Modelling the spread of AIDS among intravenous drug users including variable infectivity, HIV testing and needle exchange

In this article we discuss models of the spread of HIV among intravenous drug users where each infectious user progresses through three distinct phases of HIV infectivity prior to developing AIDS, and where each member of the population is randomly tested for the presence of HIV. We first begin with a brief review and literature survey before outlining the particular problems of modelling the spread of HIV through needle sharing. We then state two models, one which represents a lower bound on the spread of disease and a second an upper bound. We briefly discuss the motivation behind these models before stating an expression for the basic reproductive number. Next we examine the impact of HIV testing in our models using a range of different relative infectivity assumptions. We find that for HIV testing to be an effective control strategy then drug users must be tested regularly for HIV and also substantially reduce the rate at which they share needles once aware of being infected.