title: Effects of heterogeneity on the spread of HIV/AIDS among intravenous drug users in shooting galleries.
abstract: In this article we study the effects of heterogeneity on the spread of HIV and AIDS among a population of injecting drug users. We allow for variability in the rate at which addicts visit shooting galleries, their choice of shooting gallery, and whether or not they clean their needles before use. If the sizes of the different groups of drug users remain constant then there is a key parameter R0, which determines the behavior of the epidemic. If R0 is less than or equal to one then the disease will die out, whereas if R0 exceeds one then the fractions of infected individuals and the fractions of infected needles tend to their unique equilibrium values. These are global results. If we allow for recruitment of new susceptible drug users and deaths from AIDS in the population then the unique endemic equilibrium may become unstable and limit cycles can arise by Hopf bifurcation.
authors.affiliation: Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, Scotland, United Kingdom.
authors.forename: D
authors.initials: D
authors.lastname: Greenhalgh
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000150:complications / Q000635:transmission; D015658:HIV Infections / Q000150:complications / Q000635:transmission*; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D016485:Needle Sharing; D012309:Risk-Taking; D015819:Substance Abuse, Intravenous / Q000150:complications*