A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic

  1. Bernard Cazelles
  2. Clara Champagne
  3. Benjamin Nguyen-Van-Yen
  4. Catherine Comiskey
  5. Elisabeta Vergu
  6. Benjamin Roche

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Abstract

The effective reproduction number R eff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate R eff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its R eff (t) . Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

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  1. Version published to 10.1371/journal.pcbi.1009211
  2. ScreenIT

    SciScore for 10.1101/2021.02.04.21251167: (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: 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:
    Our study is not without limitations. The model used here is, like all complex SEIR models developed for COVID-19, non-identifiable which means that it is likely that several solutions exist and we only present one of the most likely ones. This point is overlooked very open but see [37]. One limitation is the use of the classical homogeneous mixing assumption in which all individuals are assumed to interact uniformly and ignores heterogeneity between groups by sex, age, geographical region. However this kind of data are not easily available and where mixing patterns among age groups are available at the individual level in contact tracing databases they are only accessible following extensive ethical reviews. Another weakness is to not consider an age-structure in the model in order to simulate age-based predictions. In all cases taking an age structure and mixing matrix appears insufficient and heterogeneity of contact is important (see Britton et al, 2020). Nevertheless, in our opinion, these limitations are more than balanced by the fact that we take into account the non-stationarity of the epidemic data and that our results are mainly driven by hospital data, which is more accurate and timely than the number of infected cases. As our main objective was to infer global Reff, and not to explore age-specific mitigation strategies, simplification of the age structure appears justified. The corroboration of our Irish findings on proportions asymptomatic with those of others pr...

    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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  3. Version published to 10.1101/2021.02.04.21251167 on medRxiv