The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.
","abstract_html":"<p>The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then <em>n</em> strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.</p>","abstract_has_math":false,"creators":["Nguyen, Thi"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dr. Chetan Prakash"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-06-01T07:00:00Z","date_published":"2014-06-01T07:00:00Z","updated_at":"2026-07-24T01:52:37Z","subjects":["nonlinear dynamics","differential equations","mathematics","evolutionary mathematics","Non-linear Dynamics","Ordinary Differential Equations and Applied Dynamics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/91","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Chetan Prakash"]},{"key":"dc:creator","label":"Author","values":["Nguyen, Thi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-05-15T07:00:00Z"]},{"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 Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonlinear dynamics","differential equations","mathematics","evolutionary mathematics","Non-linear Dynamics","Ordinary Differential Equations and Applied Dynamics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/91"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.
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