key: cord-0718581-by0r3c0o
authors: Lei, Jiali; Li, Mengyuan; Wang, Xiaosheng
title: Predicting the development trend of the second wave of COVID‐19 in five European countries
date: 2021-06-23
journal: J Med Virol
DOI: 10.1002/jmv.27143
sha: a359044eebbad5e0de9701f4503d5b651c44f0c2
doc_id: 718581
cord_uid: by0r3c0o

The second wave of COVID‐19 has caused a dramatic increase in COVID‐19 cases and deaths globally. An accurate prediction of its development trend is significant. We predicted the development trend of the second wave of COVID‐19 in five European countries, including France, Germany, Italy, Spain, and the UK. We first built models to predict daily numbers of COVID‐19 cases and deaths based on the data of the first wave of COVID‐19 in these countries. Based on these models, we built new models to predict the development trend of the second wave of COVID‐19. We predicted that the second wave of COVID‐19 would have peaked around on November 16, 2020, January 10, 2021, December 1, 2020, March 1, 2021, and January 10, 2021, in France, Germany, Italy, Spain, and the UK, respectively. It will be basically under control on April 26, 2021, September 20, 2021, August 1, 2021, September 15, 2021, and August 10, 2021, in these countries, respectively. Their total number of COVID‐19 cases will reach around 4,745,000, 7,890,000, 6,852,000, 8,071,000, and 10,198,000, respectively, and total number of COVID‐19 deaths will be around 262,000, 262,000, 231,000, 253,000, and 350,000 during the second wave of COVID‐19. The COVID‐19 mortality rate in the second wave of COVID‐19 is predicted to be about 3.4%, 3.5%, 3.4%, 3.4%, and 3.1% in France, Spain, Germany, France, and the UK. The second wave of COVID‐19 is expected to cause many more cases and deaths, last for a much longer time, and have a lower COVID‐19 mortality rate than the first wave.

The spread of COVID-19 caused by the 2019 novel coronavirus (SARS-CoV-2) is still growing rapidly across the world since its outbreak in December 2019. The COVID-19 pandemic has caused one of the most serious global public health problems in recent years. 1 It has resulted in more than 123 million cases and 2.7 million deaths worldwide as of March 22, 2021. More seriously, it is still unclear how this epidemic will evolve. Currently, the second wave of COVID-19 is raging and is expected to cause many more cases and deaths than the first wave of COVID-19. Of note, the COVID-19 pandemic affects not only global public health but also the global economy, geopolitics, culture, and society. Thus, an accurate prediction of its development trend may provide valuable advice on effectively controlling its spread and relieving its major social and economic impacts.

Although a number of studies have estimated the epidemic trend of the COVID-19 outbreak, most have used early-stage data and focused on the first wave of COVID-19. [2] [3] [4] [5] For example, using the SEIR (susceptible, exposed, infectious, and removed) model, Wang et al. 2 In this study, using the machine learning approach, we predicted the development trend of the second wave of COVID-19 in five European countries, including France, Germany, Italy, Spain, and the UK, which are the top five most-affected countries in Europe. We first built prediction models using the publicly available data for the first wave of COVID-19 in these countries. 

Based on data from the end of February 2020 to the end of August 2020, we built models to predict daily numbers of NCCs and NDs of the first wave of COVID-19 in France, Germany, Italy, Spain, and the UK, respectively, using Eureqa (Trial Version 1.24.0, https://www.nutonian. com/products/eureqa-desktop). Eureqa is a machine learning algorithm that can automatically build prediction models from data. 6 We input daily numbers of NCCs and NDs and their corresponding days to obtain a formula that perfectly shaped the relationships between the variables.

We assumed that the second wave of COVID-19 in a country had a similar development trend to its first wave, but the second wave's epidemic was more serious. Based on this assumption, we derived prediction models for the second wave from the models for the first wave in a country. The start and end dates for the first wave, the start date for the second wave, and the dates for training sets in each of the five countries are presented in Supplementary Table S1 

where Y is the number of NCCs and X is the time (days). The goodnessof-fit (R 2 ) of the model was 0.998 on the training set. We found that the daily numbers of NCCs within the 10 consecutive days starting from July 16, 2020, followed the same distribution as within the 10 consecutive days starting from March 8, 2020, in France (Kolmogorov − Smirnov (K − S) test, p = 1) ( Figure 1A ). Thus, we supposed that the second wave had a similar trend to the first wave with a 1-day advance in France.

