A mathematical model to describe the risk of infection from sharing injection equipment

A mathematical model is presented that describes the probability of a subject becoming infected as a result of sharing equipment used for percutaneous injections. This risk is a function of (a) the number of syringes shared by the subject, (b) the probability of a syringe becoming contaminated after being used once by an infective person, (c) the probability of a person becoming infected after using a contaminated syringe once, (d) the number of persons who have previously used each syringe shared by the subject, (e) the prevalence of infectivity in the group from which these previous users are drawn, (f) the number of times each syringe has been used by each previous user, and (g) the number of times the subject uses it. Simulations with the model suggest mainly that (i) when each shared syringe has been used previously by only one person, the number of persons with whom syringes are shared is more important than the number of syringes; (ii) the reverse is true when each shared syringe has previously been used by many persons; and (iii) for an equal number of injections, the "shooting gallery" type of sharing can be much more risky than other kinds of sharing, but this difference decreases as the infections becomes more prevalent.