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A Mathematical Approach to the Vicodin Abuse Problem

By Karthika Swamy Cohen

Two million people in the U.S. are known to abuse Vicodin, the most commonly prescribed pain reliever in the country. The majority of Vicodin abusers report being initially exposed to the drug via prescription. A narcotic component in the medicine can lead to physical and chemical dependency. While prescription drug addiction and abuse is a commonly known problem in the U.S., efforts to address the issue are still lacking. 

At a minisymposium talk aptly titled, “The Vicodin Abuse Problem: A Mathematical Approach” at the SIAM Annual Meeting being held in Portland, Ore., this week, Wendy Caldwell of Los Alamos National Laboratory and Arizona State University presented mathematical models of Vicodin use and abuse to better understand the epidemic.

The majority of the two million Vicodin abusers in the U.S. report being initially exposed to the drug via prescription.
 

Ninety-nine percent of the world’s hydrocodone is in the U.S.,” Caldwell began. “But I’m pretty sure we don’t have ninety-nine percent of the pain.” 

Vicodin, which contains hydrocodone and acetaminophen, is classified as a schedule II narcotic compound, which the Drug Enforcement Administration defines as one currently accepted for medical use in the U.S. with a high potential for abuse, which may lead to severe psychic or physical dependence. 

It’s called Hillbilly heroin for a reason – if a patient is in a lot of pain, Vicodin does not reduce pain, but instead prevents the brain from feeling it The drug is toxic to the liver – over four pills a day puts users at risk for liver toxicity.

With the goal of finding the most effective strategies to reduce the overall population of abusers, Caldwell seeks to determine if prevention methods educating doctors and patients on the potential for drug abuse or treatment methods implemented post-Vicodin abuse will have greater impact. “There is only one way to quit abuse and that is treatment,” Caldwell stressed. “People don’t usually quit Vicodine on their own.”

Her team considers a linear and two nonlinear compartmental models in which Vicodin users can either a. transition into the abuser compartment or b. leave the population by no longer taking the drug. Once they are identified as Vicodin abusers, individuals can move into a treatment compartment, with the possibility of a. leaving the population through successful completion of treatment or b. relapsing and re-entering the abusive compartment. 

The linear model, called the Compartmental Vicodin Transition model categorizes patients initially prescribed Vicodin according to the level of drug use. The first compartment comprises acute users – this is the group people who have been prescribed the drug enter. They move into the chronic compartment if they continue to take Vicodin for medical reasons beyond three months. If chronic individuals begin taking it recreationally or misuse the prescribed dosage, they are entered into the abuse compartment. Patients who stop taking Vicodin exit the population. Once in the abusive compartment, users can either remain there or seek treatment, and the latter can either leave the population through successful treatment or re-enter the abuse compartment through relapse.

Simulation results of the nonlinear Social Interaction with Abuse-Dependent Prescription Rate (SIAD) model.

The nonlinear models include the Social Interaction with Constant Prescription Rate (SIC) and the Social Interaction with Abuse-Dependent Prescription Rate (SIAD) models.

The SIC model incorporates social interaction between the abusers and those in treatment. Those in treatment are assumed to be more likely to enter the abuse compartment if they interact with abusers than those who do not interact. This is seen to be consistent with the data. Social interaction between abusers and patients in treatment stalls recovery and increases relapse risk.

The SIAD model expresses the entrance rate of new Vicodin patients into the system as an inverse function of the abuser population. The model helps determine how varying the number of new Vicodin patients entering the acute medical user group affects the total population of abusers.

The nonlinear models account for social interaction, while the linear model does not. Both nonlinear models factor in interaction with other abusers, which would be assumed to affect the relapse rate. 

Sensitivity analysis—conducted to determine the strategy with the highest impact—demonstrated that focusing efforts on abuse prevention rather than treatment has a higher chance of reducing the population of Vicodin abusers. While the nonlinear model showed that the parameters associated with treatment have no effect, the rate at which abusers seek treatment is seen to have a measurable effect in both the linear and nonlinear models. Preventing acute users from becoming chronic users also has an effect. 

Karthika Swamy Cohen is the managing editor of SIAM News.


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