Other Applied Mathematics Commons^™

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 …

Population Modeling For Resource Allocation And Antimicrobial Stewardship, Jason Bintz

Doctoral Dissertations

This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship.

In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the …

Analysis Of Solvability And Applications Of Stochastic Optimal Control Problems Through Systems Of Forward-Backward Stochastic Differential Equations., Kirill Yevgenyevich Yakovlev

Doctoral Dissertations

A stochastic metapopulation model is investigated. The model is motivated by a deterministic model previously presented to model the black bear population of the Great Smoky Mountains in east Tennessee. The new model involves randomness and the associated methods and results differ greatly from the deterministic analogue. A stochastic differential equation is studied and the associated results are stated and proved. Connections between a parabolic partial differential equation and a system of forward-backward stochastic differential equations is analyzed.

A "four-step" numerical scheme and a Markovian type iterative numerical scheme are implemented. Algorithms and programs in the programming languages C and …