## Undergraduate Honors Theses

#### Honors Program

Honors in Mathematics

5-2012

Michele Joyner

#### Thesis Professor Department

Mathematics and Statistics

#### Thesis Reader(s)

Ariel Cintron-Arias, Foster Levy

#### Abstract

As of now, not many pharmaceutical companies are producing new categories of antibiotics to fight bacterial infections. Therefore, bacteria are building up a resistance to the medications commonly used. Often, antibiotic resistance begins within a hospital. To combat resistance, researchers completed several studies using cycling of the medications that are already in place, but they found either no improvement or the resistance increased with this type of setting. In addition, although preventative infection control measures have been shown to decrease antibiotic resistance for some antibiotics, the level of antibiotic resistance found in hospitals is still extremely high. This motivates the main goal of this thesis: to quantify how much the overall resistance can be lowered by simply adding one new drug to the regimen.

The process of adding a new antibiotic can be quantified using mathematical models that show the flow of patients colonized with various types of bacteria into, out of, and within the hospital. Deterministic models can be used to model the spread of resistant bacteria in hospitals with a relatively large number of beds. However, not all hospitals are large enough to accurately determine the effects using a deterministic model; thus, we must use stochastic models, where mathematical formulations include probability in ways that describe intrinsic random fluctuations, typical of infection processes at smaller scales.

In examining the addition of a new antibiotic within a hospital, we consider different administration protocols, either assuming that physicians are equally likely to prescribe the new antibiotic as they are to prescribe existing antibiotics or that physicians prescribe the new antibiotic to only a targeted population of patients. We will examine the variation in the expected level of overall resistance in a hospital depending on the administration procedure as well as the whether the hospital is large (deterministic model) or small (stochastic model). We will conclude with initial results for fitting these models to simulated data using common inverse problem methodology.

#### Document Type

Honors Thesis - Open Access

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

#### Copyright

Copyright by the authors.

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