Adderall Use in the College-Age Population: A Mathematical Approach

College campuses are one of the most common places for substance abuse. Typically, these substances are thought of to be alcohol, marijuana, and cocaine. However, Adderall is the second most commonly abused drug on college campuses. It is used to treat attention deficit hyperactivity disorder (ADHD). Adderall increases attention span and focus, so it is also commonly used as a study drug. Students frequently buy Adderall from a friend with a prescription, and use it to stay up all night cramming for an exam or finishing a project. This is a topic that not much research has been done on since Adderall only became widely used starting in the mid 2000’s. Since it is unethical to run experiments to learn more about Adderall use, and there is a limited amount of data online, a different approach had to be taken to explore this issue further. As a mathematics major, I determined that the best way to do so was to create an SIR mathematical model. In this model we have five different populations, or compartments: the population susceptible to Adderall use, people who use Adderall with an Adderall prescription, people who use Adderall without an Adderall prescription, people with an Adderall prescription stop using Adderall, and people without an Adderall prescription stop using Adderall. We also observed the rates at which people move between each population. Using this model, we created a set of differential equations to analyze and run simulations with. Looking at steady state, equilibrium points, stability, best and worst-case scenarios, and parameter impact, we drew conclusions and came up with possible courses of action. Overall, creating this model taught me not only about drug abuse, but about how useful mathematical modeling can be, especially concerning substance abuse.