Effects of variable infectivity on the spread of HIV/AIDS among intravenous drug users

摘要

In t his paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. We examine the impact on the spread of disease caused by allowing addicts to progress through three distinct stages of variable infestivity prior to the onset of full blown AIDS. We first state a three stage infestivity model of the transmission of HIV and perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter R_0 which determines its behaviour. If R_0 ≤ 1 then there is a unique disease-free equilibrium which is globally stable. If R_0 > 1 then there is a unique endemic equilibrium which is locally stable. Simulations indicate hat if R_0 > 1, then provided disease is initially present it will tend to the endemic equilibrium. We also extend this model to include recruitment and mortality from AIDS, and find that its long-term behaviour is similar to that of the simple model. We then look briefly at a stochastic version of the model and simulations indicate that again the disease dies out if R_0 < 1 and if R_0 > 1 the long-term conditional mean prevalence of disease is approximately the same as in the simple model. We examine the implications of our results for the prevention of the spread of HIV and AIDS amongst drug users. A short discussion concludes the paper.