Two different epidemiological models of vaccination are commonly used in dynamical modeling studies. The leaky vaccination model assumes that all vaccinated individuals experience a reduced force of infection by the same amount. The polarized vaccination model assumes that some fraction of vaccinated individuals are completely protected, while the remaining fraction remains completely susceptible; this seemingly extreme assumption causes the polarized model to always predict lower final epidemic size than the leaky model under the same vaccine efficacy. However, the leaky model also makes an implicit, unrealistic assumption: vaccinated individuals who are exposed to infection but not infected remain just as susceptible as they were prior to exposures (i.e., independent of previous exposures). To resolve the independence assumption, we introduce an immune boosting mechanism, through which vaccinated, yet susceptible, individuals can gain protection without developing a transmissible infection. The boosting model further predicts identical epidemic dynamics as the polarized vaccination model, thereby bridging the differences between two models. We further develop a generalized vaccination model to explore how the assumptions of immunity affect epidemic dynamics and estimates of vaccine effectiveness.

Different assumptions about the long- and medium-term effects of protective vaccination can predict sharply different epidemiological dynamics. However, there has been limited discussion about which assumptions are more realistic and therefore more appropriate for making public health decisions …