Enterococci bacteria that cannot be treated eectively 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 dierential equations describes the movement of ICU patients in and out of dierent 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 dierential 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-eective prevention and treatment schedules during a VRE outbreak. / McAnulty College and Graduate School of Liberal Arts; / Computational Mathematics / MS; / Thesis;
| Identifer | oai:union.ndltd.org:DUQUESNE/oai:digital.library.duq.edu:etd/162280 |
| Date | 11 April 2015 |
| Creators | Lowden, Jonathan |
| Contributors | Rachael Miller Neilan, John Fleming, Donald Simon |
| Source Sets | Duquesne University |
| Detected Language | English |
| Rights | Two year embargo: no access to PDF file until release date by author request.; |
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