Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Talia Brown - Grand Canyon University
Co-Author(s): Alec Washington, Grand Canyon University, AZ
Prescription opioid misuse in the United States has become an overwhelming issue in recent years. This presentation specifically analyzes the epidemic in Arizona. The pressing matter in the state must be investigated due to the fact that it saw over 51,000 patients placed in hospitals for complications related to opioid misuse and spent over 431 million dollars to address the issue [ADHS, NIH]. The rate that clinicians have prescribed opioids has followed a decreasing pattern over the years; however, the number of opioid-related deaths has seen a steady climb. The prescription opioid epidemic has called much attention to itself due to the severity of the situation and, therefore, would benefit from mathematical analysis. The Centers for Disease Control and National Institutes for Health have provided many tools for healthcare providers and patients to understand the dangers of prescription opioids, as well as offered guidance for avoiding misuse of the drugs. Unfortunately, the effectiveness of this literature is still unknown. We present a compartmental model to explain the dynamics of the opioid crisis. It takes into account individuals that are susceptible, those who are currently prescribed opioids, lightly and highly addicted opioid users, and individuals in effective treatment. This model examines prescription opioid misuse based on the epidemic threshold RO. In instances where the value is less than one, the subpopulation of addicted individuals can be controlled; but, when RO is greater than one, the “disease” of opioid addiction will spread and the population of addicted individuals will continue to grow. In order to fit data, a set of numerical simulations is performed. We hypothesized that the optimal solution to reduce the RO value and subsequently lessen the threat of an opioid epidemic consisted of a combination of strategies. The results propose that prescription opioid misuse can be reduced and potentially eliminated with the increase of treatment, decrease of prescription rates, and increase of public health awareness. As time advances, estimated trends reveal a constant decline in the frequency of opioid misuse when these factors are varied. Future research will involve an age structure model based on the assumption that different age groups possess different levels of susceptibility. A mathematical model of a high risk age group could be developed to understand how opioid misuse spreads in a more age specific environment. References: Arizona Department of Health Services. Arizona Opioid Emergency Response.”ADHS, 2018, www.azdhs.gov/documents/prevention/womens-childrens-health/injury-prevention/opioid-prevention/2017-opioid-emergency-response-report.pdf. Last accessed September 27, 2019. Van den Driessche, Pauline, and James Watmough. “Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission.” Mathematical biosciences 180.1-2 (2002): 29-48. Last accessed September 27, 2019.
Funder Acknowledgement(s): Special thank you to Dr. Aprillya Lanz, Dr. Terry L. Alford, Dr. Abba Gumel, and the School for Engineering of Matter, Transport & Energy at Arizona State University. Funding was provided by the National Science Foundation HBCU-UP Research Initiation Award (grant 074754805).
Faculty Advisor: Aprillya Lanz, Ph.D., email@example.com
Role: Along with my co-author, I participated in the entire research program. I focused more on the analysis of some calculated values such as stability and R_O.