Abstract

Epidemiological models have been used to measure, understand, and respond to infectious disease outbreaks. Both model development and model validation are important when utilizing models to help inform public health responses. The goal of this work is to advance mathematical modeling efforts of infectious diseases of current worldwide importance through model development and validation. The model development portion focuses on modeling interventions strategies for two infectious diseases. The first model formulated captures education campaign as the collective effort aimed at educating the public about the nature of the Ebola virus, its transmission routes, and the importance of early detection and seeking medical assistance. The basic reproduction number is computed and used to analyze the equilibria of the model for stability. Simulations of the model successfully capture the dynamics of the 2014 West Africa and 2018 Democratic Republic of Congo outbreaks. Then we developed an age-structured model for COVID-19 using contact matrices that accounts for varying contact among different ages and used it to analyze the impact vaccinations have on COVID-19 transmission by running simulations under various vaccine regimens. Model predictions aligned with the Centers for Disease Control and Prevention reports, capturing COVID-19 dynamics among various age groups with the implementation of vaccinations. Next, we developed a validation framework for epidemiological models focused on predictive capability of quantities relevant to decision-making end-users. We applied this framework to evaluate a range of COVID-19 models. We found that when predicting the date of peak deaths, the most accurate model had errors of approximately 15 days or less for releases 3-6 weeks in advance of the peak. Death peak magnitude relative errors were generally in the 50% range 3-6 weeks before peak. All models were highly variable in predictive accuracy across regions. Lastly, we evaluated the reliability of epidemiological-based medical resource demand models. We analyzed epidemiological models that predicted hospitalizations and admissions as these predictions are typically inputs into demand calculators. We also analyzed models that predicted demand for critical resources including ventilators, personal protective equipment, and testing diagnostics. We estimated errors in these models and provided recommendations to advance this nascent field.

Library of Congress Subject Headings

COVID-19 Pandemic, 2020- --Mathematical models; Epidemiology--Mathematics; Medical care--Supply and demand--Mathematical models

Publication Date

7-10-2023

Document Type

Dissertation

Student Type

Graduate

Degree Name

Mathematical Modeling (Ph.D)

Advisor

Ephraim Agyingi

Advisor/Committee Member

Pras Pathmanathan

Advisor/Committee Member

Tamas Wiandt

Campus

RIT – Main Campus

Plan Codes

MATHML-PHD

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