During the COVID-19 pandemic, many questions arose about the effectiveness, necessity, and duration of interventions implemented to mitigate the transmission of SARS-CoV-2. For instance, limited initial supply of SARS-CoV-2 vaccine raised the question of how to prioritize available doses. In this thesis, I quantify the effectiveness of vaccination and testing policies using mathematical models to address these types of questions. Using SEIR-type mechanistic models, I investigate SARS-CoV-2 transmission dynamics in terms of age and immune status. By analyzing the cumulative number of simulated infections and deaths under different vaccination prioritization strategies, I demonstrate that prioritizing adults aged 60+ for initial COVID-19 vaccine doses minimizes mortality, and this strategy is robust across countries, transmission rates, vaccination rollout speeds, and estimates of infection-acquired immunity. I use a similar modeling approach to evaluate the effectiveness of unvaccinated-only testing programs in mixed-immunity populations, finding their effectiveness generally limited and dependent on population immunity, non-pharmaceutical interventions, and participation. Lastly, using a probabilistic model that incorporates within-host viral kinetics and theory from stochastic processes, I evaluate the potential effectiveness of screening travelers with molecular tests. This project considers screening for SARS-CoV-2 as well as influenza A, SARS-CoV-1, and Ebola to evaluate the potential effectiveness of these screening programs in general. I demonstrate how, for any pathogen or test, traveler screening is fundamentally limited by the amount of time before infection and detectability. The overarching goals for this thesis are to further our understanding of transmission dynamics and the role of targeted interventions in light of individual variation in susceptibility and infectiousness, and to evaluate and inform relevant public health policies.