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Infectious disease control measures often require collective compliance of large numbers of individuals to benefit public health. This raises ethical questions regarding the value of the public health benefit created by individual and collective compliance. Answering these requires estimating the extent to which individual actions prevent infection of others. We develop mathematical techniques enabling quantification of the impacts of individuals or groups complying with three public health measures: border quarantine, isolation of infected individuals, and prevention via vaccination/prophylaxis. The results suggest that (i) these interventions exhibit synergy: They become more effective on a per-individual basis as compliance increases, and (ii) there is often substantial "overdetermination" of transmission. If a susceptible person contacts multiple infectious individuals, an intervention preventing one transmission may not change the ultimate outcome (thus, risk imposed by some individuals may erode the benefits of others' compliance). These results have implications for public health policy during epidemics.