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Mathematical modeling offers a quantitative framework for analyzing mechanisms underlying infectious disease transmission and explaining patterns in epidemiological data. Models are also commonly applied in outbreak investigations for assessing intervention and control strategies and generating epidemic forecasts in real time. However, successful application of mathematical models depends on the ability to reliably estimate key transmission and severity parameters, which are critical for guiding public health interventions. Overall, the three studies presented provide a thorough guide for assessing and utilizing mathematical models for describing infectious disease outbreak trends. In the first study, we describe the process for analyzing identifiability of parameters of interest in mechanistic disease transmission models. In the second study, we expand this idea to simple phenomenological models and explore the idea of overdispersion in the data and how to determine an appropriate error structure within the analyses. In the third study, we use previously validated phenomenological models to generate short-term forecasts of the ongoing COVID-19 pandemic. During infectious disease epidemics, public health authorities rely on modeling results to inform intervention decisions and resource allocation. Therefore, we highlight the importance of interpreting modeling results with caution, particularly regarding theoretical aspects of mathematical models and parameter estimation methods. Further, results from modeling studies should be presented with quantified uncertainty and interpreted in terms of the assumptions and limitations of the model, methods, and data used. The methodology presented in this dissertation provides a thorough guide for conducting model-based inferences and presenting the uncertainty associated with parameter estimation results. |
