Optimal Control of Illicit Drug Epidemics

This research proposal is focused on dynamic cost-efficiency analyses of instruments to control drug use for largely unexamined types of stocks and flows models. In particular, we intend to determine the optimal mix of demand- and supply-side interventions such as prevention, treatment and law enforcement to control drug epidemics. In a previous research project (FWF P14060 `Dynamics and Control of Illicit Drug Consumption`) we analysed policies altering the course of illicit drug epidemics. The present proposal pursues this approach for several classes of new multi-compartmental models. An essential feature is the epidemic structure of the underlying processes. Social interactions are generated by the influence of prevalence rates on individual transition rates. Preliminary results suggest that the introduction of `susceptibles` can mimic important empirical regularities of actual drug epidemics. Hence, multi-state modelling may merit further investigation to parameterize more realistically various specific illicit drug epidemics. A serious lack of reality in the illicit drug models studied until now is the restriction to only one substance. From the analysis of multiple-drug-use models we expect interesting insight into substitution and complementary effects of illicit drug consumption. In another attempt we enlarge a well-known `light-heavy-user` model by including both `moderate users` as well as `quitters`. The resulting four-state model should explain the interplay of low and high frequency oscillations, which have been observed empirically. A further extension includes the acreage under cultivation as additional state variable. This provides the possibility to study increases in drug prices, which occurred recently both in Afghanistan, Australia, as well as in some Andean states. Preliminary work on these topics has stimulated parallel research innovation in other domains, including non-drug related crime (e.g., corruption), the control of the spread of infectious diseases including HIV, terror control, and marketing. We expect that our research will also lead to methodological advances, notably pertaining to multiple long-run equilibria and DNS curves separating the pertinent basins of attraction.

This research proposal was focused on dynamic cost-efficiency analyses of instruments to control drug use for largely unexamined types of stocks and flows models. In particular, we determined the optimal mix of demand- and supply-side interventions such as prevention, treatment and law enforcement to control drug epidemics. In a previous research project (FWF P14060 `Dynamics and Control of Illicit Drug Consumption`) we had analyzed policies altering the course of illicit drug epidemics. The present proposal further pursued this approach for several classes of new multi-compartmental models. An essential feature is the epidemic structure of the underlying processes. Social interactions are generated by the influence of prevalence rates on individual transition rates. The results obtained confirmed that the introduction of `susceptibles` can mimic important empirical regularities of actual drug epidemics. Hence, we modeled and analyzed multi-state problems in order to parameterize more realistically various specific illicit drug epidemics. A serious lack of reality in the illicit drug models studied before this project was the restriction to only one substance. From the analysis of multiple-drug-use models we gained interesting insight into substitution and complementary effects of illicit drug consumption. In another approach we enlarged a well-known `light-heavy-user` model by including both `moderate users` as well as `quitters`. The resulting four-state model could explain the interplay of low and high frequency oscillations, which have been observed empirically. A further extension included the acreage under cultivation as additional state variable. This provided the possibility to study increases in drug prices, which occurred a few years ago both in Afghanistan, Australia, as well as in some Andean states. Our work on these topics has stimulated parallel research innovation in other domains, including non-drug related crime (e.g., corruption), the control of the spread of infectious diseases including HIV, terror control, and marketing. We are proud to say that our research also led to methodological advances, notably pertaining to multiple long-run equilibria and DNSS curves separating the pertinent basins of attraction.