The Shape of Waning Vaccinal Immunity: Implications For Control
Graham R. Northrup, Mike Boots, Chadi M. Saad-Roy
Abstract
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.
Introduction
The COVID-19 pandemic highlighted the importance of waning immunity on epidemiological dynamics and public health interventions not least in the context of proposed nonpharmaceutical interventions that hinge on individual immune status, such as ‘shield immunity’. The watershed moment during the COVID-19 pandemic was the development and deployment of safe vaccines and while current formulations of COVID-19 vaccines only transiently prevent infection, effective transmission-blocking vaccines can result in pathogen control.
Materials and Methods:
We extend the model of Saad-Roy, Wagner et al. to include multiple partially susceptible classes. However, to focus on the waning process, we ignore characteristics of infections in priorly-immune individuals (which was modelled in). Thus, in our model, S0 is the class of completely naive hosts, S1 describes the class of vaccinated individuals where immunity has fully waned so that the relative susceptibility to infection is (e.g. describes a vaccine where immunity is eventually completely lost).
Discussion
We begin by visualizing over a variety of vaccination rates, waning rates, and over various waning schemes. We illustrate the dependence of on the duration of immunity and vaccination rate. For a particular parameter pair, we see that changing the waning scheme can dramatically alter the protection of a population. For example, a comparison of the early and late waning schemes for the same vaccination rate and duration of immunity, reveals that the can be more than four times greater if waning happens later. This is a massive difference, and has important implications for population level pathogen prevention.
Citation: Northrup GR, Boots M, Saad-Roy CM (2025) The shape of waning vaccinal immunity: Implications for control. PLOS Complex Syst 2(10): e0000071. https://doi.org/10.1371/journal.pcsy.0000071
Editor: Juan Gonzalo Barajas-Ramirez, IPICYT: Instituto Potosino de Investigacion Cientifica y Tecnologica AC, MEXICO
Received: October 14, 2024; Accepted: September 11, 2025; Published: October 14, 2025.
Copyright: © 2025 Northrup et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Code required to reproduce the figures found in the manuscript can be found at https://github.com/gnorthrup/WaningVaccines.
Funding: GRN and MB were supported by the BBSRC/NSF EEID research grant NSF-DEB- 2011109. This publication is funded in part by the Gordon and Betty Moore Foundation through grant no. GBMF10578. C.M.S.-R. gratefully acknowledges funding from the Miller Institute of UC Berkeley via a Miller Research Fellowship. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
