Discipline: Science and Mathematics Education
Subcategory: Mathematics and Statistics
Session: 1
Room: Exhibit Hall A
Alec Washington - Grand Canyon University
Co-Author(s): Talia Brown, Grand Canyon University, Phoenix, AZ
Prescription opioid misuse is a national crisis that has accounted for more overdose deaths than any other illicit drug in the past 5 years. In 2017, over $78 billion was spent in the United States to combat the public health burden caused by opioid-relate incidence toward better prevention methods, but today’s society has not seen the progress it has been pushing for. However, no significant progress has been notes as a result of the effort. In Arizona, prescription opioid sales increased by 300 percent between the years of 2002 to 2017. Furthermore, 36.4% of suspected opioid overdoses received prescription opioids from 10 or more prescribers. Thus, we investigate the influence of various control strategies in navigating the prescription opioid epidemic in Arizona via an epidemiological model. In the model, the population of adults between the ages of 18-65 years old is divided into six sub-classes: susceptible, opioid prescribed users, cessation, lightly-addicted users, heavily-addicted users and effectively-treated opioid users.
The next generation operator method is employed to determine the opioid-users generation number, R0, which is the average number of secondary opioid-addicted users generated by one opioid-addicted user during his/her addiction period. The mathematical analysis also reveals the existence of the opioid-free equilibrium and the opioid-persistent equilibrium. It is determined that when R0 < 1, the opioid epidemic can be controlled to reach the opioid-free equilibrium. Numerical analysis of the model is stimulated to investigate the underlying significance in the treatment effort, prescription rates, and public health education. Variation of the parameter values indicates that lowering the prescription rates does not help control the opioid epidemic while a hybrid strategy of the various methods proves to be the most effective method. Future study of the opioid epidemic will involve an age-structure model as the susceptibility of individuals is assumed to be dependent of age. The future study will also consider the effects of different types of treatment methods such as medically or physiologically-based approach.
Funder Acknowledgement(s): I would like to thank Dr. A.B. Gumel and Dr. T.L Alford of Arizona State University (ASU) and Dr. A. Lanz of Grand Canyon University for their guidance and mentorship throughout the summer. I would also thank the school for Engineering of Matter, Transport and Energy at ASU for providing resources and space. The funding of this research activity was provided by an NSF HBCU-UP grant (074754805).
Faculty Advisor: Dr. Aprillya Lanz, leata@asu.edu
Role: I formulated the mathematical model representing prescription opioid misuse. After defining each parameter and equation for transmission I used the next generator operator method to mathematically observe the secondary infection rate. Upon further mathematical analysis of the R0 I researched applicable parameter values to code into Matlab. I then used the Matlab code to simulate the progression of opioid misuse through a series of prevention methods.