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2. Simplified Needle Exchange Model This exercise helps you perform a cost-effectiveness analysis of needle exchange using a ridiculously simple version of the circulation theory argument. Here we go. (a) Let \ equal the shared injection rate per drug user per unit time (so X is the average number of injections with previously used needles per injector per unit time), and V be the needle exchange rate per drug injector per unit time (so V is the average number of needles exchanged per drug injector per unit time). Both of these quantities refer to drug injectors participating in a needle exchange program (and do not apply to drug injectors not in the program). Suppose a drug injector holds a previously used needle and consider the fol- lowing possible next events from the perspective of a needle: the needle is used for injection (i.e. a shared injection occurs), or the needle is exchanged. Argue that the probability that the needle is used for injection at the next event is given by Prinsect=-11 = (b) Let r be the incidence rate of new HIV infections per drug injector per unit time in the population prior to the establishment of a needle exchange program, and let r* equal the incidence rate of HIV infections in the population after the establishment of the needle exchange. Using your results from (a) argue that = + 1/ and as a consequence - Does this make sense intuitively? Ask what happens to Ar if V is very large or very small relative to A. (c) Here are some actual data from 4 different needle exchange programs in the United States. For each of the programs, estimate the cost per HIV infection averted per year using (b). Considering that each new HIV infection costs society roughly $200,000 in medical care costs alone, does needle exchange appear cost effective? City A C'ity B City C City D HIV Incidence/injector/yT 3% 3% 1.46% 2.64% Shared injection rate/week (A) 3 3 2 2 Total needles exchanged per year 40,000 450,000 75,000 350,000 Client-years of participation 300 15,000 450 1, 500 Annual program budget $250,000 $600,000 $125,000 $250,000

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