A major goal of the biomathematics discipline is to optimize mathematical models for biological processes. This optimization can take on various forms; finding the appropriate model that fits available data, allows for accurate inference, and is computationally feasible is no easy task and requires an understanding of both the biological processes at hand and the mathematics behind each potential model or algorithm. In this dissertation, I seek to understand how mathematical modeling choices affect our ability to understand human disease. I study infectious, cancerous, and polygenic disease from a variety of computational perspectives. First, I apply methods for differential sensitivity analysis in biological models for both cancerous and infectious disease spread. I compare prediction accuracy for existing first-order methods and propose a second-order method with enhanced flexibility both in terms of the model for which it is applied and the programming environment available. Second, I compare statistical approaches for uncovering genetics of complex disease in admixed populations, using likelihood ratio tests to understand how to incorporate local ancestry in genome wide association studies to achieve the highest power. Third, I utilize machine learning methods to reduce diagnostic delay for patients across the University of California Health system. I adapt a logistic regression model to find patients likely to have common variable immune deficiencies from one health system to five health systems. I also adapt this algorithm from the immunology realm to the cardiology realm to predict cardiac amyloidosis. Along the way, I use this context to study automated feature selection, longitudinal feature engineering, and observational bias in electronic health record data.