Semester Award Granted

Summer 2025

Submission Date

August 2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Thesis/Dissertation Advisor [Chair]

Necibe Tuncer

Abstract

Understanding and controlling the spread of infectious diseases requires integrative mathematical models that connect biological processes across multiple scales, from individual-level transmission dynamics to population-level epidemic behavior. In this work, we develop and analyze multiscale mathematical models to investigate the transmission of emerging and re-emerging infectious diseases, with a strong focus on structural and practical identifiability to ensure model reliability.

We begin by investigating the transmission dynamics of the Usutu virus (USUV), an emerging mosquito-borne virus of growing concern in Europe and Africa. Understanding the epidemiology of such pathogens requires a systems-level approach that captures biological processes across multiple scales, from individual bird infections to bird-to-vector transmission, population-level incidence in birds and mosquitoes, and the potential for spillover into human populations. Due to sparse field data for new pathogens, we integrate laboratory-based inoculation and transmission experiments with dynamical mathematical modeling to construct a multiscale framework. Our models link within-host viral load data and host-to-vector transmission probabilities to epidemiological-scale predictions for two USUV strains. We explore how model structure, data uncertainty, and experimental design influence predictions across scales. Our results reveal that within-host peak viremia does not consistently correlate with infection incidence at the population level and that uncertainty at one scale can propagate and impact predictions at others. Through simulation-based studies, we identify optimal experimental design strategies, such as increased sampling frequency, that enhance parameter identifiability and improve the robustness of epidemiological predictions. These insights are essential to improve forecasts and guide efforts to assess and reduce the risk of spillover events.

We also develop and analyze within-host models to assess how model structure and data availability affect parameter estimation. We use four models of increasing biological complexity for influenza A and assess identifiability under various data scenarios, offering guidelines for model selection and collection. For HIV, we evaluate nutrition-linked and immune-structured models, showing structural identifiability from clinical data but highlighting practical limitations due to data sparsity and noise. Across all models, we emphasize the importance of sampling frequency and optimal experimental design.

In addition to studying detailed biological processes through mechanistic models, we incorporate simpler data-driven phenomenological models to improve epidemic forecasting and improve understanding of disease dynamics. We investigate six phenomenological growth models, reformulating them for structural identifiability analysis using the StructuralIdentifiability.jl package. We test these models on Monkey pox, COVID-19, and Ebola data and assess practical identifiability. We also produce a tutorial-based primer on structural identifiability with DAISY and Mathematica, offering researchers practical guidance and illustrative examples.

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