The Estimated Time-Varying Reproduction Numbers during the Ongoing Epidemic of the Coronavirus Disease 2019 (COVID-19) in China

Fu-Chang Hu; Fang-Yu Wen

First, we laid out the conceptual framework below. In an epidemic of infectious disease, any susceptible subject who becomes a patient usually goes through the following three stages: infection, development of symptoms, and diagnosis of the disease. Theoretically, to estimate R0 or R0(t), we need the information about the distribution of generation time (GT), which is the time interval between the infection of the index case and the infection of the next case infected directly from the index case. 5 Yet, the time of infection is most likely unavailable or inaccurate, and thus investigators collect the data about the distribution of serial interval (SI) instead, which is the time interval between the symptom onset of the index case and the symptom onset of the next case infected directly from the index case. 5 Nevertheless, the data of symptom onset are not publically available and almost always have the problem of delayed reporting in any ongoing epidemic of infectious disease because they are usually recorded at diagnosis. 2 Hence, we took a common approach in statistics to tackle this problem by specifying the best plausible distributions of SI according to the results obtained from previous studies of similar epidemics, and then applied the novel estimation method implemented in the EpiEstim package to the data of daily new confirmed cases in practice. 4, 5 Next, we considered two plausible scenarios for studying the ongoing COVID-19 epidemic in China. The estimate_R function of the EpiEstim package assumes a Gamma distribution for SI by default to approximate the infectivity profile. 4 Technically, the transmission of an infectious disease is modeled with a Poisson process. 5 When we choose a Gamma prior distribution for SI, the Bayesian statistical inference leads to a simple analytical expression for the Gamma posterior distribution of R0(t). 5 In the first scenario, we specified the mean (SD) of the Gamma distribution for SI to be 8.4 (3.8) days to mimic the 2003 epidemic of the severe acute respiratory syndrome (SARS) in Hong Kong. 5 Then, in the second scenario, we specified the mean (SD) of the Gamma distribution for SI to be 2.6 (1.5) days to mimic the 1918 pandemic of influenza in Baltimore, Maryland. 5 Given an observed series of daily new confirmed cases, the shorter SI, the smaller R0(t). According to the current understanding, the transmissibility of COVID-19 was higher than SARS, but lower than influenza. 1 Hence, although we did not know the true distribution(s) of SI for the ongoing epidemic of COVID-19 in China, 6 these two scenarios helped us catch the behavior pattern of this epidemic along with the time evolution.