The Vicodin abuse problem: A mathematical approach

J Theor Biol. 2019 Dec 21:483:110003. doi: 10.1016/j.jtbi.2019.110003. Epub 2019 Sep 9.


The prescription drug epidemic in the United States has gained attention in recent years. Vicodin, along with its generic version, is the country's mostly widely prescribed pain reliever, and it contains a narcotic component that can lead to physical and chemical dependency. The majority of Vicodin abusers were first introduced via prescription, unlike other drugs which are often experienced for the first time due to experimentation. Most abusers report obtaining their supply from a prescription, either their own or someone else's. Although the problem with prescription drug abuse is well known, there is no standard method of addressing the problem. To better understand how to do this, we develop and analyze a mathematical model of Vicodin use and abuse, considering only those patients who were initially prescribed the drug. Through global sensitivity analysis, we show that focusing efforts on abuse prevention rather than treatment has greater success at reducing the population of Vicodin abusers. Our results demonstrate that relying solely on rehabilitation and other treatment programs is not enough to combat the prescription drug problem in the United States. We anticipate that implementing preventative measures in both prescribers and patients will reduce the number of Vicodin abusers.

Keywords: Compartmental model; Prescription drug abuse; Sensitivity analysis; Vicodin abuse.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Acetaminophen / adverse effects*
  • Computer Simulation
  • Drug Combinations
  • Humans
  • Hydrocodone / adverse effects*
  • Interpersonal Relations
  • Models, Biological*
  • Nonlinear Dynamics
  • Substance-Related Disorders / pathology*


  • Drug Combinations
  • acetaminophen, hydrocodone drug combination
  • Acetaminophen
  • Hydrocodone