MATHEMATICAL MODELS FOR HIV TRANSMISSION IN GROUPS OF INJECTING DRUG USERS VIA SHARED DRUG EQUIPMENT

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Abstract
In many western countries, including Italy, sharing drug injection equipment is one of the main causes of HIV/AIDS spread. In this paper we propose an extension of the classical one population and multiple population mathematical models for the spread of HIV, by providing explicit expressions for the force of infection in terms of a stochastic model for the behaviour of individuals in a friendship group with respect to needle sharing. For the single population model we provide a threshold theorem in terms of the basic reproductive ratio. The extension to the multiple population case is discussed in terms of mixing matrices. The qualitative behaviour for different choices of such matrices is shown by computer simulations.

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