Immune boosting model overcomes the limitations of the leaky and polarized vaccination models

Vaccination plays a vital role in preventing the incidence of new infections and associated diseases. However, vaccination often fails to provide complete protection, which is referred to as imperfect protection. Thus, it is imperative to assess vaccine effectiveness (VE) to understand how a vaccinated individual is protected against infection.

A recent study published on the medRxiv* preprint server compares different approaches to the dynamical modeling of vaccination and immunity. Here, a new model based on an immune-boosting mechanism was developed, which overcomes the limitations of the common vaccine models. Furthermore, the proposed model demonstrated that immune-boosting bridges leaky and polarized vaccination models.

Study: Immune boosting bridges leaky and polarized vaccination models. Image Credit: metamorworks /

*Important notice: medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.


There are two main vaccine modeling systems that are referred to as ‘leaky’ and ‘all-or-nothing’ models, which assess the imperfect protection of vaccines.

The leaky model (VEL) assumes that a vaccinated person experiences a reduced force of infection. Comparatively, the all-or-nothing model, which is analogous to the polarized vaccination model (VEP), assumes that a certain percentage of vaccinated individuals is completely protected while the remaining individuals are completely susceptible. In the polarized immunity or polarized vaccination model, infection from one strain provides complete or no protection against other strains.

VEL and VEP indicate how many individuals are protected from infection. However, when both models have similar nominal vaccine efficacy, as reflected by equivalent values between VEL and VEP, they predict different epidemic dynamics.

In the case of a high force of infection, the leaky model unrealistically predicts that almost all individuals will get infected. Comparatively, the polarized model in this situation predicts that many individuals are permanently protected from the infection.

Both models are associated with several limitations. For example, the leaky model assumes that individuals do not lose any susceptibility when exposed to infection; however, in reality, vaccinated individuals can effectively protect themselves against infection when they are provided with immune boosting. This booster vaccination could reduce susceptibility to future infections.

About the study

In epidemiological modeling, the polarized model has been largely neglected due to its extreme assumptions. Although the leaky model is more commonly used, it also makes an unrealistic assumption that vaccinated individuals who are exposed to infections can remain susceptible, irrespective of previous exposures. As a result, the leaky vaccination model predicts a larger epidemic size.

The transmission dynamics of this model were able to bridge the dynamics of the standard leaky and polarized models. The newly developed model assumes that a population mixes homogeneously and there is no loss of immunity. In a homogenous population, it is expected that both vaccinated and unvaccinated individuals will be challenged with identical forces of infection.

The new model includes a parameter that is associated with the proportion of unsuccessful challenges that result in immune boosting. Furthermore, a generalized vaccination model was developed based on three mechanisms including dichotomous vaccine responses, partial protection, and immune boosting.

Initially, the dynamics of the leaky vaccination, polarized vaccination, and immune-boosting models were compared. For the simplistic simulation, it was assumed that once infected, both unvaccinated and vaccinated individuals transmit at the same rate.


It is important to understand VE against infection to predict epidemic dynamics. In this study, the epidemiological and immune-status trajectories were estimated using all three models.

The polarized vaccination and immune-boosting models were associated with identical incidence trajectories, whereas the leaky vaccination model predicted increased infection among vaccinated individuals. Interestingly, all three models predicted differential immune-status trajectories.

The boosting enabled vaccinated individuals to attain protection without developing a transmissible infection. The leaky model with perfect immune boosting model estimated similar epidemic dynamics to the polarized vaccination model. This is because individuals in both cases are completely immune after experiencing a prior infection.

The newly developed generalized vaccination model demonstrates that epidemic dynamics are most sensitive to the assumptions about vaccine-derived immunity at an intermediate VE. Furthermore, assumptions related to vaccine-derived immunity also influence VE estimations.

VE can be estimated based on cumulative incidence or hazard rates. In the current study, it was assumed that natural infections provide permanent protection against future infections. In reality, immunity induced through natural infection or vaccination often wanes over time for many pathogens.

When immunity declines, polarized vaccination and immune-boosting models may not necessarily predict identical dynamics. These limitations must be addressed in the future.


The current study demonstrates that immune boosting can bridge the differences between leaky and polarized vaccination models and serve as a critical component for measuring VE. These findings challenge the fundamental assumptions of commonly used vaccination models and provide a novel framework to understand the epidemiological impact of vaccination better.

*Important notice: medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Journal reference:
  • Preliminary scientific report. Park, W. S., Li, M., C. J. E., et al. (2023) Immune boosting bridges leaky and polarized vaccination models. medRxiv. doi:10.1101/2023.07.14.23292670.

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Tags: Efficacy, immunity, Vaccine

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Written by

Dr. Priyom Bose

Priyom holds a Ph.D. in Plant Biology and Biotechnology from the University of Madras, India. She is an active researcher and an experienced science writer. Priyom has also co-authored several original research articles that have been published in reputed peer-reviewed journals. She is also an avid reader and an amateur photographer.

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