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- All Subjects: Mathematics
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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.
The ever-increasing importance of cancer and neurodegenerative diseases continues to grow as populations across the world are affected by death and aging. The vitamin A (RXR) and vitamin D (VDR) receptor pathways offer promising potential to aid in treatment of cancer and Alzheimer’s disease. This thesis discusses the potential application of novel analogs of Bexarotene (RXR agonist), MeTC7 (a new potent VDR antagonist), and vitamin D as possible therapeutics for cancer and Alzheimer’s disease.