Dynamics and control of illicit drug consumption

Research project P 14060 Illicit Drug Dynamics Gustav FEICHTINGER 11.10.1999 Illicit drugs create substantial problems for many countries and present difficult management challenges. At the strategic level, drug policy can be viewed as a resource allocation problem: How should scarce resources be divided among competing drug control programs? This topic has received considerable attention, but to date the answers have been static, finding that one intervention is so and so much more effective than another intervention, without qualification as to the stage of the drug epidemic. But drug problems are dynamic, evolving over time with significant feedback effects. Thus, one might expect the optimal mix of drug control interventions to vary over time. The expected results will be of direct interest to policy makers in consumer countries. Methodologically, they illustrate the benefits of combining optimal control theory with innovative modeling to address practical management problems that otherwise could not be described let alone analysed within a rigorous mathematical framework. Having a better understanding of initiation into drug use is one of the European Monitoring Center for Drugs and Drug Addiction`s priority questions in drug use research and policy. The straightforward reason for this research interest is that any drug user career starts when the illicit drug is consumed for the first time, and there is clear evidence from controlled trials that initiation can be reduced by appropriate (policy) interventions. In particular, the United Nations International Drug Control Programme`s ,World Drug Report" (1997, p. 203) states that the longer that initiation into drug use can be delayed the less likely it is to begin or, if it does begin, to become compulsive [ ... ]". We want to address this problem with a micro-level social network approach to the modelling of initiation, which will help to complement aggregate, market-oriented models of mature markets and give new insights into the problem of drug initiation. Drug consumption is heterogeneous. Distinguishing between `light` and heavy` users (where people who report using a drug like cocaine at least weekly are defined to be heavy users) provides a first approach to heterogeneity. Light and heavy use is only one example of a more general social choice paradigm. Consider two stages of deviancy, one milder than the other. Some individuals in the `light` pool escalate to the more severe form of delinquency. Most of the social damage is generated by the more advanced form of deviancy. One can intervene with (`punish`) members of either population in any mixture. The general policy question is how the amount and mixture of the two interventions should change as the size of the two problems changes. If milder forms of delinquency are not terribly costly to society in and of themselves but tend to feed people into more severe forms of delinquency, when is it useful to punish the mildly delinquent? Although this may seem unjust, punishing mildly delinquent behaviour might be cost-minimizing overall if it reduces the number of people who escalate into the more costly state of more highly deviant behaviour. Other examples of this set an example` policy are vandalism and petty crime` vs. serious street crime`, writing down assets too aggressively` vs. outright tax fraud` and rude comments` vs. more serious forms of sexual harassment`. In each case, one may ask whether the authorities should Jake a tough line` with the milder forms of delinquency or whether they should overlook` such behaviour. We want to deal with this issue and other problems of heterogeneity within an optimal control / dynamic game theoretic framework.

Illicit drugs create substantial problems for many countries and present difficult management challenges. At the strategic level, drug policy can be viewed as a resource allocation problem: How should scarce resources be divided among competing drug control programs? This topic has received considerable attention, but until recently the answers have been static, finding that one intervention is so and so much more effective than another intervention, without qualification as to the stage of the drug epidemic. But drug problems are dynamic, evolving over time with significant feedback effects. Thus, one might expect the optimal mix of drug control interventions to vary over time. Research conducted in this project focused on several different managerial questions. For instance, we investigated how the relative effectiveness of different types of prevention varies over the course of a drug epidemic; we studied optimal spending for drug substitution programmes in the context of a dynamic "epidemic" model of both drug use and drug-use related infections like hepatitis C or HIV; or, we extended traditional single- and multi-state dynamic models by explicitly considering the age distribution of users. The results obtained have had a significant effect on policy makers` thinking in consumer countries, even in such distant places as Australia. Methodologically, they illustrate the benefits of combining optimal control theory with innovative modeling to address practical management problems that otherwise could not be described let alone analysed within a rigorous mathematical framework. This project has stimulated parallel research innovation in other domains, including non-drug related crime, the control of the spread of infectious diseases including HIV and HCV, counter-terror, and, interestingly, marketing of legal goods. It has also led to methodological advances, notably pertaining to multiple equilibria and so-called DNS curves, as well as novel solution techniques for age-structured control systems (including their implementation on computers for numerical solution).