MATHEMATICAL-MODELING OF THE SPREAD OF HIV AIDS AMONGST INJECTING DRUG-USERS/

In this paper we develop and analyse a model for the spread of HIV/AID S amongst a population of injecting drug users. Our work is based on a model originally due to Kaplan (1989, Rev. Inf. Diseases 11, 289-98). We start off with a brief literature survey and review; this is follo wed up by a detailed description of Kaplan's model. We then outline a more realistic extension of Kaplan's model. Then we perform an equilib rium and stability analysis on this model. We find that there is a cri tical threshold parameter R(0) which determines the behaviour of the m odel. If R(0) less than or equal to 1 there is a unique disease-free e quilibrium, and if R(0) < 1 the disease dies out. If R(0) > 1 this dis ease-free equilibrium is unstable, and in addition there is a unique e ndemic equilibrium which is locally stable. If a certain condition is satisfied (and for Kaplan's model this condition is always satisfied), additional complete global-stability results are shown. These results are confirmed and explored further by simulation.