The shape of waning vaccinal immunity: Implications for control

The COVID-19 pandemic and current uncertainties about H5N1 influenza underscore the importance of vaccination for both community immunity and to prevent pathogen invasion. While the duration of a fully-immune period is often included in epidemiological models with waning immunity, the relative susceptibility to infection in fully-waned individuals and moreover their interplay that determines the shape of the trajectory of waning vaccinal immunity also may have important impacts on pathogen invasion potential. In this paper, we examine pathogen invasion outcomes with a simple mathematical framework that embeds the shape of vaccinal immunity within a buffered susceptibility framework. Using illustrative examples, we show pathogen invasion hinges on the characteristics of this shape, resulting in a large variation in outcomes. A key result is that stronger immunity (i.e. a smaller relative susceptibility in fully-waned individuals) can have a dramatic impact on such invasion characteristics, but the magnitude of this effect crucially depends on the underlying shape of immunity: the initial rate of waning is critical to the outcome. Our results highlight the importance of measuring the relative susceptibility of infection in fully-waned individuals. Additionally, they illustrate the importance of characterising host immune responses granularly and of taking this into account in pathogen-specific epidemiological models.