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
(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
(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
Shared injection rate/week (A)
Total needles exchanged per year
Client-years of participation
Annual program budget
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.