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Combining mathematical and statistical modeling approaches to inform and predict the spread of infectious diseases
Albrecht, Laura Michelle Kinney
Albrecht, Laura Michelle Kinney
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2024
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Abstract
In recent years, the field of disease surveillance and modeling has commanded global attention. The interconnected nature of the world makes understanding disease transmission and prediction more crucial now than ever, something we all witnessed first-hand during the COVID-19 pandemic. Mathematical and statistical models serve as valuable tools for understanding the underlying dynamics of diseases and predicting their spread under various scenarios. Our goal in this thesis is to harness the strengths of both mathematical and statistical models to provide insights that can help inform public health policy. We focus on COVID-19 and West Nile virus (WNV).
We develop a COVID-19 transmission model tailored to the Colorado School of Mines campus. This model extends a traditional SEIR framework by incorporating stochastic transitions, thereby capturing the unique transmission dynamics prevalent within a university setting, including testing protocols, quarantine procedures, and isolation strategies. An innovative fitting approach, leveraging Approximate Bayesian Computation (ABC), enables the refinement of the model based on critical data points, ensuring accurate parameter estimation. This enables simulations of the model to evaluate various surveillance testing strategies, assessing their potential efficacy in mitigating disease spread.
Subsequently, we shift our focus to the spread of West Nile virus (WNV) in Ontario, Canada. We first present a purely statistical model using a zero-inflated Poisson to model human data and investigate the correlation between human WNV case counts and key predictors such as mosquito infection rates, bird abundance, and environmental variables. We then apply our ABC methodology to fit a model of WNV transmission between birds and mosquitoes with mosquito trap data. This showcases the adeptness of the ABC method in fitting different models to complex and noisy datasets, emphasizing its utility in addressing sophisticated epidemiological questions.
This thesis highlights the value of blending mathematical and statistical methods in disease modeling. These combined approaches are essential for better disease surveillance and increased prediction accuracy. At a time when more public health data are available than ever before, the ability to analyze and incorporate this vast amount of data into predictive models is crucial to enhancing our understanding of disease spread and inform public health policies.
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