This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in the data through analysis of the models. Finally, the paper will develop the concept of long-term infectious diseases and cell-to-cell spread as a means for understanding a component of some very complicate diseases such as HIV and herpes; it will not get too deep into examples in this last section, but rather will set up some models to work with and some areas for further research.
","abstract_html":"<p>This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in the data through analysis of the models. Finally, the paper will develop the concept of long-term infectious diseases and cell-to-cell spread as a means for understanding a component of some very complicate diseases such as HIV and herpes; it will not get too deep into examples in this last section, but rather will set up some models to work with and some areas for further research.</p>","abstract_has_math":false,"creators":["Hauer, Jessica"],"institution":null,"degree_name":"Master of Science (MS) in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-01-01T08:00:00Z","date_published":"2013-01-01T08:00:00Z","updated_at":"2026-07-24T02:13:35Z","subjects":["Biomathematics","Lotka-Volterra equations","Differential equations","Nonlinear","Biology","Partial Differential Equations"],"languages":[],"rights":["Access is available to all users"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.ewu.edu/theses/237","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hauer, Jessica"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS) in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Biomathematics","Lotka-Volterra equations","Differential equations","Nonlinear","Biology","Partial Differential Equations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Access is available to all users"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.ewu.edu/theses/237"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in the data through analysis of the models. Finally, the paper will develop the concept of long-term infectious diseases and cell-to-cell spread as a means for understanding a component of some very complicate diseases such as HIV and herpes; it will not get too deep into examples in this last section, but rather will set up some models to work with and some areas for further research.
"]},{"key":"dc:title","label":"Title","values":["Population models"]}]}],"canonical_facts":{"dc:creator":["Hauer, Jessica"],"dc:description.abstract":["This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in the data through analysis of the models. Finally, the paper will develop the concept of long-term infectious diseases and cell-to-cell spread as a means for understanding a component of some very complicate diseases such as HIV and herpes; it will not get too deep into examples in this last section, but rather will set up some models to work with and some areas for further research.
"],"dc:identifier":["https://dc.ewu.edu/theses/237"],"dc:rights":["Access is available to all users"],"dc:subject":["Biomathematics","Lotka-Volterra equations","Differential equations","Nonlinear","Biology","Partial Differential Equations"],"dc:title":["Population models"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS) in Mathematics"]},"updated_at":"2026-07-24T02:13:35Z"}