Assessing the impact of variable infectivity on the transmission of HIV among intravenous drug users
The spread of HIV and AIDS is a serious and increasing global problem with the sharing of contaminated injection equipment a primary cause of HIV infection in the developed world. Mathematical models of disease transmission allow us to assess the impact of different epidemiological and behavioural assumptions on the long term behaviour of disease. Initially a simple deterministic model is examined which allows intravenous drug users to progress through three different infectious stages after initial infection with HIV and prior to the development of AIDS. This model is then developed to also allow contaminated injection equipment to exist in three different states of infectivity. The resulting model contains a number of parameters, which while potentially important, are extremely difficult to estimate. In response to this, several special cases are examined which represent intuitive upper and lower bounds for the spread of disease. In each case an equilibrium and stability analysis is presented. Later these special cases, together with a generalisation of them, are compared with a well established single stage infectivity model to ascertain whether the inclusion of variable infectivity increases the predicted spread of disease. We find that the impact of variable infectivity depends on a number of factors and can lead to either an increase or decrease in the prevalence of disease. Testing drug users for the presence of HIV has been proposed as a method of reducing the incidence of HIV. Using the previously discussed upper and lower bound variable infectivity models, we examine the effect of testing addicts for HIV using a number of different infectivity assumptions. We find that under certain conditions HIV testing can be an effective control strategy against the future spread of HIV. This is followed by a short discussion of sensitivity analysis of these models. While predominantly discussing deterministic models we conclude with a brief discussion of stochastic models and demonstrate the behaviour of these models using simulation.