Our results indicated all seven countries showed a significant decline of daily increase rate against cumulative cases and time, indicating that the control measures, such as lockdown of the epicenter and social distancing adopted by these countries, were effective in reducing the spread of COVID-19. However, as compared to China and R. Korea, the other countries (Iran, Italy, Spain, Germany and France) showed a lower control efficiency in the later stage than before, which may have been caused by the difference in control measures at the community level (e.g. testing, tracking and isolating patients or suspected cases). Our study suggested that the daily increase rate could be useful for earlier assessment of transmission severity and trend of COVID-19, as well as the effectiveness of control measures.
Due to the highly contagious property of COVID-19, all seven countries showed a quick response to the appearance of COVID-19 cases. On January 20, soon after COVID-19 was identified as a novel coronavirus by Chinese scientists on January 7, 2020 [2, 3], the Chinese government incorporated COVID-19 into the management of statutory infectious diseases Class B and adopted prevention and control measures for Class A infectious diseases (http://www.chinacdc.cn/jkzt/crb/zl/szkb_11803/jszl_11813/202001/t20200121_211327.html). The lockdown of Wuhan (the epicenter) began on January 23 and lockdown of the whole country went into effect on January 25 (http://www.gov.cn/xinwen/2020-01/23/content_5471751.htm). Since then, travel restrictions and means for identification, isolation and observation of suspected or infected patients or places were strictly implemented. Although the effectiveness of city lockdown and travel restrictions adopted in China was questioned in the early days , they were later proven to be effective by the fact that China successfully contained the spread of COVID-19. Therefore, these control measures were later adopted by most countries around the world. R. Korea declared a state of war against the virus on March 3 (https://epaper.chinadaily.com.cn/a/202003/04/WS5e5ef8aea310a2fabb7a2a2d.html). Italy declared a public health emergency by January 31 and imposed nationwide lockdown on March 9 (https://www.chinadaily.com.cn/a/202003/10/WS5e666e5aa31012821727d9aa.html). Spain declared a state of emergency on March 14 and lockdown on March 16 (https://www.chinadaily.com.cn/a/202003/15/WS5e6ce8f5a31012821727f20a.html). France declared the emergency on March 16 and lockdown on March 17 (https://www.chinadaily.com.cn/a/202003/17/WS5e7013efa31012821727f8d8.html). All regional governments in Germany had declared curfews or restrictions in public spaces March 22 (https://en.m.wikipedia.org/wiki/2020_coronavirus_pandemic_in_Germany). Iran declared city lockdowns on March 26 (https://www.aa.com.tr/en/health/covid-19-divergent-views-at-top-delay-lockdown-in-iran/1782835). The significant negative associations between the daily increase rate and cumulative cases or time indicated that lockdowns and travel restrictions were effective in reducing the spread of COVID-19 in all these countries, which is consistent with the simulations in several studies [6, 9, 10]. However, as compared to China and R. Korea, Italy, Spain, Germany and France showed a lower reduction of daily increase rate after the 3rd week, which resulted in lower total control efficiency of COVID-19.
Except for city lockdowns and travel restrictions, there was a big difference in control measures taken at individual and community level in these countries. In China and R. Korea, after lockdown of cities or of the country, all patients, suspected cases and closely related people were extensively examined by testing, and isolated collectively in temporary hospitals, which helped to minimize the community transmission of COVID-19. Besides, face masks were widely used by people in China and R. Korea, which helped to minimize transmission at the individual level. In Europe, social distancing and isolation at home was widely used. Face masks were rarely used. Patients or people with close contact were not tracked extensively. Patients quarantined at home could be the significant transmission source to family members or neighbors, which likely explained the lower reduction of daily increase rate in the later stage after lockdown, and the lower total control efficiency of these countries.
As compared to the number of new cases which was widely used to judge the turning point of transmission, the daily increase rate performed better in assessing the transmission trend and control efficiency. Because number of new cases often fluctuated greatly (Fig. 1B), it was often hard to determining the turning point. Besides, it took longer (over 3 weeks) to see an obvious steadily decrease of new cases of COVID-19 for the four European countries (Fig. 1B). The steady decrease of the daily increase rate was observed within 2 weeks for all countries (Fig. 2A, Fig. 3A), thus, the daily increase rate showed a quicker response to the control measures.
The daily increase rate of cumulative cases (r) is a good indicator reflecting the transmission severity of a disease. From equation 1, for a given r, the double time of cumulative cases can be calculated as: T2 =ln (2)/r. For example, for r = 0.1, 0.2, 0.3 and 0.4, the double time of cumulative cases is 6.9, 3.4, 2.1, and 1.7 days. Therefore, COVID-19 could double its number of cumulative cases within 2-7 days if the daily increase rate is 0.1-0.4. This explains why the number of COVID-19 cases with a maximum daily increase rate around 0.25-0.39 (Table 1) could explode in a very short time. Therefore, the time-window for containing the spread of COVID-19 in its early stage is very short. Quick decisions and fast actions to take control measures is essential to contain the virus in the early stage of an epidemic.
The basic reproductive number (R0) is widely used for predicting the trend and severity of disease transmission . According our previous study , the basic reproductive number can be estimated by the maximum daily increase rate (rm) and infection time of patients (IFT): R0 = rm*IFT. In a few recent modeling studies, the infection time of COVID-19 was often assumed to be 6 days, referring to that of SARS [8, 16], which may cause biased estimation. In our study, using published epidemiological data, the incubation time (IBT) and infection time (IFT) was estimated from the date of exposure to the virus to the date of patient hospitalization (Table S1). Our estimated infection time (IFT) of COVID-19 was 8.3 ± 3.7 days (Fig. S2B, Table S1), similar to the mean serial interval (i.e. the sum of the incubation period and duration of infectiveness) of a SARS-infected person (8-12 days with an average of 8.4 ± 3.8 days) in Singapore and Hong Kong [17, 18]. There was a large variation of IBT and IFT among patients of COVID-19 (Fig. S2), thus, quarantine time should consider this variation. The maximum daily increase rate based on equation 3 for the seven countries was around 0.25-0.39 (Table 1). Thus, our estimated R0 of COVID-19 was from 2.1 to 3.3 using the logistic model, which was very close to that of 2.68  and that of 3.11 .
It is notable that the early detection capacity and tests may be insufficient in some countries, resulting in low data in the early stage. Thus, we excluded data from the period of less than 100 cases from each country. However, the detection capabilities of different countries may also be different, and testing might be insufficient during epidemic periods. These problems may bring some biased estimation. Thus, it should be cautious in explaining the results of this study.
As compared to the 2002-2003 outbreak of SARS , COVID-19 spread much faster in both time and space. Furthermore, COVID-19 has caused a much higher number of infections and deaths than SARS in China and in the rest of the world. As compared to nearly two decades ago, the transportation capacity today is much more advanced in the world, which may partially explain why COVID-19 spread more rapidly than SARS. Revealing the transmission patterns of a disease is essential in taking effective prevention and control measures.
We appeal for more studies on the transmission ecology of highly contagious viruses and their influencing factors, so as to find a better solution to counter their increasing threat to public health in the modern age with advanced social and transportation networks.