Research Article

Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)

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Science  16 Mar 2020:
eabb3221
DOI: 10.1126/science.abb3221
  • Fig. 1 Best-fit model and sensitivity analysis.

    Simulation of daily reported cases in all cities (A), Wuhan city (B) and Hubei province (C). The blue box and whiskers show the median, interquartile range, and 95% credible intervals derived from 300 simulations using the best-fit model (Table 1). The red x’s are daily reported cases. The distribution of estimated Re is shown in (D). The impact of varying α and μ on Re with all other parameters held constant at Table 1 mean values (E). The black solid line indicates parameter combinations of (α,μ) yielding Re = 2.38. The estimated parameter combination α = 0.14 and μ = 0.55 is shown by the red x; the dashed box indicates the 95% credible interval of that estimate. Log-likelihood for simulations with combinations of (α,μ) and all other parameters held constant at Table 1 mean values (F). For each parameter combination, 300 simulations were performed. The best-fit estimated parameter combination α = 0.14 and μ = 0.55 is shown by the red x (note that the x is plotted at the lower left corner of its respective heat map pixel, i.e., the pixel with the highest log likelihood); the dashed box indicates the 95% credible interval of that estimate.

  • Fig. 2 Impact of undocumented infections on the transmission of SARS-CoV2.

    Simulations generated using the parameters reported in Table 1 with μ = 0.55 (red) and μ = 0 (blue) showing daily documented cases in all cities (A), daily documented cases in Wuhan city (B) and the number of cities with ≥ 10 cumulative documented cases (C). The box and whiskers show the median, interquartile range, and 95% credible intervals derived from 300 simulations.

  • Table 1 Best-fit model posterior estimates of key epidemiological parameters for simulation with the full metapopulation model during 10–23 January 2020 (Seedmax = 2000, Td = 9 days).

    ParameterMedian (95% CIs)
    Transmission rate (β, days−1)1.12 (1.06, 1.19)
    Relative transmission rate (μ)0.55 (0.46, 0.62)
    Latency period (Z, days)3.69 (3.30, 3.96)
    Infectious period (D, days)3.47 (3.15, 3.73)
    Reporting rate (α)0.14 (0.10, 0.18)
    Basic reproductive number (Re)2.38 (2.03, 2.77)
    Mobility factor (θ)1.36 (1.27, 1.45)
  • Table 2 Best-fit model posterior estimates of key epidemiological parameters for simulation of the model during 24 January–3 February and 24 January–8 February (Seedmax = 2000 on 10 January, Td = 9 days before 24 January, Td = 6 days between 24 January and 8 February).

    Travel to and from Wuhan is reduced by 98%, and other inter-city travel is reduced by 80%.

    Parameter24 January–3 February
    [Median (95% CIs)]
    24 January–8 February
    [Median (95% CIs)]
    Transmission rate (β, days−1)0.52 (0.42, 0.72)0.35 (0.28, 0.45)
    Relative transmission rate (μ)0.50 (0.37, 0.69)0.43 (0.31, 0.61)
    Latency period (Z, days)3.60 (3.41, 3.84)3.42 (3.30, 3.65)
    Infectious period (D, days)3.14 (2.71, 3.72)3.31 (2.96, 3.88)
    Reporting rate (α)0.65 (0.60, 0.69)0.69 (0.65, 0.72)
    Effective reproductive number (Re)1.34 (1.10, 1.67)0.98 (0.83, 1.16)

Supplementary Materials

  • Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)

    Ruiyun Li, Sen Pei, Bin Chen, Yimeng Song, Tao Zhang, Wan Yang, Jeffrey Shaman

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

    Download Supplement
    • Materials and Methods
    • Figs. S1 to S26
    • Tables S1 to S3
    • Caption for Data S1
    • References
    Data S1
    MDAR Reproducibility Checklist
     
    Correction (25 March 2020): Li et al. have identified an error in the code in lines 44 to 49 of SEIR.m and in equation 4 of the supplementary materials. This produces a very small error in the denominator population size in some of the model terms. The authors have rerun the model and find that the parameter estimates are almost identical and the conclusions are unchanged. Corrections have been made in Tables 1 and 2, the supplementary materials (including tables S1 and S3), and the code.
    The original PDF is accessible here and the original Data file is accessible here.

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