Epidemic trend of COVID-19 in Taiwan, May to June 2021.

The epidemic curve, the plot of the number of new cases against the date, week, or month of illness onset, plays a key role in infectious disease epidemiology. It shows the disease's magnitude and provides valuable information regarding the pattern of spread, mode of transmission, incubation period, and possible sources of an outbreak. Since the early May of 2021 when a large-scale community outbreak of coronavirus disease 2019 (COVID-19) erupted in Taiwan, the Central Epidemic Command Center (CECC) in Taiwan releases the updated COVID-19 epidemic curve in a press conference held daily.

Here, we propose that the growth rate curve provides additional insights into the trend of the epidemic. The growth rate (x 100%) per day is the symmetric percentage change for one day in the number of new cases. A positive growth rate indicates that the number of new cases is on the rise, a negative growth rate, that the number is declining, and a zero growth rate, that the number remains stable (at least temporally). The growth rate at a particular date, t, can be calculated as the natural logarithm of the ratio of the cumulative number of new cases from t+1 to t+3 and that from t-3 to t-1, followed by a division of 4 (Appendix 1). A plot of the growth rate per day against t is the growth rate curve. This should be a smooth curve since the above growth rate calculation entails a 7-day moving window, otherwise, a wider window may be needed. The growth rate plot is purely descriptive except for the very mild assumption that the number of new cases in the narrow time window around t follows an exponential growth or decay (Appendix 1); yet, it can also be linked to solid epidemic models just as Yu's ratio plot. By contrast, to plot the time-varying reproduction number (R ), one needs a priori information on the distribution of the serial interval (the time between the onset of symptoms in a primary case and the onset of symptoms in secondary cases) which is difficult to obtain during an outbreak.

We present a case study of the epidemic trend of the laboratory-confirmed indigenous COVID-19 cases in Taiwan from May 11 (when CECC issued a Level 2 Alert for COVID-19 outbreak) to June 9 (the 30th day on Alert Level 2 or higher). On May 22, CECC recognized a reporting delay problem and henceforth reallocated the backlog cases to the earlier dates when the specimens of these cases were collected (sampling date) and when the symptoms of the cases first appeared (onset date). The upper panels of Fig. 1 present the epidemic curves organized by reporting date (A), sampling date (B), and onset date (C), respectively, while the lower panels of the same figure, the corresponding growth rate curves (D, E, and F; shaded areas: 95% bootstrapped confidence intervals assuming Poisson distribution for the occurrence of the cases).

Figure 1

Epidemic curves (A, B, C) and growth rate curves (D, E, F; shaded areas: 95% bootstrapped confidence intervals assuming Poisson distribution for the occurrence of the cases) of COVID-19 in Taiwan from May 11, 2021, to June 9, 2021.

The epidemic curve by reporting date (A) initially rose to a small peak on May 17, to the summit on May 22, and then the curve fluctuated profoundly. The epidemic curve by sampling date (B) rose earlier to the summit on May 17 and then leveled off. The epidemic curve by onset date (C) leveled off even earlier on May 15, albeit with some fluctuations subsequently. CECC raised the Alert to Level 3 on May 19, partly because the outbreak showed no sign of abating as revealed from the epidemic curve by reporting date (A). In retrospect (i.e., after backlog correction), we see that the epidemic curve either by sampling date (B) or by onset date (C) had already leveled off at that time. This does not mean the raise of the Alert Level is unnecessary, though, since the cases of preclinical or asymptomatic infections at that time may still be on the rise.

The growth rate curves provided additional information. The growth rate curve by reporting date (D) began to decline on May 14, bounced back to a small peak on May 21, and then dropped near zero on May 25. The growth rate curve by sampling date (E) began to decline on the same date (May 14) but it dropped to near zero on a much earlier date (May 19). The timelines for the growth rate curve by onset date (F) are two days ahead of that by sampling date (E); the curve began to decline on May 12 (one day after the start of the intervention on closing the high-risk contact scenarios as per Level 2 Alert) and dropped near zero on May 17. The time interval between a growth rate curve's starting to decline and its dropping near-zero (or equivalently, its corresponding epidemic curve's peaking or leveling off) is 5 days by either sampling date or onset date, which corresponds incidentally to the average incubation period of COVID-19. By comparison, the time interval between the starting to decline and the dropping to zero is much longer (19 days) for the growth rate curve by reporting date, indicating substantial variability in the reporting delay distribution.

The growth rate of a disease is simple to calculate. A growth rate curve shows how the number of cases changes over time. We advocate presenting the growth rate curve alongside the epidemic curve of COVID-19 in Taiwan for better delineation of the epidemic trend and better communication with the public.

Funding

This paper is supported by grants from the in Taiwan (MOST 108-3017-F-002-001, MOST 108-2314-B-002-127-MY3), and the Innovation and Policy Center for Population Health and Sustainable Environment (Population Health Research Center, PHRC) from Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education in Taiwan (NTU-109L900308).

Declaration of competing interest

The authors have no conflicts of interest relevant to this article.