The basic reproduction number can be accurately estimated within 14 days after societal lockdown: The early stage of the COVID-19 epidemic in Denmark

  1. Jan Brink Valentin
  2. Henrik Møller
  3. Søren Paaske Johnsen

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Abstract

Early identification of the basic reproduction number (BRN) is imperative to political decision making during an epidemic. In this study, we estimated the BRN 7, 14, 21 and 28 days after societal lockdown of Denmark during the early stage of the COVID-19 epidemic.

Method

We implemented the SEIR dynamical system for disease spread without vital dynamics. The BRN was modulated using a sigmoid function. Model parameters were estimated on number of admitted patients, number of patients in intensive care and cumulative number of deaths using the simulated annealing Monte Carlo algorithm. Results are presented with 95% prediction intervals (PI).

Results

We were unable to determine any reliable estimate of the BRN at 7 days following lockdown. The BRN had stabilised at day 14 throughout day 28, with the estimate ranging from 0.95 (95% PI: 0.92–0.98) at day 7 to 0.92 (95% PI: 0.92–0.93) at day 28. We estimated the BRN prior to lockdown to be 3.32 (95% PI: 3.31–3.33). The effect of the lockdown was occurring over a period of a few days centred at March 18th (95% PI: 17th-18th) 2020.

Conclusion

We believe our model provides a valuable tool for decision makers to reliably estimate the effect of a politically determined lockdown during an epidemic.

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  1. Version published to 10.1371/journal.pone.0247021
  2. ScreenIT

    SciScore for 10.1101/2020.08.14.20174805: (What is this?)

    Please note, not all rigor criteria are appropriate for all manuscripts.

    Table 1: Rigor

    NIH rigor criteria are not applicable to paper type.

    Table 2: Resources

    Software and Algorithms
    SentencesResources
    Initial statistical analysis were conducted using Stata 14 (StataCorp. 2015. Stata Statistical Software: Release 14.
    StataCorp
    suggested: (Stata, RRID:SCR_012763)
    College Station, TX: StataCorp LP), while we employed Python version 2.7 (Python Software Foundation.
    Python
    suggested: (IPython, RRID:SCR_001658)

    Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).

    Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:
    Model limitations: A few of the model parameters is obtained from the literature, which may have some impact on estimated model parameters, considering these may not be fully generalizable to a Danish population. In addition, the model assumes that the time from symptom onset to hospitalisation is the same for severe cases as for in-patients in general. This lack of differential initial symptom load may explain the decreasing fraction of symptomatic cases and ratio of ICU cases compared to the external population, as the model may be unable to accurately predict the number of ICU beds needed. Nevertheless, the model also assumes constant proportion of symptomatic cases over time, however, as the epidemic progresses, high risk subjects may be more likely to be isolated by their own choice or as part of a political strategy. Therefore, the proportion of symptomatic cases may be better fitted using the same dynamical model as for the BRN. Moreover, our current model is subject to bias from changes in treatment availability, such as increased use of remdesivir, though current treatment opportunities have limited effect[12,22].

    Results from TrialIdentifier: No clinical trial numbers were referenced.

    Results from Barzooka: We did not find any issues relating to the usage of bar graphs.

    Results from JetFighter: We did not find any issues relating to colormaps.

    Results from rtransparent:
    • Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
    • Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
    • No protocol registration statement was detected.

    About SciScore

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  3. Version published to 10.1101/2020.08.14.20174805v1 on medRxiv