Accounting for the Potential of Overdispersion in Estimation of the Time-varying Reproduction Number

Abstract

Background: The time-varying reproduction number, Rt, is commonly used to monitor the transmissibility of an infectious disease during an epidemic, but standard methods for estimating Rtseldom account for the impact of overdispersion on transmission. Methods: We developed a negative binomial framework to estimate Rtand a time-varying dispersion parameter (kt). We applied the framework to COVID-19 incidence data in Hong Kong in 2020 and 2021. We conducted a simulation study to compare the performance of our model with the conventional Poisson-based approach. Results: Our framework estimated an Rtpeaking around 4 (95% credible interval = 3.13, 4.30), similar to that from the Poisson approach but with a better model fit. Our approach further estimated kt<0.5 at the start of both waves, indicating appreciable heterogeneity in transmission. We also found that ktdecreased sharply to around 0.4 when a large cluster of infections occurred. Conclusions: Our proposed approach can contribute to the estimation of Rtand monitoring of the time-varying dispersion parameters to quantify the role of superspreading.