Epidemic transmission with quarantine measures: application to COVID-19

  1. S.A. Trigger
  2. E.B. Czerniawski
  3. A.M. Ignatov

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Abstract

Equations for infection spread in a closed population are found in discrete approximation, corresponding to the published statistical data, and in continuous time in the form of delay differential equations. We consider the epidemic as dependent upon four key parameters: the size of population involved, the mean number of dangerous contacts of one infected person per day, the probability to transmit infection due to such contact and the mean duration of disease. In the simplest case of free-running epidemic in an infinite population, the number of infected rises exponentially day by day. Here we show the model for epidemic process in a closed population, constrained by isolation, treatment and so on. The four parameters introduced here have the clear sense and are in association with the well-known concept of reproduction number in the continuous susceptible– infectious–removed, susceptible–exposed–infectious–removed (SIR, SEIR) models. We derive the initial rate of infection spread from the published statistical data for the initial stage of epidemic, when the quarantine measures were absent. On this basis, we can found the corresponding basic reproduction number mentioned above. Our approach allows evaluating the influence of quarantine measures on free pandemic process that leads to the time-dependent rate of infection and suppression of infection. We found a good correspondence of the theory and reliable statistical data. The initially formulated discrete model, describing epidemic course day by day is transferred to differential form. The conditions for saturation of epidemic are found by solving the delay differential equations. They differ essentially from ones in SIR model due to finite delay, typical for COVID-19 The proposed model opens up the possibility to predict the optimal level of social quarantine measures. The model is quite flexible and it can be extended to more complex cases.

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  1. ScreenIT

    SciScore for 10.1101/2021.02.09.21251288: (What is this?)

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

    Table 1: Rigor

    Ethicsnot detected.
    Sex as a biological variablenot detected.
    Randomizationnot detected.
    Blindingnot detected.
    Power Analysisnot detected.

    Table 2: Resources

    No key resources detected.

    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: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.

    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.

    Results from scite Reference Check: We found no unreliable references.

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  2. Version published to 10.1101/2021.02.09.21251288 on medRxiv