Presenter Information

Lindsay Moskal, Duquesne University Department of Chemistry and Biochemistry, Duquesne University Department of Mathematics and Computer Science

Lauren Sines, Duquesne University Department of Biological Sciences

Rachael Neilan, Ph.D., Duquesne University Department of Mathematics and Computer Science

Abstract

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is three times that of the national rate.

In collaboration with the Allegheny County Department of Human Services (DHS), we developed a comprehensive mathematical model to describe the opioid epidemic in Allegheny County. The model is a system of differential equations describing how the size of each population class–Susceptible, Prescribed, Addicted, and Recovered–changes over time. Variables describing the presence of fentanyl (a synthetic opioid) and the use of Narcan (medication used to block the effects of opioids) were included in the model. Model parameters were estimated to reflect the addiction and overdose rates in Allegheny County using data provided by the DHS. Model simulations highlight the impact of fentanyl and Narcan on the annual overdose death rates. Additional results show that increasing the availability of Narcan in the community will result in a meaningful reduction in overdose deaths; however, an increased presence of fentanyl will render Narcan less effective.

School

Bayer School of Natural and Environmental Sciences; McAnulty College and Graduate School of Liberal Arts

Advisor

Dr. Rachael Neilan

Submission Type

Paper

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Modeling the Effects of Fentanyl and Narcan on the Opioid Epidemic in Allegheny County Using Mathematics

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is three times that of the national rate.

In collaboration with the Allegheny County Department of Human Services (DHS), we developed a comprehensive mathematical model to describe the opioid epidemic in Allegheny County. The model is a system of differential equations describing how the size of each population class–Susceptible, Prescribed, Addicted, and Recovered–changes over time. Variables describing the presence of fentanyl (a synthetic opioid) and the use of Narcan (medication used to block the effects of opioids) were included in the model. Model parameters were estimated to reflect the addiction and overdose rates in Allegheny County using data provided by the DHS. Model simulations highlight the impact of fentanyl and Narcan on the annual overdose death rates. Additional results show that increasing the availability of Narcan in the community will result in a meaningful reduction in overdose deaths; however, an increased presence of fentanyl will render Narcan less effective.

 

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