Modelling the spread of HIV/AIDS amongst injecting drug users
The sharing of injecting equipment by injecting drug users (IDUs) is one of the primary causes of the spread of HIV in Scotland. Mathematical models of disease spread can explore the transmission dynamics and can assist in evaluating control strategies such as needle exchanges. A simple deterministic model is examined and local and global stability results are presented. A deterministic model in which infected IDUs are considered separately from uninfected IDUs is created. The infectivity of a needle is then examined. It is first assumed that the infectivity of a needle depends on the amount of infectious material within it, then models in which this infectivity varies over time from injection are explored. Models in which the initial infectiousness of a needle depend on the length of time the person who infected it had been infected with HIV are also presented. A stochastic model is developed and explored in a threefold manner; analytically, numerically and using Monte-Carlo simulation methods. In particular, the probability that the disease dies out is examined. Although these simple models use only a small number of parameters, little is known about the values that these parameters may take. Seroprevalence and behavioural data from Glasgow are used to inform these models, and also to provide an estimate for the probability than an IDU becomes infected after injecting with an infected needle. The effect that the variability in the parameter values may have on the spread of the disease is examined by performing both an uncertainty analysis and a sensitivity analysis. These show that the two behavioural parameters that can be altered by control strategies have a greater influence on the spread of the disease than some other parameters.