Doctoral Dissertations

Date of Award

5-2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Suzanne Lenhart

Committee Members

Christopher Strickland, Orou Gaoue, Judy Day

Abstract

The opioid epidemic has had a strong presence in the United States in recent years. Drug overdose deaths involving opioids have skyrocketed and the lacing of heroin with fentanyl has played a significant role in this. In order to investigate the dynamics behind the opioid epidemic and predict its trajectory, we formulate a system of ordinary differential equations that incorporate the movement of individuals among classes of opioid use. We estimate parameter values by fitting to Tennessee data since the time the epidemic was established in the state. The trajectory of the epidemic suggests the number of addicts and overdose deaths will increase over the next few years and is driven by the size of the heroin/fentanyl addicted class. We measure the sensitivity of the size of the opioid addicted classes to each of the parameters at the beginning of 2023. From these results, with the hopes of mitigating the increasing trajectory of the epidemic in the near future, management scenarios for decreasing the number of addicted individuals and overdose deaths from 2020-2023 are explored. The most effective include increasing accessibility to treatment programs, monitoring individuals who have stably recovered, and increasing the use of opioid overdose-reversal drugs. Khaya senegalensis is a tree species in Benin, West Africa that is harvested both lethally and non-lethally for its non-timber forest products by the local people for cultural and economic reasons. Both adult and juvenile trees are harvested which affects various vital rates for the tree population. To investigate the effect of size-dependent harvesting strategies on tree population dynamics, we develop a size-structured, seasonal system of difference equations with time-varying harvest for this tree species. Using data from a specific population of the species, the Soassararou population, we estimate harvesting rates and rates affected by harvest for our harvesting model applied to the Soassararou and Nipuni populations. Eigenvalue analysis is then carried out to compare population dynamics.

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