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When to boost: How dose timing determines the epidemic threshold

Alessandro Celestini1, Francesca Colaiori2,3,*, Stefano Guarino1, Enrico Mastrostefano1, Francesca Pelusi4, and Lena Rebecca Zastrow5

  • 1CNR, Institute for Applied Mathematics, Rome, Italy
  • 2CNR, Institute for Complex Systems, Rome, Italy
  • 3Department of Physics, Sapienza University, Rome, Italy
  • 4CNR, Institute for Applied Mathematics, Naples, Italy
  • 5ISPRA, Department of the Geological Survey of Italy, Rome, Italy

  • *Contact author: francesca.colaiori@cnr.it
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Phys. Rev. Research 7, 033125 – Published 6 August, 2025

DOI: https://doi.org/10.1103/cykd-2rjn

Abstract

Most vaccines require multiple doses, the first to induce recognition and antibody production and subsequent doses to boost the primary response and achieve optimal protection. We show that properly prioritizing the administration of first and second doses can shift the epidemic threshold, separating the disease-free from the endemic state and potentially preventing widespread outbreaks. Assuming homogeneous mixing, we prove that at a low vaccination rate, the best strategy is to give absolute priority to first doses. In contrast, for high vaccination rates, we propose a scheduling that outperforms a first-come first-served approach. We identify the threshold that separates these two scenarios and derive the optimal prioritization scheme and interdose interval. Agent-based simulations on real and synthetic contact networks validate our findings. We provide specific guidelines for effective resource allocation, showing that adjusting the timing between the primer and booster significantly impacts epidemic outcomes and can determine whether the disease persists or disappears.

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Phys. Rev. Research 7, 033125– Published 6 August, 2025
  • Received 25 February 2025
  • Accepted 11 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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