Date of Award:

5-2012

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

James A. Powell, Mevin B. Hooten

Committee

James A. Powell

Committee

Mevin B. Hooten

Committee

Brynja Kohler

Committee

Nghiem Nguyen

Committee

David Koons

Abstract

Chronic wasting disease (CWD) is a transmissible spongiform encephalopathy (TSE) that affects deer, elk, and moose. TSEs are prion diseases which include mad cow disease and scrapie in sheep and goats. The disease agent is a misshapen protein called a prion, which causes lesions in the brain, and to date, there is no cure. CWD is a slow-developing, fatal disease, which is rare in the free-ranging mule deer population of Utah. Infected deer shed prions into the environment through saliva, feces, and decaying carcasses. These prions remain infective in soils for many years and healthy deer may contract CWD by ingesting them while grazing, as well as through direct contact with infected deer. CWD positive deer shed prions into the environment for as long as two years before they appear visibly sick. This complicates detection and control of this potentially devastating disease.

Mathematical modeling is one of the tools used in analyzing how wildlife diseases spread across the landscape. Historically, diffusion models with constant coefficients have been used to predict spread. They are limited, however, in their ability to connect disease spread to how animals move across differing habitats. Individuals make movement decisions based on local information, i.e. they move quickly through areas that do not provide needed resources and linger in areas that do. Ecological diffusion is a form of spatially varying diffusion that accommodates this through a motility coefficient. In this work we develop two disease models with ecological diffusion: a simple, general disease model and a sex-specific CWD model. We use GPS location data gathered from collared mule deer in the La Sal mountains of Utah (2005-2006) to estimate the motility (a measure of how animals move) for each land cover type in Southeast Utah to use in our models.

Real environments are often spatially complex, limiting application of a direct approach to modeling with ecological diffusion. Here we derive a homogenization procedure for ecological diffusion, which allows us to determine the impact of small-scale (10-100 m) habitat variability on large-scale movement (10-100 km). Our homogenized models take 1/10000 the computational time to solve than small scale ecological diffusion models. Also the average coefficients in the homogenized equations can be used in analysis of speed of disease spread and critical population size necessary for the speed of spread to be zero. This work is important from a disease management point of view. Possible applications are identification of barriers or corridors for disease spread and estimation of population size needed to control spread from disease hotspots. These methods may also be applied to other dispersal problems, such as invasive species, insect invasions, and escaped genetically modified organisms.

Checksum

0dcb62f7029d571aeb5918a45261b0d2

Comments

This work made publicly available electronically on September 18, 2012.

Download

Included in

Mathematics Commons

Share

COinS

Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .