SEIR Filter: A Stochastic Model of Epidemics

  1. Martin Šmíd
  2. Luděk Berec
  3. Aleš Antonín Kuběna
  4. René Levínský
  5. Jan Trnka
  6. Vít Tuček
  7. Milan Zajíček

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Abstract

There are many epidemiological models at hand to cope with the present pandemic; it is, however, difficult to calibrate these models when data are noisy, partial or observed only indirectly. It is also difficult to distinguish relevant data from noise, and to distinguish the impact of individual determinants of the epidemic.

In mathematical statistics, the tools to handle all of these phenomena exist; however, they are seldom used for epidemiological models. The goal of this paper is to start filling this gap by proposing a general stochastic epidemiological model, which we call SEIR Filter.

Technically our model is a heterogeneous partially observable vector autoregression model, in which we are able to express closed form formulas for the distribution of compartments and observations, so both maximum likelihood and least square estimators are analytically tractable. We give conditions for vanishing, explosion and stationary behaviour of the epidemic and we are able to express a closed form formula for reproduction number.

Finally, we present several examples of the model’s application. We construct an estimate age-cohort model of the COVID-19 pandemic in the Czech Republic. To demonstrate the strengths of the model, we employ it to analyse and compare three vaccination scenarios.

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  1. ScreenIT

    SciScore for 10.1101/2021.02.16.21251834: (What is this?)

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

    Table 1: Rigor

    Institutional Review Board Statementnot detected.
    Randomizationnot detected.
    Blindingnot detected.
    Power Analysisnot detected.
    Sex as a biological variablenot detected.

    Table 2: Resources

    No key resources detected.

    Results from OddPub: Thank you for sharing your code and data.

    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.

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  2. Version published to 10.1101/2021.02.16.21251834v1 on medRxiv