Year of Award


Document Type


Degree Type

Doctor of Philosophy (PhD)

Degree Name


Department or School/College

Department of Mathematical Sciences

Committee Chair

Leonid Kalachev

Commitee Members

Johnathan Bardsley, Javier Perez Alvaro, Frederick Peck, Douglas Brinkerhoff


COVID-19, Dynamical Systems, SIR Models


University of Montana


The outbreak of the novel coronavirus (SARS-CoV-2) in Wuhan, China and subsequent global pandemic illustrated the need of accurate forecasting and a greater understanding of the underlying dynamics of infectious diseases.

In this dissertation, we examine the six most populous towns in the State of Montana through the lens of the classic SIR model. With this, we show that the six towns in question exhibit similar disease dynamics and population behavior within each wave. Furthermore, we conduct analysis on the age demographics of COVID-19 cases and deaths. This analysis corroborates the findings of the SIR model fits, in that the age demographics of cases, deaths, and case fatality rates are remarkably similar across all six towns, lending credence to the hypothesis that the dynamics of infectious diseases are fundamentally the same within rural towns in America.



© Copyright 2023 Ian Gabriel Derickson