Outbreak analysis with a logistic growth model shows COVID-19 suppression dynamics in China

China reported a major outbreak of a novel coronavirus, SARS-CoV2, from mid-January till mid-March 2020. We review the epidemic virus growth and decline curves in China using a phenomenological logistic growth model to summarize the outbreak dynamics using three parameters that characterize the epidemic’s timing, rate and peak. During the initial phase, the number of virus cases doubled every 2.7 days (range 2.2–4.4 across provinces). The rate of increase in the number of reported cases peaked approximately 10 days after suppression measures were started on 23–25 January 2020. The peak in the number of reported sick cases occurred on average 18 days after the start of suppression measures. From the time of starting measures till the peak, the number of cases increased by a factor 39 in the province Hubei, and by a factor 9.5 for all of China (range: 6.2–20.4 in the other provinces). Complete suppression took up to 2 months (range: 23-57d.), during which period severe restrictions, social distancing measures, testing and isolation of cases were in place. The suppression of the disease in China has been successful, demonstrating that suppression is a viable strategy to contain SARS-CoV2.

outbreak using three parameters that characterize the epidemic's timing, rate and peak. During 23 the initial phase, the number of cases doubled every 2.7 (range 2.2 -4.4) days. The rate of 24 increase in the number of reported cases peaked approximately 10 days after suppression 25 measures were started on 23-25 January 2020. The peak in the number of reported sick cases 26 occurred on average 18 days after the start of measures. From the time of starting measures 27 till the peak, the number of cases increased by a factor 38.5 in the province Hubei, and by a 28 factor 9.5 for all of China (range: 6.2-20.4 in the other provinces). Complete suppression took 29 up to 2 months (range: 23-57d.), during which period severe restrictions, social distancing 30 measures, testing and isolation of cases were in place. The suppression of the disease in China 31 has been successful, acting as a beacon of hope for countries outside China where the 32 epidemic is still in a phase of increase and authorities need to decide their course of action. 33 essentially by bringing the effective reproduction number Re (the number of new cases per 48 existing case) below one 4,5 . Social distancing is a key factor in suppression 6 . In mitigation the 49 aim is not to necessarily stop all transmission, but rather to reduce the rate of transmission and 50 in effect lower the number of infected people at any given time 3,7 . It has been suggested that 51 mitigation strategies might prevent inundation of the health care system by "flattening" the 52 peak of sick people" 3 . However, even in the most optimistic scenarios for mitigation, 53 healthcare capacity is likely to be still seriously overwhelmed, as it was in Wuhan in February 54 2020 and as is now in Italy in March 2020. Herd immunity has been suggested as a 55 component of mitigation, but is only a viable option once a vaccine is available because up to 56 management, have a place along mechanistic models to inform on disease dynamics 15 . Using 84 data from China, logistic models shows the key disease dynamic parameters before and after 85 suppression policies were implemented 16 . 86   87 The cumulative number of cases (confirmed by testing or based on clinical symptoms) was 88 described very well by a logistic growth pattern with R 2 greater than 0.99 for all provinces, 89 except Shandong (R 2 >0.98, Table A1). Three provinces enacted suppression measures on 23 90 January, five implemented measures on 24 January, and the remaining 12 provinces started 91 measures on 25 January. The time scale for the increase was ! = 3.91 d. for China 92 (excluding Hubei, range 3.13 -6.39) and 4.13 d. for Hubei (Table A1) Hubei, respectively, during the early epidemic. Some lack of fit during the early phase of the 95 epidemic (before measures) suggests the actual doubling times may be even shorter than these 96 estimates (Table A1). 97

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The number of reported active sick cases (total infected minus recovered minus deceased) in 99 Hubei peaked 25 days after suppression measures were implemented, which in the model also 100 indicates the peak of number of deaths on the same day. Outside Hubei, the peak number of 101 reported sick cases (and peak of daily number dying) was on average reached 18 days after 102 The analysis shown in these figures was continually updated from 1 February to 3 March 151 while the epidemic was progressing 18 . Based on the data up till 16 February 2020, a peak in 152 sick incidence was identified for 12 February, which was proven correct 19 . Thus, logistic 153 models may be used to determine early when suppression measures are expected to result in 154 decreased rate of epidemic growth and a decline in number of sick cases. However, any model 155 shows lack of fit 16 . The logistic model does not capture that the rate of increase in the early 156 epidemic is faster than the rate of decline during the tapering out of the epidemic (Appendix 157 A1). Thus, the logistic underestimates both the early relative growth rate and the increase of 158 the number of sick people from the start of measures till the peak for the Chinese data 159 (Appendix A1). Uncertainties in predictions also result from unknown reporting delay 9 . 160 Improvements may be possible by defining better tailored models, and especially, by 161 collecting better data, e.g. more (random) testing. 162

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The results show that suppression can lead to (almost) complete removal of active virus 164 infected cases from the population, although given that not all active cases have recovered, 165 the outbreak is not completely over. The virus can still be present in asymptomatic individuals 166 or it can be re-introduced from unknown reservoirs or foreign countries. Because the vast 167 establish. Therefore, suppression needs to be followed up by containment, a strategy based 169 on strict surveillance, testing of all individuals with symptoms, and followed by isolation of 170 all infected individuals and their recent contacts. Currently, in many provinces, except for 171 Hubei, quarantine restrictions are slowly being lifted, after no new cases have been detected 172 for several weeks, allowing people to return to work and businesses to start up again. Based on the fitted model, we then calculated the peak date of 1) active sick people, which is 244 also the date of peak number of daily death, 2) number of sick cases during the peak, 3) the 245 date of maximum increase in the number of infected cases and 4) the daily rate of increase on 246 this date, 5) total infected cases on this date, 6) the relative rate on this date, 7) the end date of 247 daily increase (<1) case (operationally the end of the epidemic), and 8) time from maximum 248 increase till sick peak. Taking the date of public health emergency action as the 249 implementation of suppression measures 26 , which varied between 23 January to 25 January 250 across provinces (we set the median date, 24 January as the date for entire China), we then 251 calculated 9) the delay from the action date until the sick peak, 10) the delay from the action 252 date until the date at which the rate of increase peaked, 11) the time from suppression measure 253 till the end date of daily increase in number of reported infections, 12) the ratio between sick 254 cases at peak and total infected case at the action date, as well as 13) the same ratio 255 considering a reporting delay of 6 days 9 , i.e. by taking the ratio of sick(tpeak)/sick(taction+6). 256 257 Calculations were made for 20 Chinese provinces with more than 150 infected cases, and also 258 for China excluding Hubei, by far the worst affected province. . The built-in function 259 "SSlogis" in R 27 was used to fit logistic growth curves. Data were obtained using package 260 "nCov2019" 28,29  the COVID-19 outbreak in 29 provinces in China and in the rest of the world. arXiv 313 (2020). 314 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in  in the lower panel mean that the number of active cases is decreasing.
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