### Abstract

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

Pages | 491-512 |

Number of pages | 21 |

Journal | Stochastic Models |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 |

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### Keywords

- statistics
- stochastic models
- mathematics
- HIV
- AIDS
- epidemiology

### Cite this

*Stochastic Models*,

*17*(4), 491-512. https://doi.org/10.1081/STM-120001220

}

*Stochastic Models*, vol. 17, no. 4, pp. 491-512. https://doi.org/10.1081/STM-120001220

**Stochastic models for the spread of HIV among intravenous drug users.** / Greenhalgh, David; Lewis, Fraser.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Stochastic models for the spread of HIV among intravenous drug users

AU - Greenhalgh, David

AU - Lewis, Fraser

PY - 2001

Y1 - 2001

N2 - In this paper we examine the spread of HIV when this disease is transmitted through the random sharing of contaminated drug injection equipment. We first model the spread of disease using a standard set of behavioral assumptions discussed by Kaplan [1]. We demonstrate that deterministic and stochastic models based on these assumptions behave very similarly and use a branching process approximation to show that if the basic reproductive number, R0, is less than or equal to unity then the disease will always become extinct. If R0>1 then, although the disease might take off, it is still possible for it to die out, and we calculate the probability of extinction. This is not of the simple form R0-a, where a is the initial number of infectious addicts, which might have been expected from Whittle's stochastic threshold theorem [2]. We next discuss an extended model that incorporates a three-stage AIDS incubation period and again examine a branching process approximation. We finally explore the extent to which control strategies such as needle exchange and improved needle cleaning can reduce the risk of a HIV epidemic before concluding with a brief discussion.

AB - In this paper we examine the spread of HIV when this disease is transmitted through the random sharing of contaminated drug injection equipment. We first model the spread of disease using a standard set of behavioral assumptions discussed by Kaplan [1]. We demonstrate that deterministic and stochastic models based on these assumptions behave very similarly and use a branching process approximation to show that if the basic reproductive number, R0, is less than or equal to unity then the disease will always become extinct. If R0>1 then, although the disease might take off, it is still possible for it to die out, and we calculate the probability of extinction. This is not of the simple form R0-a, where a is the initial number of infectious addicts, which might have been expected from Whittle's stochastic threshold theorem [2]. We next discuss an extended model that incorporates a three-stage AIDS incubation period and again examine a branching process approximation. We finally explore the extent to which control strategies such as needle exchange and improved needle cleaning can reduce the risk of a HIV epidemic before concluding with a brief discussion.

KW - statistics

KW - stochastic models

KW - mathematics

KW - HIV

KW - AIDS

KW - epidemiology

UR - http://www.tandfonline.com/toc/lstm20/17/4

U2 - 10.1081/STM-120001220

DO - 10.1081/STM-120001220

M3 - Article

VL - 17

SP - 491

EP - 512

JO - Stochastic Models

T2 - Stochastic Models

JF - Stochastic Models

SN - 1532-6349

IS - 4

ER -