The COVID-19 pandemic has inflicted significant losses and disruptions on the society since its emergence in 2020. During this difficult time, colleges and universities faced numerous operational decisions that needed to balance safety, educational quality, and cost. This dissertation focuses on a few projects that partly supported safe in-person instruction at Cornell University during COVID-19 and hold great promise for broader applications. First, we study the risk of returning to pre-pandemic level in-person instruction through mathematical modeling and agent-based simulation. We estimate the risk associated with different policies and recommend that fully masked in-person classrooms would be safe without needing to assign seats or update the rooms for better ventilation. This result supported the university's decision to return to regular in-person instruction in Fall 2021. Second, we conduct survival analysis to evaluate the risk of infection associated with attending classes in person. Using data on surveillance testing, class schedules, and class enrollments in Fall 2021 and Spring 2022, we construct a novel feature to quantify the amount of exposure that a student has in the classroom. Using extended Cox regression and logistic regression, we find that attending classes was associated with minimal increase in the risk of infection. Third, we investigate group testing under the presence of correlation among samples. In large-scale screenings, correlation between samples in the same pool is naturally induced through human behavior and the process of sample collection. By realistically modeling network contagion, viral load progression, and the dilution effect in pooled testing, we show that such correlation improves the sensitivity and resource efficiency of population-wide testing. Thus, policy-makers envisioning using group testing for large-scale screening should take correlation into account and intentionally maximize it when possible. Fourth, we present an approach for uncertainty quantification of simulation models with a large number of parameters. Using a linear approximation, we quantify the sensitivity of simulation output to each parameter. Furthermore, we adapt ideas from robust optimization and identify a one-dimensional family of parameter configurations associated with different pessimism levels. This method provides insight into the uncertainty of the compartmental simulation developed by the Cornell COVID-19 modeling team, and can be broadly used for sensitivity analysis and scenario analysis in an interpretable way for various simulation models.