title: Mathematical modelling of the spread of HIV/AIDS amongst injecting drug users.
abstract: In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. Our work is based on a model originally due to Kaplan (1989, Rev. Inf. Diseases 11, 289-98). We start off with a brief literature survey and review; this is followed up by a detailed description of Kaplan's model. We then outline a more realistic extension of Kaplan's model. Then we perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter Rzero which determines the behaviour of the model. If Rzero < or = 1 there is a unique disease-free equilibrium, and if Rzero < 1 the disease dies out. If Rzero > 1 this disease-free equilibrium is unstable, and in addition there is a unique endemic equilibrium which is locally stable. If a certain condition is satisfied (and for Kaplan's model this condition is always satisfied), additional complete global-stability results are shown. These results are confirmed and explored further by simulation.
authors.affiliation: Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, UK.
authors.forename: D
authors.initials: D
authors.lastname: Greenhalgh
authors.forename: G
authors.initials: G
authors.lastname: Hay
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000150:complications* / Q000635:transmission*; D003198:Computer Simulation; D015658:HIV Infections / Q000150:complications* / Q000635:transmission*; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D016485:Needle Sharing; D015819:Substance Abuse, Intravenous / Q000150:complications*