### 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 language | English (US) |
---|---|

Pages (from-to) | 181-195 |

Number of pages | 15 |

Journal | Mathematical and Computer Modelling |

Volume | 32 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1 2000 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Modeling and Simulation
- Computer Science Applications

### Cite this

*Mathematical and Computer Modelling*,

*32*(1-2), 181-195. https://doi.org/10.1016/S0895-7177(00)00128-X

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

Research output: Contribution to journal › Article

*Mathematical and Computer Modelling*, vol. 32, no. 1-2, pp. 181-195. https://doi.org/10.1016/S0895-7177(00)00128-X

}

TY - JOUR

T1 - A steady-state model for the spread of HIV among drug users

AU - Haynatzki, Gleb

AU - Gani, J. M.

AU - Rache V, S. T.

PY - 2000/7/1

Y1 - 2000/7/1

N2 - 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.

AB - 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.

KW - Limit theorems

KW - Probability metrics

KW - Spread of HIV/AIDS

KW - Stable distributions.

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UR - http://www.scopus.com/inward/citedby.url?scp=0034234079&partnerID=8YFLogxK

U2 - 10.1016/S0895-7177(00)00128-X

DO - 10.1016/S0895-7177(00)00128-X

M3 - Article

VL - 32

SP - 181

EP - 195

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 1-2

ER -