Transmission characteristics of the COVID-19 outbreak in China: a study driven by data

S2 for details. Mathematically, 𝑁-. = 𝑖𝑃-. where 𝑃-. is the probability that an individual who infected 𝑗 others was infected by a patient who infected 𝑖 individuals. The basic reproduction number ℛ" is the dominant eigenvalue of 𝑁. The average number of secondary infections is calculated from data is 1.53. The next generation

gives ℛ" = 1.54. Thus, the correlation of secondary infections has negligible effect on ℛ". The incubation period distribution is estimated from the nodes in Figure 3 with contact date information. The distribution of the generation time is estimated from the edges in Figure 3 with contact date information for both the source and target nodes. The results are shown in Figure 5. The best fit incubation period distribution is a gamma distribution with a mean 7.2 (6.8, 7.6) days and a variance 16.9 (14.0, 20.2), which correspond to a shape parameter 3.07 (2.62, 3.56) and a scale parameter 2.35 (2.00, 2.75). The generation time is estimated to be gamma distributed with a mean 3.3 (2.3, 4.3) days and a variance 3.1 (1.0, 8.0), corresponding to a shape parameter 4.44 (1.32, 10.02), and a scale parameter 0.95 (0.32, 2.32). Since the mean generation time is smaller than the mean incubation period, on average, a patient may become infectious 3.9 days before showing major symptoms. Figure 6 shows the probability distribution of the fraction of individuals whose incubation period is longer than 14, 21, and 22 days, respectively. On average, a quarantine period of 14 days may lead to a failure rate of 6.7%, i.e., 6.7% quarantined patients may show symptom after quarantine. If we aim to control the failure rate of quarantine to be b elow 1% with 95% confidence, then the quarantine period must be at least 22 days. In summary, we estimated the distribution of the generation time, incubation period, and the periods from symptom onset to isolation and to diagnosis for patients in Chinese provinces excluding Hubei. The current recommendation of 14 -day quarantine period may be too short, resulting in a 6.7% failure rate. We recommend to increase the quarantine period to 22 days. The periods from symptom onset to isolation and to diagnosis changed significantly for patients who showed symptom before and after the lockdown of Wuhan on January 23, mostly likely driven by behavior change of the general public, and more effective public health control measures after January 23 . On average , p atients may become infecti ous 3.9 days before the onset of major symptoms. This, and the 6.6 days delay from symptom onset to diagnosi s, severely hinders the effectiveness of contact tracing and quarantine, as evidenced by the 2.5% success rate of quarantine before symptom onset. The basic reproduction number is 1.54 with contact tracing, quarantine and isolation. However, the majority of patients infects no more than one individual, . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint 4 and thus the outbreak s in these provinces are mostly driven by super spreaders. Because transmission can occur before symptom onset, the latent period (from being infected to becoming infectious) and infectious period cannot easily be estimated from case descriptions.

This research is supported by National Natural Science Foundation of China (No. 11771075) (ML), State Scholarship Fund of China (CSC No. 201906635011) (ML), a Fundamental Research Grant for Chinese Universities (ML), and a Natural Sciences and Engineering Research Council Canada Discovery Grant (JM). ML’s work is carried out when she is a visiting scholar at Montclair State University.

