A reductive analysis of a compartmental model for COVID-19: data assimilation and forecasting for the United Kingdom

  1. G. Ananthakrishna
  2. Jagadish Kumar

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Abstract

We introduce a deterministic model that partitions the total population into the susceptible, infected, quarantined, and those traced after exposure, the recovered and the deceased. We hypothesize ‘accessible population for transmission of the disease’ to be a small fraction of the total population, for instance when interventions are in force. This hypothesis, together with the structure of the set of coupled nonlinear ordinary differential equations for the populations, allows us to decouple the equations into just two equations. This further reduces to a logistic type of equation for the total infected population. The equation can be solved analytically and therefore allows for a clear interpretation of the growth and inhibiting factors in terms of the parameters in the full model. The validity of the ‘accessible population’ hypothesis and the efficacy of the reduced logistic model is demonstrated by the ease of fitting the United Kingdom data for the cumulative infected and daily new infected cases. The model can also be used to forecast further progression of the disease. In an effort to find optimized parameter values compatible with the United Kingdom coronavirus data, we first determine the relative importance of the various transition rates participating in the original model. Using this we show that the original model equations provide a very good fit with the United Kingdom data for the cumulative number of infections and the daily new cases. The fact that the model calculated daily new cases exhibits a turning point, suggests the beginning of a slow-down in the spread of infections. However, since the rate of slowing down beyond the turning point is small, the cumulative number of infections is likely to saturate to about 3.52 × 10 5 around late July, provided the lock-down conditions continue to prevail. Noting that the fit obtained from the reduced logistic equation is comparable to that with the full model equations, the underlying causes for the limited forecasting ability of the reduced logistic equation are elucidated. The model and the procedure adopted here are expected to be useful in fitting the data for other countries and in forecasting the progression of the disease.

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  1. ScreenIT

    SciScore for 10.1101/2020.05.27.20114868: (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:
    Recall that one limitation particularly applicable to the deterministic compartmental models is the difficulty in getting proper estimates of the parameters, particularly when the number of compartments is large. In this respect, simpler models with fewer compartments have an advantage. However, several factors may contribute to a single parameter. This is also a model-dependent feature. Therefore the ability of such parameters to represent the mitigating efficacy of interventions appears limited (see below). Furthermore, the number of parameters in such models is not necessarily small, making numerical solutions often the only choice. Therefore, any method - whether mathematical or conceptual - which simplifies analysis and easy interpretation is welcome. Motivated by this, we hypothesize accessible population for transmission of the disease that can be the total or a small fraction of the total population depending on whether the transmission dynamics evolves in the absence or presence of interventions. Indeed, the effect of lock-down is evident in all counties where the disease has been controlled or nearly eliminated. At the mathematical level, we introduce a decoupling scheme to aid mathematical analysis that also helps easy interpretation. The model equations have been devised in such a way that the susceptible and active infected populations form the main populations. The decoupling is affected by dropping all inward and outward transitions excepting the direct transit...

    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 10.1101/2020.05.27.20114868v3 on medRxiv
  3. Version published to 10.1101/2020.05.27.20114868v2 on medRxiv
  4. Version published to 10.1101/2020.05.27.20114868v1 on medRxiv