{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-1868"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-1868","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"On Modeling HIV Infection Of Cd4+ T Cells","abstract":"We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per actively infected T cell, is less than a critical value, , then the uninfected state is the only steady state in the non negative orthant, and this state is stable. We establish an expression for . If , then the uninfected steady state is unstable, and the endemically infected state can be stable or unstable, depending on the value of the parameters utilized.","abstract_html":"We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per actively infected T cell, is less than a critical value, , then the uninfected state is the only steady state in the non negative orthant, and this state is stable. We establish an expression for . If , then the uninfected steady state is unstable, and the endemically infected state can be stable or unstable, depending on the value of the parameters utilized.","abstract_has_math":false,"creators":["Comerford, Amy"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Mohapatra, Ram N."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-01-01T08:00:00Z","date_published":"2006-01-01T08:00:00Z","updated_at":"2026-07-24T05:09:25Z","subjects":["HIV","T cell","Modeling","Equilibrium Points","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0001093"],"render_values":[{"text":"CFE0001093","href":null,"code":true}]}]},"links":{"outbound_url":"https://stars.library.ucf.edu/etd/869","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mohapatra, Ram N."]},{"key":"dc:creator","label":"Author","values":["Comerford, Amy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Masters Thesis (Open Access)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["HIV","T cell","Modeling","Equilibrium Points","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0001093"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stars.library.ucf.edu/etd/869"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Master of Science (M.S.)","College of Arts and Sciences","Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per actively infected T cell, is less than a critical value, , then the uninfected state is the only steady state in the non negative orthant, and this state is stable. We establish an expression for . If , then the uninfected steady state is unstable, and the endemically infected state can be stable or unstable, depending on the value of the parameters utilized."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On Modeling HIV Infection Of Cd4+ T Cells"]}]}],"canonical_facts":{"dc:contributor":["Mohapatra, Ram N."],"dc:creator":["Comerford, Amy"],"dc:description":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Master of Science (M.S.)","College of Arts and Sciences","Mathematics"],"dc:description.abstract":["We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per actively infected T cell, is less than a critical value, , then the uninfected state is the only steady state in the non negative orthant, and this state is stable. We establish an expression for . If , then the uninfected steady state is unstable, and the endemically infected state can be stable or unstable, depending on the value of the parameters utilized."],"dc:format":["application/pdf"],"dc:identifier":["CFE0001093"],"dc:identifier.uri":["https://stars.library.ucf.edu/etd/869"],"dc:language":["English"],"dc:subject":["HIV","T cell","Modeling","Equilibrium Points","Mathematics"],"dc:title":["On Modeling HIV Infection Of Cd4+ T Cells"],"dc:type":["Masters Thesis (Open Access)"]},"updated_at":"2026-07-24T05:09:25Z"}