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. 2023 Jan 5:9:1079842.
doi: 10.3389/fmed.2022.1079842. eCollection 2022.

A comparative study on the three calculation methods for reproduction numbers of COVID-19

Buasiyamu Abudunaibi  1 , Weikang Liu  1 , Zhinan Guo  2 , Zeyu Zhao  1   3 , Jia Rui  1   3 , Wentao Song  1 , Yao Wang  1 , Qiuping Chen  3 , Roger Frutos  3 , Chenghao Su  4 , Tianmu Chen  1
Affiliations

A comparative study on the three calculation methods for reproduction numbers of COVID-19

Buasiyamu Abudunaibi et al. Front Med (Lausanne). .

Abstract

Objective: This study uses four COVID-19 outbreaks as examples to calculate and compare merits and demerits, as well as applicational scenarios, of three methods for calculating reproduction numbers.

Method: The epidemiological characteristics of the COVID-19 outbreaks are described. Through the definition method, the next-generation matrix-based method, and the epidemic curve and serial interval (SI)-based method, corresponding reproduction numbers were obtained and compared.

Results: Reproduction numbers (R eff ), obtained by the definition method of the four regions, are 1.20, 1.14, 1.66, and 1.12. Through the next generation matrix method, in region H R eff = 4.30, 0.44; region P R eff = 6.5, 1.39, 0; region X R eff = 6.82, 1.39, 0; and region Z R eff = 2.99, 0.65. Time-varying reproduction numbers (R t ), which are attained by SI of onset dates, are decreasing with time. Region H reached its highest R t = 2.8 on July 29 and decreased to R t < 1 after August 4; region P reached its highest R t = 5.8 on September 9 and dropped to R t < 1 by September 14; region X had a fluctuation in the R t and R t < 1 after September 22; R t in region Z reached a maximum of 1.8 on September 15 and decreased continuously to R t < 1 on September 19.

Conclusion: The reproduction number obtained by the definition method is optimal in the early stage of epidemics with a small number of cases that have clear transmission chains to predict the trend of epidemics accurately. The effective reproduction number R eff , calculated by the next generation matrix, could assess the scale of the epidemic and be used to evaluate the effectiveness of prevention and control measures used in epidemics with a large number of cases. Time-varying reproduction number R t , obtained via epidemic curve and SI, can give a clear picture of the change in transmissibility over time, but the conditions of use are more rigorous, requiring a greater sample size and clear transmission chains to perform the calculation. The rational use of the three methods for reproduction numbers plays a role in the further study of the transmissibility of COVID-19.

Keywords: COVID-19; definition methods; next generation matrix; reproduction number (R); serial interval (SI).

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Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Figures

Figure 1
Figure 1
The framework of this study.
Figure 2
Figure 2
The temporal distribution for COVID-19 outbreaks in four regions studied in this research. The horizontal axis is the dates when the outbreaks happened, and we used different shades of color for the bars in each figure to show the number of cases in different areas in these regions. (A) Region H, (B) Region P, (C) Region X, and (D) Region Z.
Figure 3
Figure 3
The transmission chains for COVID-19 outbreaks in four regions studied in this research. The dots in each figure represent the COVID-19 cases during each outbreak, while the bars between dots mean that these cases were on the same transmission chain. (A) Region H, (B) Region P, (C) Region X, and (D) Region Z.
Figure 4
Figure 4
The gamma distribution for the transmission chains for COVID-19 outbreaks in four regions studied in this research. The horizontal axis in each figure shows the number of transmissions caused by a single case, while the vertical axis is the frequency of the transmission number. The bars present the actual frequency in each outbreak, and the red curves are the curves of fitting, which follow a gamma distribution. (A) Region H, (B) Region P, (C) Region X, and (D) Region Z.
Figure 5
Figure 5
The simulation results of epidemic trends based on the different values of Reff in each region. (A) Region H, (B) Region P, (C) Region X, and (D) Region Z.
Figure 6
Figure 6
The simulation results of epidemic trends based on the different values of Rt in each region. (A) Region H, (B) Region P, (C) Region X, and (D) Region Z.
Figure 7
Figure 7
The decision tree for choosing the optimal reproduction number as an index for the transmissibility of SARS-CoV-2 during a COVID-19 epidemic.
See this image and copyright information in PMC

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