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

Abstract

Background: The time-varying reproduction number, R t , is commonly used to monitor the transmissibility of an infectious disease during an epidemic, but standard methods for estimating R t seldom account for the impact of overdispersion on transmission. Methods: We developed a negative binomial framework to estimate R t and a time-varying dispersion parameter (k t ). 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 R t peaking 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 k t <0.5 at the start of both waves, indicating appreciable heterogeneity in transmission. We also found that k t decreased sharply to around 0.4 when a large cluster of infections occurred. Conclusions: Our proposed approach can contribute to the estimation of R t and monitoring of the time-varying dispersion parameters to quantify the role of superspreading.