Three stage AIDS incubation period: a worst case scenario using addict-needle interaction assumptions

In this paper we develop and analyse a model for the spread of HIV/AIDS amo ngst a population of injecting drug users. We start off with a brief litera ture survey and review; this is followed by the derivation of a model which allows addicts to progress through three distinct stages of variable infec tivity prior to the onset of full blown AIDS and where the class of infecti ous needles is split into three according to the different levels of infect ivity in addicts, Given the structure of this model we are required to make assumptions regarding the interaction of addicts and needles of different infectivity levels. We deliberately choose these assumptions so that our mo del serves as an upper bound for the prevalence of HIV under the assumption of a three stage AIDS incubation period. We then perform an equilibrium an d stability analysis on this model. We find that there is a critical thresh old parameter Ro which determines the behaviour of the model. If R-0 less t han or equal to 1, then irrespective of the initial conditions of the syste m HIV will die out in all addicts and all needles. If R-0 > 1, then there i s a unique endemic equilibrium which is locally stable if, as is realistic, the time scale on which addicts inject is much shorter than that of the ot her epidemiological and demographic processes. Simulations indicate that if R0 > 1, then provided that disease is initially present in at least one ad dict or needle it will tend to the endemic equilibrium. In addition eye der ive conditions which guarantee this. We also find that under calibration th e long term prevalence of disease in our variable infectivity model is alwa ys greater than in an equivalent constant infectivity model. These results are confirmed and explored further by simulation. We conclude with a short discussion. (C) 2001 Elsevier Science Inc. All rights reserved.