AND NOTES 1. World Health Organization (WHO). Novel Coronavirus. [Accessed February 25, 2020]. https://www.who.int/csr/don/archive/disease/novel_coronavirus/en/. 2. World Health Organization (WHO). Coronavirus disease (COVID-19) situation reports. [Accessed February 25, 2020]. https://www.who.int/emergencies/diseases/novel-coronavirus- 2019/situation-reports/. 3. National Health Commission of the People’s Republic of China. Briefing of the epidemic. [Accessed February 25 2020]. http://www.nhc.gov.cn/xcs/xxgzbd/gzbd_index.shtml. 4. Jantien A Backer, Don Klinkenberg, Jacco Wallinga, Incubation period of 2019 novel coronavirus (2019-nCoV) infections among travellers from Wuhan, China, 20–28 January 2020. Euro Surveill 25(5) (2020): pii=2000062. https://doi.org/10.2807/1560- 7917.ES.2020.25.5.2000062. 5. J. Li, A robust stochastic method of estimating the transmission potential of 2019-nCoV. [Accessed February 25, 2020]. https://arxiv.org/abs/2002.03828. 6. Laurent Hébert-Dufresne et al, Beyond ℛ": the importance of contact tracing when predicting epidemics. [Accessed February 25, 2020]. https://arxiv.org/abs/2002.04004. 7. H. W. Wang et al., Estimating the number of 2019 novel Coronavirus cases in Chinese Mainland. [Accessed February 25, 2020]. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3529449. 8. B. Tang et al., Estimation of transmission risk of 2019-nCov and its implication for public health interventions. Journal of Clinical Medicine 9, 462(2020). 9. J. Wu et al., Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV out break originating in Wuhan, China: a modelling study. Lancet. [Published Online January 31, 2020]. https://www.sciencedirect.com/science/article/pii/S0140673620302609. 10. J. M. Read et al., 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions. [Accessed February 25, 2020]. https://www.medrxiv.org/content/10.1101/2020.01.23.20018549v2. 11. Q. Li et al., Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. The New England Journal of Medicine https://www.nejm.org/doi/full/10.1056/NEJMoa2001316. 12. T. Liu et al., Time-varying transmission dynamics of Novel Coronavirus Pneumonia in China. [Accessed February 25, 2020]. https://www.biorxiv.org/content/10.1101/2020.01.25.919787v2. . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint 5 13. P. van den Driessche, James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 180, 29-42(2002). 14. M.E.J. Newman, Assortative mixing in networks. Physical Review Letters 89, 208701(2002). Figure 1 The upper panels show he observed distributions of the period from symptom onset to quarantine (negative periods) or isolation (positive periods). The lower panels show the best fit distributions of the period from symptom onset to isolation calculated from the mean of MCMC samples. The quarantined patients were isolated on the same day of symptom onset. There is a clear difference between individuals who showed symptom before and after January 23, 2020, onset before Jan 23 onset after Jan 23 all dataestimate -10 0 10 20 -10 0 10 20 -10 0 10 20 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 days probability . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint 6 Figure 2 The observed and best fit distributions of the period from symptom onset to diagnosis calculated from the mean of MCMC samples. There is a clear difference between individuals who showed symptom before and after January 23, 2020. onset before Jan 23 onset after Jan 23 all dataestimate 0 10 20 30 0 10 20 30 0 10 20 30 0.00 0.05 0.10 0.15 0.00 0.05 0.10 0.15 days probability . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint 7 Figure 3 The graph of transmission s for individually documented cases with a contact tracing information. The nodes are patients, and edges show possible transmission. The nodes and edges are colored by province. Patient information, including their labels and provinces, are listed in Supplementary Material S1. 14 46 ? ? 197 ? 201 202 198 204 218 224 ? 199 205 213 208 209 212 258 ? 210 221 250 255 216 243 217 251 ? 