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Substance Abuse via Legally Prescribed Drugs: The Case of Vicodin in the United States

Vicodin is the most commonly prescribed pain reliever in the United States. Research indicates that there are two million people who are currently abusing Vicodin, and the majority of those who abuse Vicodin were initially exposed to it via prescription. Our goal is to determine the most effective strategies for reducing the overall population of Vicodin abusers. More specifically, we focus on whether prevention methods aimed at educating doctors and patients on the potential for drug abuse or treatment methods implemented after a person abuses Vicodin will have a greater overall impact. We consider one linear and two non-linear compartmental models in which medical users of Vicodin can transition into the abuser compartment or leave the population by no longer taking the drug. Once Vicodin abusers, people can transition into a treatment compartment, with the possibility of leaving the population through successful completion of treatment or of relapsing and re-entering the abusive compartment. The linear model assumes no social interaction, while both non-linear models consider interaction. One considers interaction with abusers affecting the relapse rate, while the other assumes both this and an additional interaction between the number of abusers and the number of new prescriptions. Sensitivity analyses are conducted varying the rates of success of these intervention methods measured by the parameters to determine which strategy has the greatest impact on controlling the population of Vicodin abusers. From these models and analyses, we determine that manipulating parameters tied to prevention measures has a greater impact on reducing the population of abusers than manipulating parameters associated with treatment. We also note that increasing the rate at which abusers seek treatment affects the population of abusers more than the success rate of treatment itself.