Ordinary Differential Equations and Applied Dynamics Commons^™

Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens

Doctoral Dissertations

Mathematical modeling can achieve otherwise inaccessible insights into bio-logical questions. We use ODE (ordinary differential equations) and Game Theory models to demonstrate the breadth and power of these models by studying three very different biological questions, involving socio-behavioral and socio-economic systems, conservation biology, policy and decision making, and organismal homeostasis.

We adapt techniques from Susceptible-Infected-Recovered (SIR) epidemiological models to examine the mental well-being of a community facing the collapse of the industry on which it’s economically dependent. We consider the case study of a fishing community facing the extinction of its primary harvest species. Using an ODE framework with a …

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 …

Optimal Control Of Species Augmentation Conservation Strategies, Erin Nicole Bodine

Doctoral Dissertations

Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this dissertation, species augmentation is analyzed in an optimal control setting to determine the optimal augmentation strategies given various constraints and settings. In each setting, we consider the effects on both the target/endangered population and a reserve population from which the individuals translocated in the augmentation are harvested. Four different optimal control formulations are explored. The first two optimal control formulations model the underlying population dynamics with a system of ordinary differential equations. Each of these …