Characterizing the effective reproduction number during the COVID-19 pandemic: Insights from Qatar's experience

Abstract

Background: The effective reproduction number, R_t , is a tool to track and understand pandemic dynamics. This investigation of R_t estimations was conducted to guide the national COVID-19 response in Qatar, from the onset of the pandemic until August 18, 2021.

Methods: Real-time "empirical" R_t ^Empirical was estimated using five methods, including the Robert Koch Institute, Cislaghi, Systrom-Bettencourt and Ribeiro, Wallinga and Teunis, and Cori et al. methods. R_t was also estimated using a transmission dynamics model (R_t ^Model-based ). Uncertainty and sensitivity analyses were conducted. Correlations between different R_t estimates were assessed by calculating correlation coefficients, and agreements between these estimates were assessed through Bland-Altman plots.

Results: R_t ^Empirical captured the evolution of the pandemic through three waves, public health response landmarks, effects of major social events, transient fluctuations coinciding with significant clusters of infection, and introduction and expansion of the Alpha (B.1.1.7) variant. The various estimation methods produced consistent and overall comparable R_t ^Empirical estimates with generally large correlation coefficients. The Wallinga and Teunis method was the fastest at detecting changes in pandemic dynamics. R_t ^Empirical estimates were consistent whether using time series of symptomatic PCR-confirmed cases, all PCR-confirmed cases, acute-care hospital admissions, or ICU-care hospital admissions, to proxy trends in true infection incidence. R_t ^Model-based correlated strongly with R_t ^Empirical and provided an average R_t ^Empirical .

Conclusions: R_t estimations were robust and generated consistent results regardless of the data source or the method of estimation. Findings affirmed an influential role for R_t estimations in guiding national responses to the COVID-19 pandemic, even in resource-limited settings.

Figure 1

Effective reproduction numbers R_t^Empirical and R_t^Model-based in Qatar. A) Trend in R_t^Empirical and R_t^Model-based, April 1, 2020 to August 18, 2021, and association with major events, response landmarks, and introduction and expansion of the Alpha (B.1.1.7) and Beta (B.1.135) variants. B) Trend in R_t^Empirical for only the Alpha variant cases, February 1, 2021 to April 1, 2021. R_t^Empirical was estimated using the Robert Koch Institute method [23] applied to symptomatic case series data. The dashed green line represents the threshold of R₀ = 1.

Figure 2

Sensitivity analyses of estimated R_t^Empirical using the Robert Koch Institute method. A) Sensitivity analysis using the time series of all diagnosed cases instead of only symptomatic cases in estimating R_t^Empirical. B) Sensitivity analysis using the time series of hospital admissions in acute-care beds instead of symptomatic cases in estimating R_t^Empirical. C) Sensitivity analysis using the time series of hospital admissions in ICU-care beds instead of symptomatic cases in estimating R_t^Empirical. D) Sensitivity analysis using different values for the generation time in estimating R_t^Empirical. The dashed green line represents the threshold of R₀ = 1.

Figure 3

Trend in R_t^Empirical in Qatar, April 1, 2020 to August 18, 2021, using the A) Robert Koch Institute method [23], B) Cislaghi method [35], C) Systrom-Bettencourt and Ribeiro method [12,38-40], D) Wallinga and Teunis method [36], and E) Cori et al. method [32]. The figure includes the 95% uncertainty or credible interval, as applicable for each method. The dashed green line represents the threshold of R₀ = 1.

Figure 4

Bland-Altman plots for agreement between different methods for estimating R_t. A) Bland-Altman comparison between R_t^Empirical estimated using the Robert Koch Institute method [23] and R_t^Model-based. Bland-Altman comparison between R_t^Empirical estimated using the Robert Koch Institute method [23] and that estimated using the B) Cislaghi method [35], C) Systrom-Bettencourt and Ribeiro method [12,38-40], D) Wallinga and Teunis method [36], and E) Cori et al. method [32]. The black line is the mean difference (bias) and the dashed red lines show the 95% limits of agreement.

Figure 5

Pairwise comparison between R_t^Empirical estimated using the Robert Koch Institute method [23] and that estimated using the A) Cislaghi method [35], B) Systrom-Bettencourt and Ribeiro method [12,38-40], C) Wallinga and Teunis method [36], and D) Cori et al. method [32]. The dashed green line represents the threshold of R₀ = 1.