Date of Award:

8-2020

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee

Kevin R. Moon

Committee

Kezia Manlove

Committee

David Brown

Abstract

When modeling the spread of disease, ecologists use ecological or contact networks to model how species interact with their environment and one another. The structure of these networks can vary widely depending on the study, where the nodes of a network can be defined as individuals, groups, or locations among other things. With this wide range of definition and with the difficulty of collecting samples, it is difficult to capture every factor of every population. Thus ecologists are limited to creating smaller networks that both fit their budget as well as what is reasonable within the population of interest. With smaller networks, there is a concern of information loss when generalizing collected results to the whole population. In this work, we use the von Neumann entropy as a measure of the amount of information contained in a given ecological network. We compute the von Neumann entropy of a simulated contact network over a variety of parameters. The goal is this will introduce a standard for ecologists when designing their studies to minimize information loss and thus reduce costs, reduce time, and minimize human error particularly during sample collection. We further demonstrate our approach on data measured from bighorn sheep.

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Included in

Mathematics Commons

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