key: cord-1017435-sil86t9n authors: Yue, TianXiang; Fan, Bin; Zhao, YaPeng; Wilson, John; Du, ZhengPing; Wang, Qing; Yin, XiaoZhe; Duan, XiaoNan; Zhao, Na; Fan, ZeMeng; Lin, Hui; Zhou, ChengHu title: Dynamics of the COVID-19 basic reproduction numbers in different countries date: 2020-10-15 journal: Sci Bull (Beijing) DOI: 10.1016/j.scib.2020.10.008 sha: 6e6ed5126842c22b55f1240f99c419a4ac1210f9 doc_id: 1017435 cord_uid: sil86t9n nan Received 2020-06-26，revised 2020-09-17，accepted 2020-09-18 The reproduction number, R, is the average number of secondary infectious cases produced by one infectious case during a disease outbreak [1] . When a population is totally susceptible, R becomes the basic reproduction number, . It is a key parameter 0 R regulating the transmission dynamics of a pandemic [2] . provides an indication of 0 R whether the introduction of disease will result in a localized burnout or signal the beginning of a pandemic that could move through all geographic scales [3] . The disease-free equilibrium is globally asymptotically stable and the epidemic eventually disappears if <1. Whenever >1, then an epidemic will occur and the infection 0 R 0 R spreads in the population, no matter how small the initial number of infected individuals. When >2, a major outbreak is possible. When >3, the emergence of a pandemic 0 R 0 R is generally considered to be inevitable [4] . The World Health Organization (WHO) named the corona virus disease as COVID-19 on February 11, 2020 and declared a pandemic on March 11, 2020. The basic reproduction number ( ) has been employed to measure the transmission 0 R dynamics of COVID-19 both before and after the interventions. Various approaches for calculating for COVID-19 have been introduced, which are based on deterministic 0 R or stochastic models. Unfortunately, these results were not comparable because different algorithms for estimating are employed. 0 R For instance, an algorithm based on the Susceptible-Infected-Recovered (SIR) model showed that monotonically rose from 0.60 on January 10 to its maximum 0 R value of 4.87 on January 25, and dropped below 1 on February 16 in Hubei Province, China [5] . Another study assumed that the epidemic curve displayed exponential growth, and the basic reproduction number for COVID-19 at the early stage, estimated in terms of the intrinsic growth rate of the epidemic curve, ranged from 2.24 to 3.58 [6] . Another study calculated an infectiousness function in terms of the average time since infection for those individuals who infect few others and those who infect many, and used the area under the curve to estimate in the early stages of the epidemic in 0 =2.0 R China [7] . A fourth study relied on the dominant eigenvalue of a next-generation operator [8] to show how reached ~6 in Wuhan and ~7.8 in Shanghai before 0 R interventions were implemented [9] . A fifth study found that gradually increased 0 R from January 10 to January 24 with a peak of 3.82, and then fell below 1 on February 6 in Wuhan using a method to estimate the household reproduction number and calculate time-varying reproduction numbers in Wuhan city [10] . Another study used a stochastic transmission model [11] to estimate how transmission in Wuhan between December, 2019, and February, 2020 declined from 2.35, one week before travel restrictions were introduced on January 23 to 1.05 one week later [12] . The seventh and final study used a chain-binomial model [13] to estimate an of 6.94 for COVID-19 on the "Diamond Princess" cruise ship during 0 R the early intensive social contacts and that everyone on board would have been infected in one month if control and prevention measures had not been implemented [14] . In this study, we propose an improved algorithm for calculating based on the 0 R SIR-based model developed for the COVID-19 outbreak in Hubei Province of China [5] : This improved algorithm utilizes the actual data without assuming a specific pattern and has less parameters than the original model. Our tests indicated that the improved performs well on provincial and prefectural levels in China and on a national level across the world under any circumstances. The original model, in contrast, was not very stable when estimating the demise of the pandemic in several of the prefectures in Hubei province. The number of infected individuals of COVID-19 surpassed 28.21 million worldwide on September 11, 2020, according to the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. The first 6 countries with the largest cumulative numbers of infected individuals were the United States of America, India, Brazil, Russia, Peru and Colombia in rank order. These countries were distributed across the Americas (4), Asia (1) and Europe (1) . We here apply the improved algorithm for on the reported data about infected 0 R individuals, recovered individuals, and deaths caused by COVID-19 (Tables S1−8 online) to monitor the transmission dynamics in the 6 countries. The natural logarithm of the basic reproduction number ( ) is utilized to more clearly express the curves for ln 0 the COVID-19 transmission dynamics across the six countries (Fig. 1) . Similar interventions were eventually implemented in all 6 countries. fell 0 R below 2 in all 6 countries on April 24, which means that major outbreaks are no longer likely. However, COVID-19 is continuing to spread in these countries because there is no country with <1.0. Peru (2.23%), Brazil (2.06%), the United States of America 0 R (2.00%), and Colombia (1.43%) led in terms of the percentages of infected individuals as of September 11 (Tables S10 and S11 online). The results clearly show that the interventions have produced large variations in effectiveness in different countries due to the various ways in which executive powers are exercised from one country to the next. For instance, the interventions were very effective in Germany. Tough measures to limit social contacts were conducted uniformly in all 16 federal states of Germany in March and April 2020. It took just 26 d for to fall from its peak to < 1 during the first 0 R outbreak in Germany (Table S9 online) . However, COVID-2019 started to rebound in Germany on May 11 because the pandemic interventions were relaxed. An of 1 has 0 R been continuously sustained in Germany for 130 d. The efficacy of the interventions is quite low in the United States of America. started to decline approximately one 0 R week after the interventions were implemented in the United States of America when most of the other countries highlighted in this paper saw rapid declines in in a few 0 R days following the initial interventions. 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He has been working as a professor at State Key Laboratory of Resources and Environmental Information System since Bin Fan is a Ph.D. student of State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences. His major is Cartography and Geographical Information System and his research activities mainly focus on eco-environmental surface modelling All authors took part in the acquisition and interpretation of the related data included in this paper. TianXiang Yue wrote the paper and each co-author contributed comments and suggestions. The authors declare that they have no conflict of interest.