### Abstract

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

Pages | 286-299 |

Number of pages | 13 |

Journal | Discrete and Continuous Dynamical Systems - Series A |

Volume | 2009 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- hiv
- aids
- infectivity
- equilibrium analysis
- stability analysis
- global stability

### Cite this

*Discrete and Continuous Dynamical Systems - Series A*,

*2009*, 286-299. https://doi.org/10.3934/proc.2009.2009.286

}

*Discrete and Continuous Dynamical Systems - Series A*, vol. 2009, pp. 286-299. https://doi.org/10.3934/proc.2009.2009.286

**An improved optimistic three-stage model for the spread of HIV amongst injecting intravenous drug users.** / Greenhalgh, David; Al-Fwzan, Wafa; Saudi-Arabian Government (Funder).

Research output: Contribution to journal › Article

TY - JOUR

T1 - An improved optimistic three-stage model for the spread of HIV amongst injecting intravenous drug users

AU - Greenhalgh, David

AU - Al-Fwzan, Wafa

AU - Saudi-Arabian Government (Funder)

PY - 2009

Y1 - 2009

N2 - We start off this paper with a brief introduction to modeling Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) amongst sharing, injecting drug users (IDUs). Then we describe the mathematical model which we shall use which extends an existing model of the spread of HIV and AIDS amongst IDUs by incorporating loss of HIV infectivity over time. This is followed by the derivation of a key epidemiological parameter, the basic reproduction number R0. Next we give some analytical equilibrium, local and global stability results. We show that if R0 >e 1 then the disease will always die out. For R0 > 1 there is the disease-free equilibrium (DFE) and a unique endemic equilibrium. The DFE is unstable. An approximation argument shows that we expect the endemic equilibrium to be locally stable. We next discuss a more realistic version of the model, relaxing the assumption that the number of addicts remains constant and obtain some results for this model. The subsequent section gives simulations for both models confirming that if R0 >e 1 then the disease will die out and if R0 > 1 then if it is initially present the disease will tend to the unique endemic equilibrium. The simulation results are compared with the original model with no loss of HIV infectivity. Next the implications of these results for control strategies are considered. A brief summary concludes the paper.

AB - We start off this paper with a brief introduction to modeling Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) amongst sharing, injecting drug users (IDUs). Then we describe the mathematical model which we shall use which extends an existing model of the spread of HIV and AIDS amongst IDUs by incorporating loss of HIV infectivity over time. This is followed by the derivation of a key epidemiological parameter, the basic reproduction number R0. Next we give some analytical equilibrium, local and global stability results. We show that if R0 >e 1 then the disease will always die out. For R0 > 1 there is the disease-free equilibrium (DFE) and a unique endemic equilibrium. The DFE is unstable. An approximation argument shows that we expect the endemic equilibrium to be locally stable. We next discuss a more realistic version of the model, relaxing the assumption that the number of addicts remains constant and obtain some results for this model. The subsequent section gives simulations for both models confirming that if R0 >e 1 then the disease will die out and if R0 > 1 then if it is initially present the disease will tend to the unique endemic equilibrium. The simulation results are compared with the original model with no loss of HIV infectivity. Next the implications of these results for control strategies are considered. A brief summary concludes the paper.

KW - hiv

KW - aids

KW - infectivity

KW - equilibrium analysis

KW - stability analysis

KW - global stability

U2 - 10.3934/proc.2009.2009.286

DO - 10.3934/proc.2009.2009.286

M3 - Article

VL - 2009

SP - 286

EP - 299

JO - Discrete and Continuous Dynamical Systems - Series A

T2 - Discrete and Continuous Dynamical Systems - Series A

JF - Discrete and Continuous Dynamical Systems - Series A

SN - 1078-0947

ER -