Defense Date

3-27-2013

Graduation Date

2013

Availability

Immediate Access

Submission Type

thesis

Degree Name

MS

Department

Computational Mathematics

School

McAnulty College and Graduate School of Liberal Arts

Committee Chair

Rachael Miller Neilan

Committee Member

John Fleming

Committee Member

Donald Simon

Keywords

Enterococci, Optimal control, Vancomycin, 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.

Format

PDF

Language

English

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