Dynamic Estimation of Epidemiological Parameters of COVID-19 Outbreak and Effects of Interventions on Its Spread

Hongzhe Zhang; Xiaohang Zhao; Kexin Yin; Yiren Yan; Wei Qian; Bintong Chen; Xiao Fang

A key feature of our method is an attempt to recover true numbers of infections from their respective official numbers reported by the government. This is done by introducing transformation functions with under-reporting factors, and calibrating them via a Bayesian estimation approach, which is discussed in detail in the Method section. Fig. 3 shows the dynamics of the under-reporting factor a for the period between January 19, 2020 and February 24, 2020. Note that a is the ratio of the official daily increased number of infected and quarantined cases to its respective true number. Like R, a is also estimated using a rolling-window approach and a of day t denotes the under-reporting ratio over the time window of [t, t + 10]. Fig. 3 plots a of Wuhan in a solid black line, with the shaded area representing the 95% credible interval. As shown, a of January 19, 2020 was 0.28 [95% CI 0.14-0.73], indicating that official daily increased numbers of infected and quarantined cases over the window of January 19, 2020 to January 29, 2020 were on average 28% of their respective true numbers. The under-reporting factor of Wuhan gradually increased over time. For example, the underreporting ratio over the window of January 29, 2020 to February 8, 2020 was 0.55 [95% CI 0.20-0.99] and that over the window of February 15, 2020 to February 25, 2020 was 0.94 [95% CI 0.43-0.99]. The evolution of a in Wuhan is in alignment with the reality. Due to insufficient testing and treatment capacities at the beginning of the observation period, many infected people were not tested or hospitalized hence not on government statistics. Through the addition of testing and treatment facilities, more infected people got tested and hospitalized, thereby increasing the under-reporting factor. Fig. 3 also presents the under-reporting factor of Shanghai and Beijing in a solid blue line and a solid green line, respectively. Clearly, all three cities underreported the actual number of quarantined cases at the beginning. While Shanghai and Beijing improved the reporting accuracy quickly, Wuhan did not catch up until the end of period. This result is consistent with the fact that Wuhan experienced explosive number of COVID-19 infections in contrast to the other two cities. But it did not have sufficient medical resources and hospital capacity to test and treat all the infected cases. The discrepancies between true and official numbers of infections in Fig. 3 imply that a data transformation approach, such as the one proposed in this paper, is necessary before estimating the epidemiological parameters of the COVID-19 outbreak in Wuhan.