2026/07/22 by David J. D. Earn, Todd L. Parsons
#q-bio.PE #q-bio.QM
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.