Doctoral Dissertations

Date of Award

8-2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Judy D. Day

Committee Members

Nina H. Fefferman, Michael W. Frazier, Suzanne M. Lenhart

Abstract

The spore-forming, gram-positive bacteria Clostridium difficile can cause severe intestinal illness. A striking increase in the number of cases of C. difficile infection (CDI) among hospitals has highlighted the need to better understand how to prevent its spread. In this dissertation, I discuss the development and structure of two different models of nosocomial C. difficile transmission that we used to evaluate the efficacy of various control strategies and to determine optimal interventions.We begin with an update and modification of a compartmental model of nosocomial C. difficile transmission to include vaccination. We then apply optimal control theory on this epidemiological model to determine the time-varying optimal vaccination rate that minimizes a combination of (1) disease prevalence and spread in the hospital population and (2) the cost, in terms of time and money, associated with vaccination. Various hospital scenarios are considered, such as times of increased antibiotic prescription rates and periods of outbreak, to see how such scenarios affect the optimal vaccination rate. By comparing the values of our objective functional with constant vaccination rates to those with time-varying optimal vaccination rates, we illustrate the benefits of time-varying controls.The second model is an agent-based model that also simulates the transmission of C. difficile in a healthcare setting. This model explicitly incorporates healthcare workers (HCWs) as vectors of transmission, tracks individual patient antibiotic histories, incorporates varying risk levels of antibiotics with respect to CDI, and tracks contamination levels of ward rooms by C. difficile. Using this model, we evaluated the efficacy of a variety of control interventions and combinations of interventions on reducing C. difficile nosocomial colonizations and infections. The control techniques included two forms of antimicrobial stewardship, increased environmental decontamination through room cleaning, improved HCW compliance, and a preliminary assessment of vaccination.

Comments

Portions of this document were previously published in the Journal of Mathematical Biology

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