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Published on May 25, 2013
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 five 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 finite time period. Pontryagin's Minimum Principle is used to characterize optimal controls by deriving a Hamiltonian expression and differential equations for five 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.
Video filmed and edited by Alyssa Kramer, a graduate student in Duquesne's Journalism and Multimedia Department