Abstract
The 2019 novel coronavirus (2019-nCoV) have emerged from Wuhan, China. Studying the 14 epidemic dynamics is crucial for further surveillance and control of the outbreak. We employed 15 a Bayesian framework to infer the time-calibrated phylogeny and the epidemic dynamics 16 represented by the effective reproductive number (Re) changing over time from the genomic 17 sequences available from GISAID. The origin time is estimated to be December 17, 2019 (95% 18 CI: December 5, 2019 -December 23, 2019). The median estimate of Re ranges from 0.2 to 19 2.2 and changes drastically over time. This study provides an early insight of the 2019-nCoV 20 epidemic. 21 22 101 We used the lognormal independent relaxed clock (Drummond et al. 2006; Rannala and 102 Yang 2007) to model evolutionary rate variation along the branches. The mean clock rate r was 103 assigned a gamma(2, 0.0005) prior with mean of 0.001 substitutions per site per year and the 104 standard deviation σ was a gamma (0.54, 0.38) prior with mean 0.2 and median 0.1 by default.
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The substitution model used was HKY+Γ4 (Hasegawa et al. 1985; Yang 1994) in which the 106 transition-transversion rate ratio κ was set a lognormal(1, 1.25) prior and the gamma shape 107 parameter α was an exponential(1) prior.
The analysis was performed in the BEAST 2 platform (Bouckaert et al. 2019). We ran 150 109 million MCMC iterations and sampled every 5000 iterations. The first 30% samples were 110 discarded as burn-in. Convergence was diagnosed in Tracer (Rambaut et al. 2018) to confirm 111 that independent runs gave consensus results and all parameters had effective sample size (ESS) 112 larger than 100. The remaining 70% samples were used to build the maximum clade credibility 113 (MCC) tree and to summarize the parameter estimates. The common ancestor heights were 114 used to annotate the clade ages in the MCC tree.
Introduction 23
An outbreak of a novel coronavirus (2019-nCoV) was reported in Wuhan, a city in central 24 China (WHO). Coronaviruses cause diseases range from common cold to severe pneumonia. 25 Two fatal coronavirus epidemics over the last two decades were severe acute respiratory 26 syndrome (SARS) in 2003 and Middle East respiratory syndrome (MERS) in 2012 (WHO) . 27 Human to human transmission has been confirmed for this new type of coronavirus (Wang et 28 al. 2020) and more than 1,000 cases have been reported as of January 25, 2020 29 (https://bnonews.com/index.php/2020/01/the-latest-coronavirus-cases). 30 Studying the virus epidemic dynamics is crucial for further surveillance and control of the 
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They are also lacking a stochastic process to model the epidemic dynamics over time. However, 36 both the timing and dynamics are critical to understand the early outbreak of 2019-nCoV.
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Furthermore, various sources of information and uncertainties are hard to be integrated in the 38 analyses without employing a Bayesian approach.
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In this study, we used the birth-death skyline serial (BDSS) model (Stadler et al. 2013) to 40 infer the phylogeny, divergence times and epidemic dynamics of 2019-nCoV. This approach 41 takes the genomic sequences and sampling times of the viruses as input, and co-estimates the 42 phylogeny and key epidemic parameters in a Bayesian framework. To our knowledge, this is 43 the first study to perform such estimation on 2019-nCoV.
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Results and Discussion

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The phylogeny in Figure 1 shows the divergence times and relationships of the 24 summarized as a 50% majority-rule consensus tree (GISAID).
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The time of origin is estimated with median 31.9 days and 95% highest posterior density 55 (HPD) interval from 26.3 to 43.8 days before the date of the latest sample (January 18, 2020), 56 that is, December 17, 2019 (December 5, 2019 -December 23, 2019) (Table 1, ten intervals).
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This is in agreement with the symptom onset reported by WHO, showing again an early phase 58 of the epidemic. 59 We investigate the epidemic dynamics of 2019-nCoV by estimating Re changing over time 60 in the BDSS model. Re > 1.0 means that the number of cases are increasing and the epidemic 61 is growing, whereas Re < 1.0 means that the epidemic is declining and will die out. Interestingly, 62 the epidemic has an early boost with Re at around 2.2, then decreases dramatically to 0.2, and 63 increases again to about 1.7 during the last phase (Table 1 ). In general, this is in agreement 64 with some other studies reporting Re ranging from 1.4 to 5.5 (Read et al. 2020; Zhao et al. 2020; 65 Riou and Althaus 2020). In comparison, the estimated Re was 2.7 to 3.6 for SARS during the 66 precontrol phase in Hong Kong (Riley et al. 2003; Wallinga and Teunis 2004) . Dividing Re 67 into ten intervals rather than three give us a better resolution (Figure 2 ). This drastic change 68 could reflect the epidemic to some extent but is likely sensitive to the virus sampling. Keep in 69 mind that we used only 24 samples in our analysis, which is less than 2% of the reported 70 number of infected patients, thus one needs to be cautious when interpreting this result. With 71 more viruses sequenced, we would expect more reliable estimates which would provide better 72 insights into the epidemic of 2019-nCoV. 73 Overall, this study provides an early insight of the 2019-nCoV epidemic by inferring key 74 epidemiological parameters from the virus sequences. Such estimates would help public health 75 officials to coordinate effectively to control the outbreak.
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Methods

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The original data downloaded from GISAID (https://www.gisaid.org) consists of 26 78 sequences of 2019-nCoV (as of January 24, 2020). We excluded two outliers, one is the virus 79 from Kanagawa, Japan (EPI_ISL_402126) which contained only a small segment of 369bp, 80 another is from Wuhan, China (EPI_ISL_403928) which contains suspiciously many 81 mutations and has genetic distance about ten times longer than the rest of the sequences 82 (GISAID). Sequence alignment was done using MUSCLE (Edgar 2004) , resulting in a total 83 length of 29904bp for the whole genome. The sampling times of the viruses ranged from 84 December 24, 2019 (EPI_ISL_402123) to January 18, 2020 (EPI_ISL_403937) and they 85 were used as fixed ages (in unit of years) in subsequent analysis. 86 We used the BDSS model (Stadler et al. 2013) (1/δ) to be about a month. The sampling proportion of infected individuals p was a beta (1, 9) 100 distribution with mean 0.1. Re Jan-Jan-0 Jan---2 -20

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