Graduation Year

2025

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Christina Edholm

Reader 2

Konrad Aguilar

Abstract

Methicillin-resistant Staphylococcus aureus, (MRSA) remains a significant public health threat due to its continued prevalence in communities and hospitals across the country and its growing resistance to š¯›½ lactam antibiotics. This paper is concerned with modeling a hospital in which both strains of MRSA, Community Acquired MRSA and Hospital Acquired MRSA, are present as well as individuals who are co-colonized with both strains. In addition to a system of Ordinary Differential Equations, our model will utilize both a Continuous Time Markov Chain and a system of Stochastic Differential Equations to better model the emerging epidemic in the hospital. Before building these two models, we outline the theory behind Discrete Markov Chains, Continuous Time Markov Chains, and Branching Processes. We will use our model to understand how hospital hygiene and the prevalence of MRSA in the community affect how endemic MRSA becomes in the hospital. We find that both increased hospital-hygiene and lower levels of CA-MRSA in the surrounding community decreases the peak levels of the MRSA epidemic. As hospital-hygiene decreases and MRSA becomes more prevalent in the community, the MRSA epidemic becomes much more variable and harder to predict, making it more difficult to track and mitigate the epidemic.

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This thesis is restricted to the Claremont Colleges current faculty, students, and staff.

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