Jointly estimating transmissibility and prior immunity from epidemic time series
Abstract
Infectious disease time series are often used to estimate a pathogen's basic reproduction number, R0. However, fits of epidemic models to time series conflate pathogen transmissibility with pre-existing population immunity, so only the *effective* reproduction number, Reff, can be inferred. This composite parameter is the product of the underlying R0 and the pre-epidemic susceptible fraction, x-. We show that a conservation law associated with epidemic momentum---prevalence weighted by potential to infect---makes it possible to disentangle transmissibility from prior immunity and to infer R0 and x- separately from a single epidemic time series. We test the methodology using stochastic epidemic simulations, and illustrate the approach with a reappraisal of influenza transmissibility during the 1918 pandemic, estimating rather than assuming the degree of prior population immunity. For the autumn wave in Philadelphia, USA, we find R0≈2.7 and x-≈0.8, implying that about 20% of the population was already immune before that wave, plausibly as a result of infection during the spring 1918 herald wave.
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BibTeX
@misc{earn2026jointly,
title = {{Jointly estimating transmissibility and prior immunity from epidemic time series}},
author = {David J. D. Earn and Todd L. Parsons},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.21657},
eprint = {2607.21657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21657},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Jointly estimating transmissibility and prior immunity from epidemic time series
AU - David J. D. Earn
AU - Todd L. Parsons
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2607.21657
UR - https://arxiv.org/abs/2607.21657
AB - Infectious disease time series are often used to estimate a pathogen's basic reproduction number, R_0. However, fits of epidemic models to time series conflate pathogen transmissibility with pre-existing population immunity, so only the *effective* reproduction number, R_eff, can be inferred. This composite parameter is the product of the underlying R_0 and the pre-epidemic susceptible fraction, x^-. We show that a conservation law associated with epidemic momentum---prevalence weighted by potential to infect---makes it possible to disentangle transmissibility from prior immunity and to infer R_0 and x^- separately from a single epidemic time series. We test the methodology using stochastic epidemic simulations, and illustrate the approach with a reappraisal of influenza transmissibility during the 1918 pandemic, estimating rather than assuming the degree of prior population immunity. For the autumn wave in Philadelphia, USA, we find R_0≈2.7 and x^-≈0.8, implying that about 20% of the population was already immune before that wave, plausibly as a result of infection during the spring 1918 herald wave.
ER -