Time-varying reproductive number estimation for practical application in structured populations

EpiEstim is a popular statistical framework designed to produce real-time estimates of the time-varying reproductive number, ${ℛ}_t$ . However, the methods in EpiEstim have not been tested in small, non-randomly mixing populations to determine if the resulting ${\widehat{ℛ}}_t$ estimates are temporally biased. Thus, we evaluate the temporal performance of EpiEstim ${\widehat{ℛ}}_t$ estimates when population structure is present, and then demonstrate how to recover temporal accuracy using an approximation with EpiEstim.

Following a real-world example of a COVID-19 outbreak in a small university town, we generate simulated case report data from a two-population mechanistic model with an explicit generation interval distribution and expression to compute true ${ℛ}_t$ . To quantify the temporal bias, we compare the time points when true ${ℛ}_t$ and estimated ${\widehat{ℛ}}_t$ from EpiEstim fall below the critical threshold of 1.

When population structure is present but not accounted for ${\widehat{ℛ}}_t$ estimates from EpiEstim prematurely fall below 1. When incidence data is aggregated over weeks the estimates from EpiEstim fall below the critical threshold at a later time point than estimates from daily data, however, population structure does not further affect timing differences between aggregated and daily data. Last, we show it is possible to recover the correct timing when by using the lagging subpopulation outbreak to estimate ${\widehat{ℛ}}_t$ for the total population with EpiEstim.

${ℛ}_t$ is a key parameter used for epidemic response. Since population structure can bias ${ℛ}_t$ near the critical threshold of 1, EpiEstim should be prudently applied to incidence data from structured populations.