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

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.