{"id":{"repo_id":"duquesne","oai_identifier":"oai:dsc.duq.edu:etd-1853"},"canonical_url":"https://search.dev.ndltd.org/etd/duquesne/oai:dsc.duq.edu:etd-1853","repository":{"repo_id":"duquesne","name":"Duquesne","base_url":"https://dsc.duq.edu/do/oai/"},"display":{"title":"Optimal Control Applied to a Mathematical Model for Vancomycin-Resistant Enterococci","abstract":"Enterococci bacteria that cannot be treated effectively with the antibiotic vancomycin are termed Vancomycin-Resistant Enterococci (VRE). In this thesis, we develop a mathematical framework for determining optimal strategies for prevention and treatment of VRE in an Intensive Care Unit (ICU). A system of ve ordinary differential equations describes the movement of ICU patients in and out of different states related to VRE infection. Two control variables representing the prevention and treatment of VRE are incorporated into the system. An optimal control problem is formulated to minimize the VRE-related deaths and costs associated with controls over a nite time period. Pontryagin's Minimum Principle is used to characterize optimal controls by deriving a Hamiltonian expression and differential equations for ve adjoint variables. Numerical solutions to the optimal control problem illustrate how hospital policy makers can use our mathematical framework to investigate optimal cost-effective prevention and treatment schedules during a VRE outbreak.","abstract_html":"Enterococci bacteria that cannot be treated effectively with the antibiotic vancomycin are termed Vancomycin-Resistant Enterococci (VRE). In this thesis, we develop a mathematical framework for determining optimal strategies for prevention and treatment of VRE in an Intensive Care Unit (ICU). A system of ve ordinary differential equations describes the movement of ICU patients in and out of different states related to VRE infection. Two control variables representing the prevention and treatment of VRE are incorporated into the system. An optimal control problem is formulated to minimize the VRE-related deaths and costs associated with controls over a nite time period. Pontryagin's Minimum Principle is used to characterize optimal controls by deriving a Hamiltonian expression and differential equations for ve adjoint variables. Numerical solutions to the optimal control problem illustrate how hospital policy makers can use our mathematical framework to investigate optimal cost-effective prevention and treatment schedules during a VRE outbreak.","abstract_has_math":false,"creators":["Lowden, Jonathan"],"institution":null,"degree_name":"MS","degree_level":"Immediate Access","degree_discipline":"Computational Mathematics","degree_department":null,"school":null,"contributors":["Rachael Miller Neilan","John Fleming","Donald Simon"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-01-01T08:00:00Z","date_published":"2013-01-01T08:00:00Z","updated_at":"2026-07-24T02:10:02Z","subjects":["Enterococci","Optimal control","Vancomycin","Vancomycin-Resistant Enterococci"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dsc.duq.edu/etd/837","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rachael Miller Neilan","John Fleming","Donald Simon"]},{"key":"dc:creator","label":"Author","values":["Lowden, Jonathan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-08-03T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computational Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Immediate Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Enterococci","Optimal control","Vancomycin","Vancomycin-Resistant Enterococci"]}]},{"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":["https://dsc.duq.edu/etd/837"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Enterococci bacteria that cannot be treated effectively with the antibiotic vancomycin are termed Vancomycin-Resistant Enterococci (VRE). In this thesis, we develop a mathematical framework for determining optimal strategies for prevention and treatment of VRE in an Intensive Care Unit (ICU). A system of ve ordinary differential equations describes the movement of ICU patients in and out of different states related to VRE infection. Two control variables representing the prevention and treatment of VRE are incorporated into the system. An optimal control problem is formulated to minimize the VRE-related deaths and costs associated with controls over a nite time period. Pontryagin's Minimum Principle is used to characterize optimal controls by deriving a Hamiltonian expression and differential equations for ve adjoint variables. Numerical solutions to the optimal control problem illustrate how hospital policy makers can use our mathematical framework to investigate optimal cost-effective prevention and treatment schedules during a VRE outbreak."]},{"key":"dc:title","label":"Title","values":["Optimal Control Applied to a Mathematical Model for Vancomycin-Resistant Enterococci"]}]}],"canonical_facts":{"dc:contributor":["Rachael Miller Neilan","John Fleming","Donald Simon"],"dc:creator":["Lowden, Jonathan"],"dc:date.available":["2018-08-03T07:00:00Z"],"dc:description.abstract":["Enterococci bacteria that cannot be treated effectively with the antibiotic vancomycin are termed Vancomycin-Resistant Enterococci (VRE). In this thesis, we develop a mathematical framework for determining optimal strategies for prevention and treatment of VRE in an Intensive Care Unit (ICU). A system of ve ordinary differential equations describes the movement of ICU patients in and out of different states related to VRE infection. Two control variables representing the prevention and treatment of VRE are incorporated into the system. An optimal control problem is formulated to minimize the VRE-related deaths and costs associated with controls over a nite time period. Pontryagin's Minimum Principle is used to characterize optimal controls by deriving a Hamiltonian expression and differential equations for ve adjoint variables. Numerical solutions to the optimal control problem illustrate how hospital policy makers can use our mathematical framework to investigate optimal cost-effective prevention and treatment schedules during a VRE outbreak."],"dc:identifier":["https://dsc.duq.edu/etd/837"],"dc:language":["English"],"dc:subject":["Enterococci","Optimal control","Vancomycin","Vancomycin-Resistant Enterococci"],"dc:title":["Optimal Control Applied to a Mathematical Model for Vancomycin-Resistant Enterococci"],"thesis:degree_discipline":["Computational Mathematics"],"thesis:degree_level":["Immediate Access"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T02:10:02Z"}