A novel coronavirus disease, designated as COVID-19, has become a pandemic worldwide. This study aims to estimate the incubation period and serial interval of COVID-19. We collected contact tracing data in a municipality in Hubei province during a full outbreak period. The date of infection and infector–infectee pairs were inferred from the history of travel in Wuhan or exposed to confirmed cases. The incubation periods and serial intervals were estimated using parametric accelerated failure time models, accounting for interval censoring of the exposures. Our estimated median incubation period of COVID-19 is 5.4 days (bootstrapped 95% confidence interval (CI) 4.8–6.0), and the 2.5th and 97.5th percentiles are 1 and 15 days, respectively; while the estimated serial interval of COVID-19 falls within the range of −4 to 13 days with 95% confidence and has a median of 4.6 days (95% CI 3.7–5.5). Ninety-five per cent of symptomatic cases showed symptoms by 13.7 days (95% CI 12.5–14.9). The incubation periods and serial intervals were not significantly different between male and female, and among age groups. Our results suggest a considerable proportion of secondary transmission occurred prior to symptom onset. And the current practice of 14-day quarantine period in many regions is reasonable.

Highlights The study comprehensively evaluate predictive value of myocardial injury markers. cTnI-ultra on admission might be the best predictor of in-hospital mortality. Elevated cTnI-ultra was an independent biomarker of the death.

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Structure, stability, charge transfer, chemical bonding, and spectroscopic properties of Ga atom-doped neutral Mgn (n=2-12) clusters have been systematically investigated by CALYPSO and density functional theory. All cluster structures are based on "tetrahedral" and "yurt-like" growth except for GaMg2. The ground state isomer of GaMg with high symmetry strcture is predicted to be the best-fit candidate for the "magic" cluster because of its excellent stability. Natural bond orbital calculations reveal that Ga and Mg atoms play the role of electron acceptor and donor in all ground state isomers, while the orbitals in both Ga and Mg are sp-hybridized. Most importantly, chemical bonding studies based on atom-in-mole ular theory have shown that the lowest-energy state of GaMg4 is so special in that it is not only the critical size for the appearance of Mg-Mg covalent bonds but also the only cluster that has both Ga-Mg covalent and non-covalent bonds. Finally, theoretical calculations of IR and Raman spectra of all ground state isomers indicate that the spectra of these clusters are observable in the low-frequency band, and thus they can be identified by spectroscopic experiments. Furthermore, the bond heterogeneity of the Ga-Mg in the GaMg4 ground state isomer has also been specically investigated, includingfixed GaMg4 structure with Mg atoms added in different directions as well as ab initio molecular dynamics sampling at different temperatures.

By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery's argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.