Open AccessInferring the reproduction number using the renewal equation in heterogeneous epidemics
Author(s) -
Will Green,
Neil Ferguson,
Anne Cori
Publication year - 2022
Publication title -
journal of the royal society interface
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.655
H-Index - 139
eISSN - 1742-5689
pISSN - 1742-5662
DOI - 10.1098/rsif.2021.0429
Subject(s) - transmissibility (structural dynamics) , basic reproduction number , transmission (telecommunications) , reproduction , population , biology , generation time , statistics , inference , pandemic , demography , mathematics , covid-19 , computer science , medicine , disease , ecology , infectious disease (medical specialty) , telecommunications , physics , artificial intelligence , vibration isolation , quantum mechanics , pathology , sociology , vibration
Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the generation time distribution. In this paper, we derive a multi-type equivalent to the renewal equation to estimate a reproduction number which accounts for heterogeneity in transmissibility including through asymptomatic transmission, symptomatic isolation and vaccination. We demonstrate how use of the renewal equation that misses these heterogeneities can result in biased estimates of the reproduction number. While the bias is small with symptomatic isolation, it can be much larger with asymptomatic transmission or transmission from vaccinated individuals if these groups exhibit substantially different generation time distributions to unvaccinated symptomatic transmitters, whose generation time distribution is often well defined. The bias in estimate becomes larger with greater population size or transmissibility of the poorly characterized group. We apply our methodology to Ebola in West Africa in 2014 and the SARS-CoV-2 in the UK in 2020–2021.