Optimal control of drug epidemics: Prevent and treat - But not at the sametime?

Drug use and related problems change substantially over time, so it seems p lausible that drug interventions should vary too. To investigate this possi bility, we set up a continuous time version of the first-order difference e quation model of cocaine use introduced by Everingham and Rydell (1994), ex tended to make initiation an endogenous function of prevalence. We then for mulate and solve drug treatment and prevention spending decisions in the fr amework of dynamic optimal control under different assumptions about how fr eely drug control budgets can be manipulated. Insights include: (1) The eff ectiveness of prevention and treatment depend critically on the stage in th e 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 intervent ions 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.