A statistical framework for tracking the time-varying superspreading potential of COVID-19 epidemic

Abstract

Timely detection of an evolving event of an infectious disease with superspreading potential is imperative for territory-wide disease control as well as preventing future outbreaks. While the reproduction number (R) is a commonly-adopted metric for disease transmissibility, the transmission heterogeneity quantified by dispersion parameter k, a metric for superspreading potential is seldom tracked. In this study, we developed an estimation framework to track the time-varying risk of superspreading events (SSEs) and demonstrated the method using the three epidemic waves of COVID-19 in Hong Kong. Epidemiological contact tracing data of the confirmed COVID-19 cases from 23 January 2020 to 30 September 2021 were obtained. By applying branching process models, we jointly estimated the time-varying R and k. Individual-based outbreak simulations were conducted to compare the time-varying assessment of the superspreading potential with the typical non-time-varying estimate of k over a period of time. We found that the COVID-19 transmission in Hong Kong exhibited substantial superspreading during the initial phase of the epidemics, with only 1 % (95 % Credible interval [CrI]: 0.6-2 %), 5 % (95 % CrI: 3-7 %) and 10 % (95 % CrI: 8-14 %) of the most infectious cases generated 80 % of all transmission for the first, second and third epidemic waves, respectively. After implementing local public health interventions, R estimates dropped gradually and k estimates increased thereby reducing the risk of SSEs to approaching zero. Outbreak simulations indicated that the non-time-varying estimate of k may overlook the possibility of large outbreaks. Hence, an estimation of the time-varying k as a compliment of R as a monitoring of both disease transmissibility and superspreading potential, particularly when public health interventions were relaxed is crucial for minimizing the risk of future outbreaks.

Keywords: COVID-19; SARS-CoV-2; Superspreading; Transmission heterogeneity.

Fig. 1

Epidemic curve of confirmed cases in Hong Kong by week (n = 12,209). All cases were categorized into transmission clusters by colors based on the settings where the infections occurred.

Fig. 2

Observed secondary case distributions by month in Hong Kong. Secondary case distributions of identified 2130 infectors and 5689 infectees in Hong Kong during study period. No transmission pairs were detected in January 2020 and from July to September 2021.

Fig. 3

Identified SSEs by 30 September 2021 in Hong Kong. The SSEs were defined with as a single generation of spread from the source case, who had at least 6 secondary cases. The size of the bubble represents the number of the secondary cases of a superspreading event. The bubbles were colored by transmission settings, shaped by asymptomatic or symptomatic super-spreaders. The location of the bubble is the report date of the first infectee and the error bar represents the duration of the SSEs from the illness onset date of the super-spreaders to the report date of the last infectee. The labeled SSEs were the three largest among others and were suspected as the key initiators of the subsequent new outbreaks (Adam et al., 2020, Westbrook, 2020, Lee, 2021).

Fig. 4

Time-varying estimations by illness onset date. (a) Epidemic curve by illness onset date in Hong Kong by 25 July 2021. The shaded area represents the intervention (red) and relaxation (blue) phases, respectively. The black bar denotes the incidence, and the purple solid line represents the Hong Kong government stringency index reflecting the intensity of implemented public health interventions, which was displayed in the scale of 7-day moving averages in percentage. (b) Time-varying estimation of R. (c) Time-varying estimation of k. (d) Estimated time-varying proportion of cases that generates 80 % of all transmissions. (e) Estimated time-varying risks of SSEs, which is the expected probability of SSEs obtained from the NBD secondary case distributions for given R and k estimates. The solid points represent the median estimates and the error bars in (b), (c), (d) and (e) denote the 95 % credible intervals. The red horizontal dashed lines in (b) and (c) denote values of estimates equal to 1. The y-axis in (b) and (c) were log10 transformed though the values on the ticks remained untransformed.

Fig. 5

Outbreaks simulations by branching process. Fifty outbreaks initiated by 5 cases were simulated under different scenarios of R and k values. First two rows of figures represented the epidemic curve and cumulative cases by generation of infections, and the last two rows represented the distributions of simulated outbreak sizes and distributions of secondary cases by the source cases over the course of the 50 simulated outbreaks. The solid black curve in the distributions of simulated outbreak sizes plots represented the kernel density. The y-axis in the epidemic curve and cumulative cases plots were square root transformed though the values on the ticks remained untransformed. The y-axis in the secondary case distribution were log transformed though the values on the ticks remained untransformed.