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Article Excerpt
Two empirical regularities concerning illicit drug use seem hard to reconcile. Initiation ebbs and flows over time, sometimes dramatically, but drug problems tend only to get worse or at best stabilize. These observations appear inconsistent, but to the extent that they can both hold for the same substance, they seem to suggest that interventions designed to reduce initiation and overall prevalence are of limited value. Both those inferences can, however, be exactly wrong.
Drug use at the individual and societal levels progresses through stages (Everingham, Rydell, & Caulkins, 1995; Kandel, 2002). Many individuals start by using only cannabis. Some quit; others progress to other substances. A few who progress go on to problematic use (e.g., injection or dependent use). At the societal level, new drugs can pass through phases of exponential growth in initiation, stabilization at endemic levels, and sometimes subsequent decline. Systems models, also known as compartment or stocks and flows models are used to describe these staged patterns of use, particularly for heroin (Rossi, 2001; 2004), cocaine (Homer, 1993; Everingham et al. 1995; Caulkins, Behrens. Knoll, Tragler, & Zuba, 2004), and tobacco (Mendez & Warner, 2000; Levy, Chaloupka, Gitchell, Mendez, & Warner, 2002; Levy & Friend, 2002).
Systems models can reconcile the mystery of fluctuating initiation and steadily worsening drug problems and show that their coexistence in no way implies that upstream interventions are not cost-effective. The mechanisms are not novel for systems theorists. There are even terms of art (a.k.a. jargon) for describing them, but such jargon obscures more than it illuminates, so this article illustrates the concept with numerical examples grounded in real data.
The model of how individuals stochastically progress through stages of use comes from a recent compartmental model of drug use in Australia (Caulkins, Dietze, & Ritter, 2007). The trajectory of initiation over time is a new composite based on U.S. data for ten different substances. We are not trying to model any single drug or country. Rather, the point is to illustrate how general characteristics of drug use combine to create the apparent paradox (fluctuating initiation coinciding with ever worsening problems) and the temptation to be unduly pessimistic concerning the value of upstream drug use control interventions.
The next section describes the drug use and initiation models. The subsequent section uses numerical simulations to illustrate the key points. The final section discusses implications for drug control evaluation and policy.
Data and methods
Model of drug use trajectories
We use a discrete-time, annual-step compartmental model of illicit drug use with constant annual transition probabilities that was developed for the Australian Drug Policy Modeling Program (DPMP) (Caulkins et al., 2007; Ritter, Bammer, Hamilton, & Mazerolle, 2007). The model has states representing five types of drug use. Initiation is into one of two non-injecting states, one representing the use only of cannabis (denoted C), the other (state M) reflecting non-injection use of other substances (and possibly cannabis as well). From these states, people may quit or escalate into any of three injecting drug use states. One (state H) reflects frequent or heavy injection drug use. The other two both represent less frequent (light) injection drug use, one each for people who will and who will not eventually escalate to frequent injection ([L.sub.e] and [L.sub.o], respectively). (That distinction was driven by data availability. Infrequent injection by people who will eventually escalate can be studied retrospectively via samples of dependent injectors. Parameters for infrequent injectors who never escalate had to be estimated in other ways.)
Figure 1 shows the five states along with all possible transitions. Escalation from cannabis-only directly to frequent injection is possible, though it occurs at a lower rate than does either escalation from cannabis-only to other non-injection use or escalation from other non-injection use to injection use. The model was parameterized using data from general population surveys, data from heroin users who were resuscitated by ambulance paramedics, and other efforts to model injection drug use (IDU) in Australia. The parameterized model fit well historical patterns of drug use up through the onset of the so-called Australian heroin drought (Day, Degenhardt, Gilmour, & Hall, 2004; Degenhardt, Reuter, Collins, & Hall, 2005). (The model does not track supply or availability, so it cannot be expected to reproduce the effects of supply shocks on patterns of use.) With constant initiation the system approaches a unique, stable steady state.
[FIGURE 1 OMITTED]
The model can be expressed concisely in mathematical terms as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where
C(t) = number of users of cannabis only in year t,
M(t) = number of non-injection users of other drugs in year t,
[L.sub.e](t) = number of occasional IDUs in year t who will escalate to regular use,
[L.sub.o](t) = number of occasional IDUs in year t who will not escalate to regular use,
H(t) = number of regular injection users in year t, and
I(t)...
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