Although there were cases confirmed on or before January 16, the official diagnostic protocol was released by WHO on January 17 (World Health Organization, 2020b). To adjust the impact of this event, we considered a time-varying reporting rate that follows a linear increasing trend, motivated by the previous study (Wu et al., 2010). We assumed that the reporting rate, r(t), started increasing on January 17, and stopped at the maximal level on January 21. The reporting rate increase corresponds to accounts for the announcement on improving the 2019-nCoV surveillance of the Hubei provincial government (Hubei provincial government, 2020). The length of the reporting increasing part roughly equals the average of the incubation periods of two other well-known coronavirus diseases, i.e., the Middle East Respiratory Syndrome (MERS) and the Severe Acute Respiratory Syndrome (SARS), i.e., 5 days (Bauch et al., 2005, Lin et al., 2018, Donnelly et al., 2003). Denoting the daily reported number of new cases by c(t) for the t-th day, then the adjusted cumulative number of cases, C(t), is C(t)=∑τ=0tc(τ)/r(τ). Instead of finding the exact value of r(t), we calculated the fold change in r(t) that is defined by the ratio of r on January 10 over that on January 24 minus 1. We illustrated six scenarios with 0- (no change), 0.5-, 1-, 2-, 4- and 8-fold increase in reporting rate, see Figure 1 (a), (c), (e), (g), (i) and (k).
Figure 1 The scenarios of the change in the reporting rate (top panels) and the exponential growth fitting (bottom panels). The top panels, i.e., (a), (c), (e), (g), (i) and (k), show the assumed change in the reporting rate. The bottom panels, i.e., (b), (d), (f), (h), (j) and (l), show the reported (or observed, green circles), adjusted (blue dots) and fitted (blue curve) number of 2019-nCoV infections, and the blue dashed lines are the 95%CI. The vertical grey line represents the date of January 16, 2020, after which the official diagnostic protocol was released by the WHO (World Health Organization, 2020). Panels (a) and (b) show the scenarios that the reporting rate was unchanged. Panels (c) and (d) show the scenarios that the reporting rate increased by 0.5-fold. Panels (e) and (f) show the scenarios that the reporting rate increased by 1-fold. Panels (g) and (h) show the scenarios that the reporting rate increased by 2-fold. Panels (i) and (j) show the scenarios that the reporting rate increased by 4-fold. Panels (k) and (l) show the scenarios that the reporting rate increased by 8-fold.