Modeling the Impact of Immune Boosting on Population-Level Vaccine Effectiveness

We extend the standard susceptible-infected-recovered framework to incorporate natural immune boosting during a short-scale outbreak.

By deriving closed-form final size relations, we analytically link total attack rates to boosting dynamics and vaccine coverage.

This framework identifies a critical boosting threshold: above it, higher vaccine coverage paradoxically decreases relative vaccine effectiveness.

This occurs because successful epidemic suppression deprives vaccinated individuals of the silent pathogen exposures required to maintain their relative immunological advantage.

Crucially, the overall population-level impact remains beneficial, consistently reducing absolute disease burden.

For highly transmissible variants, asymptotic analysis reveals that relative vaccine effectiveness converges to a positive limit entirely independent of coverage.