Modeling Supply Shocks in Optimal Control Models of Illicit Drug Consumption
Large-Scale Scientific Computing
Stochastic skiba sets: an example from models of illicit drug consumption
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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Drug use and related problems change substantially over time, so it seems plausible that drug interventions should vary too. To investigate this possibility, we set up a continuous time version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell (1994), extended to make initiation an endogenous function of prevalence. We then formulate and solve drug treatment and prevention spending decisions in the framework of dynamic optimal control under different assumptions about how freely drug control budgets can be manipulated. Insights include: (1) The effectiveness of prevention and treatment depend critically on the stage in the epidemic in which they are employed. Prevention is most appropriate when there are relatively few heavy users, e.g. in the beginning of an epidemic. Treatment is more effective later. (2) Hence, the optimal mix of interventions varies over time. (3) The transition period when it is optimal to use extensively both prevention and treatment is brief. (4) Total social costs increase dramatically if control is delayed.