Accordingly, based on the model to predict daily numbers of NCCs of the first wave, we generated a model to predict daily numbers of NCCs of the second wave using the data of NCCs from August 14, 2020, to 

2549.73 (0.093 ( ( 1)))).

where Y is the number of NCCs, X is the time (days), and α (= 0.43) and β (= 12.11) are the tuning parameters. Y X X a t a n X X X s i n X atan X X 

Y a t a n X X a t a n X 

where Y is the number of NCCs and X is the time (days). The goodness-of-fit (R 2 ) of these models were 0.999, 0.996, 0.983, 0.996 on the training set, respectively. We found that the daily numbers of NCCs within the 8 consecutive days starting from August 2, 2020, followed the same distribution as within the 8 consecutive days starting from March 7, 2020, in Germany (K − S test, p = .98) ( Figure 1B) . The daily numbers of NCCs within the 7 consecutive days starting from August 1, 2020, followed the same distribution as within the 7 consecutive days starting from February 26, 2020, in Italy (K − S test, p = 1) ( Figure 1C ). The daily numbers of NCCs within the 7 consecutive days starting from July 21, 2020, followed the same distribution as within the 7 consecutive days starting from March 14, 2020, in Spain (K − S test, p = 1) ( Figure 1D ). The daily numbers of NCCs within the 7 consecutive days starting from August 22, 2020, followed the same distribution as within the 7 consecutive days starting from

March 17, 2020, in the UK (K − S test, p = 1) ( Figure 1E ). We supposed that the second wave of COVID-19 followed a similar pattern to the first wave with a 13-, 7-, 0-, and 22-day lag in 13)), ( ( 13)) 28.82) ),

Y a t a n 

2000.54 2( 9.14, 1.97 ( ( 7)) 44.91))), 

Y a t a n e X X a t a n 

))) (2.31 6 ( ( 22)) )),

where Y is the number of NCCs, X is the time (days), α is the ratio of the duration from the start date to the date when NCCs 

where Y is the number of NDs and X is the time (days). The goodness-of-fit (R 2 ) of these models were 0.996, 0.999, 0.996, 0.998, and 0.997, respectively. We found that the daily numbers of NDs within the 8 consecutive days starting from October 2, 2020, followed the same distribution as within the 8 consecutive days starting from March 13, 2020, in France (K − S test, p = .98) ( Figure 2A ). The daily numbers of NDs within the 7 consecutive days starting from October 10, 2020, followed the same distribution as within the 7 consecutive days starting from March 19, 2020, in Germany (K − S test, p = 1) ( Figure 2B ). The daily numbers of NDs within the 7 consecutive days starting from October 9, 2020, followed the same distribution as within the 7 consecutive days starting from March 2, 2020, in Italy (K − S test, p = 1) ( Figure 2C ). The daily numbers of NDs within the 7 consecutive days starting from August 28, 2020, followed the same distribution as within the 7 consecutive days starting from March 10, 2020, in Spain (K − S test, p = 1) ( Figure 2D ). The daily numbers of NDs within the 7 consecutive days starting from September 17, 2020, followed the same distribution as within the 7 consecutive days starting from March 14, 2020, in the UK (K − S test, p = 1) ( Figure 2E ). We assumed that the second wave of COVID-19 followed a similar pattern to the first wave with a 20-, 20)), 3.92))), 

) )),

Y X X a t a n X X a t a n 

))))), Spain, and the UK, respectively. Strikingly, the numbers of CCCs in the second wave of COVID-19 were expected to increase by more than 20 times in these countries, as estimated to be around 4,551,000, 7,703,000, 6,609,000, 7,827,000, and 9,914,000 CCCs in France, Germany, Italy, Spain, and the UK, respectively (Figure 4) .

Further, the number of COVID-19 deaths was predicted to be around 232,000, 253,000, 196,000, 224,000, and 308,000 during the second wave of COVID-19 in France, Germany, Italy, Spain, and the UK, respectively, compared to 30,000, 9000, 35,000, 28,000, and 41,000 deaths caused by COVID-19 during the first wave of COVID-19 in these countries ( Figure 4 ). These data demonstrate that the second wave of COVID-19 will cause much more serious devastation than the first wave. Moreover, the duration of the second wave was expected to be much longer than that of the first wave in these countries. We predicted that the duration of the second wave would be 10 months (from July 2020 to April 2021) in France, 15 months (from July 2020 to September 2021) in Germany, 14 months (from July 2020 to August 2021) in Italy, 15 months (from July 2020 to September 2021) in Spain, and 14 months (from July 2020 to August 2021) in the UK, compared to 4-6 month duration of the first wave in these countries ( Figure 4) should emerge this summer. In this situation, comprehensive and stringent control measures must be taken to mitigate the spread of the third wave of COVID-19.

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This study was supported by the China Pharmaceutical University (Grant No.: 3150120001).

The authors declare that there are no conflict of interests.

Ethical approval was waived since we used only publicly available data and materials in this study.

Methodology, software, validation, formal analysis, investigation, data curation, 

The statistics of COVID-19 cases were obtained from the Center for Systems Science and Engineering at Johns Hopkins University (https://coronavirus.jhu.edu/map.html).

http://orcid.org/0000-0002-7199-7093