228 229 233 230 239 249 285 246 247 281 283 2303 264 244 253 254 262 267 269 270 274 276 288 295 307 2305 231 240 232 ? 234 242252 279 280 265 248 256 241 257 ? 223 259 ? 260 308 268 282 271 314 ? 275 277 290 289 315 292 293 313 2306 2308 ? 303 ? 291 297 312 300 2304 ? 306 4 319 316 317 318 5 6 7 8 320 328 354 ? 329 ? 335 383 384 ? 412 413 438 439 440 451 ? 414 415 416 417 ? 391 423 424 425 ? 402 435 436 642 ? ? 463 399 468 ? ? 476 430 484 ? 327 503 ? 448 570 531 2311 ? 529 568 ? 576 579 582 404 590 ? 456 598 ? ? 609 695 358 635 ? 486 638 ? 677 650 2310 ? ? 657 658 ? 659 ? 661 662 699 ? 2422 758 760 761 ? 712 762 765 ? 779 782 783 784 ? 787 789 ? 786 790 791 792 793 ? 808 809 852 853 ? 818 819 ? 884 885 886 887 ? 902 903905 906 ? 904 ? 843 911 912 ?909 917 918 ? 940 942 943 ? 941 ? 955 957 959 ? 960 961 953 962 ? 954 ? 970 972 ? 1033 998 ? 990 999 1000 1008 1009 1010 1011 1016 1017 1018 1019 ? 983 1003 ? 1001 1014 ? 987 1022 ? 1029 ? 1060 1066 ? 1550 1552 1554 ? ? 1568 1570 1584 1590 1611 ? 1587 1588 ? 1607 1608 ? 1593 1612 1618 1619 1639 1643 1669 1693 1728 ? 1594 1616 ? 16521623 1692 ? 1627 1628 ? 1617 1695 1632 1656 1768 ? 1613 1635 1657 ? 1641 1642 ? 1630 1651 1697 ? 16221671 1667 1702 ? 1659 1682 ? 1634 1691 1714 ? 1753 1701 ? 1705 1712 1662 1716 ? 1719 1720 ? 1673 1722 2360 ? 1723 1711 1726 1739 ? 1740 1729 1741 ? 1689 1732 1733 ? 1638 ? 1698 1734 ? 2367 1735 ? 1764 1742 ? 1751 1715 1754 ? 1615 1762 ? 1648 ? 1649 ? 1650 ? 1757 1767 2359 2378 ? 1759 1772 ? 1731 1773 1774 1775 ? 1796 1811 ? 1816 1812 1817 ? 1797 1824 ? 1827 1841 ? 1869 1876 ? 1882 1883 ? 1897 1900 1912 ? 1904 1903 ? ? 1914 1930 1928 1938 1946 ? 1915 1941 ? 1916 1948 ? 1920 1950 ? 2379 1982 1983 1984 1988 1989 ? 1997 2001 ? 19982002 2026 ? 2004 2005 ? 2011 2017 2018 2024 ? 2019 2027 2042 2043 ? 2053 2056 ? 2067 2071 2072 2073 ? 2083 2087 2092 2093 ? 2074 2094 ? 2097 2100 2101 ? 2095 2103 2104 2105 ? 2106 2109 2114 ? 2098 2111 2115 ? 2113 2119 ? 2121 2122 2387 ? 2124 2128 2125 2126 ? 2129 2131 2132 2140 2143 2142 ? 2151 2152 2153 2154 2155 2156 2157 ? 2268 2269 ? 2272 2273 ? 2302 2307 1551 23272328 2323 ? 2315 2324 ? 2331 2325 2332 2333 2330 2326 ? 2321 2329 ? 2335 2336 ? 2334 2337 ? 2338 2339 2341 ? 2340 23422345 2343 2344 ? 2347 2348 2346 ? 2349 2350 2351 2352 23532355 2356 2354 ? 2357 2358 1688 2361 2371 ? 1965 2362 ? 1747 2363 ? 1746 2364 ? 1683 2365 ? 1660 2366 ?1661 ? 1743 ? 1761 2369 2376 ? 1760 2370 ? 2372 2373 2374 2375 ? 2117 2384 ? 2120 ? 1015 2424 2425 2426 ? 2437 2439 Colors Anhui Beijing Guangdong Guangxi Guizhou Hong Kong Inner Mongolia Jiangsu Ningxia Shaanxi Shandong Sichuan Tianjin Yunnan Zhejiang . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint 8 Figure 4 The observed secondary infections caused by a patient. If an individual may be infected by 𝑛 patients, then the individual counts 1/𝑛 as each patient’s secondary infection. The fraction of patients caused one or less secondary infections is 64.0%. The average number of secondary infections is 1.53. Figure 5 The estimated distributions for the incubation period and the generation time calculated from the mean of the MCMC samples. The mean incubation period is longer than the mean generation time, implying that patients may become infectious before they show major symptoms. 0.0 0.1 0.2 0.3 0 0.1 0.2 0.3 0.5 0.6 0.8 1 1.3 1.5 1.6 1.8 10 2 2.2 2.4 2.5 2.6 2.8 3 4 4.1 4.5 5 5.3 5.8 6 secondary infections fraction incubation periodgeneration time 0 5 10 15 20 0.0 0.1 0.2 0.0 0.1 0.2 days probability . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint 9 Figure 6 The distributions of the fraction of the patients whose incubation period is longer than 14, 21, and 22 days, represented by the histograms of the probabilities of showing symptoms after the quarantine period calculated from the MCMC samples. quarantine 14 days quarantine 21 days quarantine 22 days 0.04 0.06 0.08 0.10 0.005 0.010 0.015 0.005 0.010 0.015 0.000 0.025 0.050 0.075 0.100 fraction probability . CC-BY-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted March 1, 2020. ; https://doi.org/10.1101/2020.02.26.20028431doi: medRxiv preprint