Vicodin is a pain relieving drug available on prescription that is currently abused by some 2 million people in the US. So an interesting question is how best to reduce the number of Vicodin abusers.

Today, Wendy Caldwell at the University of Tennessee-Knoxville and a few pals come up with a number of recommendations based on a mathematical model of the way people make the transition between Vicodin use and Vicodin abuse.

The model provides a mathematical validation of Benjamin Franklin’s saying that an ounce of prevention is worth a pound of cure.

The model is relatively straightforward. Caldwell and co start by considering the population of medical users of Vicodin. These can either stop taking the drug, in which case they leave the population, or become chronic users and then Vicodin abusers.

Of the abusers, a certain proportion seek treatment for their addiction. These are either successful, in which case they leave the population, or unsuccessful in which case they return to the population of abusers.

The team studied various parameters that govern the rate at which people move from one population to another. An important factor, of course, is the success rate of those being treated, which can depend on factors such as social interaction with other abusers or the number of new prescriptions they are given.

Caldwell and co say the model clearly shows how to reduce the number people who abuse Vicodin. “Manipulating parameters tied to prevention measures has a greater impact on reducing the population of abusers than manipulating parameters associated with treatment,” they say.

In other words, preventing abuse is more effective than curing it.

But the model also reveals another important factor– that the rate at which abusers seek treatment affects the population of abusers more than the success rate of the treatment itself.

Of course, the model has a number of shortcomings. For example, in the first few months of each model, the number of medical users of Vicodin decreases dramatically. However this does not seem to be consistent with the data.

That’s probably because the parameters in the model are constant over time but in real life are likely to fluctuate, say the team.

Interesting and straightforward advice. These kinds of models can help to influence the way that substance abuse is tackled but only if the recommendations are accepted and widely used. And therein lies another significant problem in tackling substance abuse.

Ref: arxiv.org/abs/1308.3673 : Substance Abuse via Legally Prescribed Drugs: The Case of Vicodin in the United States