Background: Pre-pandemic empirical studies have produced mixed statistical results on the effectiveness of masks against respiratory viruses, leading to confusion that may have contributed to organizations such as the WHO and CDC initially not recommending that the general public wear masks during the COVID-19 pandemic. Methods: A threshold-based dose–response curve framework is used to analyse the effects of interventions on infection probabilities for both single and repeated exposure events. Empirical studies on mask effectiveness are evaluated with a statistical power analysis that includes the effect of adherence to mask usage protocols. Results: When the adherence to mask-usage guidelines is taken into account, the empirical evidence indicates that masks prevent disease transmission: all studies we analysed that did not find surgical masks to be effective were under-powered to such an extent that even if masks were 100% effective, the studies in question would still have been unlikely to find a statistically significant effect. We also provide a framework for understanding the effect of masks on the probability of infection for single and repeated exposures. The framework demonstrates that masks can have a disproportionately large protective effect and that more frequently wearing a mask provides super-linearly compounding protection. Conclusions: This work shows (1) that both theoretical and empirical evidence is consistent with masks protecting against respiratory infections and (2) that nonlinear effects and statistical considerations regarding the percentage of exposures for which masks are worn must be taken into account when designing empirical studies and interpreting their results.

Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models’ assumptions but less often justify their validity in the specific context in which they are being used. Our purpose is not to argue for specific alternatives or modifications to compartmental models, but rather to show how assumptions can constrain model outcomes to a narrow portion of the wide landscape of potential epidemic behaviors. This concrete examination of well-known models also serves to illustrate general principles of modeling that can be applied in other contexts.

Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less often justify their validity in the specific context in which they are being used. Our purpose is not to argue for specific alternatives or modifications to compartmental models, but rather to show how assumptions can constrain model outcomes to a narrow portion of the wide landscape of potential epidemic behaviors. This concrete examination of well-known models also serves to illustrate general principles of modeling that can be applied in other contexts.