Optimal Dynamic Allocation of Treatment and Enforcement in Illicit Drug Control

Abstract

There has been considerable debate about what share of drug control resources should be allocated to treatment vs. enforcement. Most of the debate has presumed that there is one answer to that question, but it seems plausible that the mix of interventions should vary as the size of the problem changes. We formulate the choice between treatment and enforcement as an optimal control problem and reach the following conclusions. If initiation into drug use is an increasing function of the current number of users and control begins early, then it is optimal to use very large amounts of both enforcement and treatment to cut short the epidemic. Otherwise the optimal policy is not to stop the growth of the epidemic, but rather to moderate it. Initially this should be done primarily with enforcement. Over time, enforcement spending should increase, but not nearly so fast as treatment spending. Hence, treatment should receive a larger share of control resources when a drug problem is mature than when it is first growing. If initiation rates subsequently decline, enforcement's budget share should drop further in the ensuing declining stage of the epidemic.

Macroeconomic Aspects of Substance Abuse: Diffusion, Productivity and Optimal Control

“…It follows from the above arguments that the depiction of 1 SS and 2 SS in Figure 1 as an unstable focus point and a saddle point, respectively, which bears a resemblance to the phase portrait in the unconstrained model of Tragler et al (2001), is possible in our framework if, in addition to exceeding ) 0 ( F ′ , the planner's discount rate satisfies the inequality…”

“…Similar to the special case described by Tragler et al (2001) of unconstrained control budget and slowly diminishing returns on treatment, as proposed by Clark (1971Clark ( , 1976 and proven by Majumdar and Mitra (1980) for the analogous case of efficient management of renewable natural resources with a convex-concave growth function in the state variable, there exists a critical point (DNS threshold) separating the basin of attraction around the high control and small user number equilibrium 1 SS from the convergent arm leading to the low control and large user number equilibrium 2 SS . If the initial number of users is lower than the DNS threshold, it is optimal for the government to eliminate drug-use by applying, for a while, a concerted drugcontrol effort which subsequently diminishes as the number of users dwindles.…”

“…This positive relationship between user full price and enforcement has been incorporated by Behrens, Caulkins, Tragler and Feichtinger (1997) and Tragler, Caulkins and Feichtinger (2001) in optimal control analyses of the cost-minimising mix of spending on enforcement and treatment. This paper, though not incorporating the price-raising effect of drug-control explicitly, complements the analyses of Behrens et al (1997) and Tragler et al (2001) by focusing concerns on aggregate production and growth and the debilitating effects of illicit drugs. More specifically we focus on the relationships between disposable national income, the decomposition of the labour force between users and nonusers, and government control efforts.…”

High and Low Frequency Oscillations in Drug Epidemics

“…Prevention, specifically "primary" prevention, seeks to keep non-users from ever trying the drug . Drug treatment can be seen as an intervention that increases the outflow from heavy use [Rydell et al, 1996;Behrens et al, 2000;Tragler et al 2001]. …”

Gustav Feichtinger celebrates his 70th birthday

“…The work by Gustav and his group in this area resulted in dozens of publications, most of which appeared in prestigious journals such as Operations Research and Management Science [5,119,14]. In addition to the broad acceptance by the operations research community, it is remarkable that some of the work not only appeared in drug policy oriented outlets [1,8] but also had an influence on real life problems.…”