Digital Commons Network^™

Applications With Discrete And Continuous Models: Harvesting And Contact Tracing, Danielle L. Burton

Doctoral Dissertations

Harvest plays an important role in management decisions, from fisheries to pest control. Discrete models enable us to explore the importance of timing of management decisions including the order of events of particular actions. We derive novel mechanistic models featuring explicit within season harvest timing and level. Our models feature explicit discrete density independent birth pulses, continuous density dependent mortality, and density independent harvest level at a within season harvest time. We explore optimization of within-season harvest level and timing through optimal control of these population models. With a fixed harvest level, harvest timing is taken as the control. Then …

Data-Driven Modeling Of The Heroin And Fentanyl Epidemic And The Harvesting Of Trees In West Africa, Tricia Marie Phillips

Doctoral Dissertations

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 …

Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong

Doctoral Dissertations

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior.

Cholera remains a public health threat in many parts of the world and improved …