6

ER -