A Mathematical Analysis of a Model of Adderall Abuse

Adderall remains to be one of the most commonly abused drug among college campuses. Although it is a prescription drug that is primarily used to treat attention deficit hyperactivity disorder (ADHD), it has become one of the many "study drugs" due to its usage among college students during stressful school times, such as exams, where increased concentration and energy levels are thought to improve work efficiency. However, Adderall is notable for having a high potential for abuse and a risk of psychological and physical side effects. In this paper, we conducted a mathematical analysis on an existing epidemiological model of Adderall abuse. We started by verifying the positivity of solutions using techniques from dynamical systems because this is a population model dealing with people. Then, we found and investigated different equilibrium solutions to analyze their stability using both analytical and graphical approaches. Finally, the results were tied back into the Adderall model and conclusions were drawn.