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Abstract
Biological phenomena are generally complex networks that involve several interactions between components (genes, proteins, cells, other biochemical species, etc.). These networks drive physiological functions and understanding these functions allows researchers to understand diseases, specifically when perturbing these networks. Mathematical modeling is a method to fully encompass these interactions and nuances of these networks, by using computational and mathematical representations of these systems. These models incorporate data from several sources and combining these data with a physiological understanding of the system at hand results in large sets of differential equations to provide a mechanistic understanding of the processes involved. When modeling however, several sources of variability arise when considering the data used, the system modeled, and the equations used to represent the system. In this dissertation we 1) extended an existing mathematical model of the RAS to quantify the interplay of therapy, SARS-CoV-2 infection, and chronic diseases or aging between pro-and anti-inflammatory arms of the RAS. 2) developed a mechanistic model of heart failure biomarkers and integrate it into an existing model of cardiorenal function, in order to describe and explain changes in biomarker levels with drug treatments and reduced kidney function observed in clinical trials, and 3) developed a framework to analyze how parameters in ODE models vary as a function of available covariates. In this thesis, three different problems involving the application of ODE models and understanding of the related uncertainty will be addressed.