Date of Award:

12-2025

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

James Powell

Committee

James Powell

Committee

Nghiem Nguyen

Committee

Yan Sun

Committee

Kezia Manlove

Committee

Noelle Beckman

Abstract

Wildlife diseases can be difficult to control once they are established. This is especially true when they spread through contact with infectious material left in the environment. One such disease is chronic wasting disease (CWD), a fatal illness affecting deer and related species in North America and other regions. CWD is caused by prions, misfolded proteins that can remain infectious for years after shedding by infected hosts.

Recent research shows that CWD infection does not always follow from the gradual accumulation of prions through small contact events. Rather, an individual may need to encounter a certain prion dose all at once to become infected. This thesis explores what happens when this threshold dosage phenomenon is treated as a core feature in disease models.

Using mathematical tools that model animals across space and time at the population scale, I show how infection thresholds can change the way CWD spreads through a population. One mode of spread is a pulled front, in which an infected animal passes CWD directly to more than one healthy individual on average. This may be likened to a fire spreading through dry brush; even a single ember moving to unspent fuel is enough to carry the blaze ahead. Thresholds, conversely, may lead to pushed fronts, in which enough infected animals must arrive together to overcome the threshold. This is more like fire moving through damp material, where enough burning material must accumulate to dry the wood before it can ignite. The front types behave differently across highly variable landscapes, and are affected in complex ways by the frequency and distance of juvenile dispersal.

To understand how these findings play out in the real world, I build a model of CWD in Wisconsin white-tailed deer, based on years of disease sampling data from deer taken by hunters. The findings offer a realistic ballpark estimate for how threshold-based infection may shape the geographic spread of outbreaks. These insights could inform future efforts in surveillance and control.

Download

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 .