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    Review of 'An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation Initiatives'

    An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation InitiativesCrossref
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    An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation Initiatives

    Much media and societal attention is today focused on how to best control the spread of Covid-19. Every day brings us new data, and policymakers are implementing different strategies in different countries to manage the impact of Covid-19. To respond to the first wave of infection, several countries, including the UK, opted for isolation/lockdown initiatives, with different degrees of rigour. Data showed that these initiatives have yield the expected results in terms of containing the rapid trajectory of the virus. When this manuscript was first prepared, the affected societies were wondering when the isolation/lockdown initiatives should be lifted. While detailed epidemiologic, economic as well as social studies would be required to answer this question completely, we employ here a simple engineering model. Albeit simple, the model is capable of reproducing the main features of the data reported in the literature concerning the Covid-19 trajectory in different countries, including the increase in cases in countries following the initially successful isolation/lockdown initiatives. Keeping in mind the simplicity of the model, we attempt to draw some conclusions, which seem to suggest that a decrease in the number of infected individuals after the initiation of isolation/lockdown initiatives does not necessarily guarantee that the virus trajectory is under control. Within the limit of this model, it would appear that rigid isolation/lockdown initiatives for the medium term would lead to achieving the desired control over the spread of the virus. This observation seems consistent with the past summer months, during which the Covid-19 trajectory seemed to be almost under control across most European countries. However, recent data show that the virus trajectory is again on the rise. The latter is also consistent with the simple model proposed here. Because the optimal solution will achieve control over the spread of the virus while minimising negative societal impacts due to isolation/lockdown, which include but are not limited to economic and mental health aspects, the engineering model presented here is not sufficient to provide the desired answer. However, the model seems to suggest that to keep the Covid-19 trajectory under control, a series of short-to-medium term isolation measures should be put in place until one or more of the following scenarios is achieved: a cure has been developed and has become accessible to the population at large; a vaccine has been developed, tested, and distributed to large portions of the population; a sufficiently large portion of the population has developed resistance to the Covid-19 virus; or the virus itself has become less aggressive. It is somewhat remarkable that an engineering model, despite all its approximations, provides suggestions consistent with advanced epidemiologic models developed by several experts in the field.

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      Review of “An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation Initiatives” by King and Striolo

      In this article, King and Striolo have developed a simple engineering model to understand the trajectory of COVID-19 cases. The model is based on three population-related variables and two rate constants. The model also takes into account the effect of intervention strategies applied by the government by scaling down the growth rate of cases. The authors applied this simple model to WHO data from three countries around the world, namely China, Singapore, and South Korea. The authors have also applied the model to the COVID trajectory in the U.K. during the revisions. Although the model is simple and cannot be used to inform complex and far-reaching public health decisions, as the authors rightly caution, the model results in some notable conclusions regarding the pandemic and lockdown strategies to contain it. Over the course of the previous two rounds of review, the authors have improved the manuscript based on the suggestions made. Nevertheless, the manuscript may be improved further by implementing the following revisions, prior to publication:

      1. On page 2, the authors introduce SIR-type models and provide a brief overview of such models. The authors should explain the abbreviation SIR and also how such models work. The authors should also briefly describe any alternative or superior strategies for modeling the spread of infectious diseases, which may already have been explored or could be explored in the future.
      2. On page 4, the authors mention that “Fitting is not shown here because abundant analysis is reported on the news as well as on specialist literature.” However, the authors should report the values of k1 and k2 used in their model and how these values were obtained/chosen, along with their 95% confidence intervals. This should be done for all the cases considered in the manuscript.
      3. In Figure 1, the authors mention a R2 value of 1.0 for the exponential fit during the initial stage of the pandemic; however, they do not indicate till what time point the data was included in the fit.
      4. Although the authors provide R2 values for their fits, they do not provide 95% confidence intervals for any of their parameters and error bars for their predictions. These should be added to the manuscript, to quantify the robustness of the model and the predictions.
      5. The authors should clearly mention and indicate that in Figure 1 and all other figures, the vertical axis refers to the percentage of cases, rather than the absolute number of cases. Further, what is the unit of time in the plots shown in the manuscript? This should be mentioned in the manuscript. In Figure 1, the maximum time considered is less than 10, whereas in Figure 2, the maximum time considered is 500. Could the authors explain this choice?
      6. In Figure 3, it appears that the top two panels plot the absolute number of cases; however, the bottom plot seems to depict the cases as a fraction of the population. The authors must clarify this point.
      7. On page 11, the authors mention that the “fit of the South Korean data is more promising…, as shown by the data in Table 2”. The authors should explain how the ratios A/B and C/D that they have defined can be used to infer the quality of the fit. The authors should also provide concise physical interpretations of these ratios.
      8. Regarding the proposed expression for dX/dt on page 3, could other types of functional expressions (e.g., power laws) in terms of X  and Y  work better in modeling the spread of disease?
      9. On page 4, the authors mention that N=X+Y+Po , but in so doing they have not considered the individuals labeled as REC . Why shouldn’t N = X + Y + REC ?
      10. On pages 4-5, the authors should fix the spellings ‘Hetohcote’ to ‘Hethcote’, ‘mode’ to ‘model’, and ‘out’ to ‘our’.
      11. On page 6, the authors include the effects of government intervention in the simplified model where X, i.e., the number of uninfected individuals, is assumed to be equal to Po. This seems to be a major simplification, which may not be true as the pandemic progresses. What would be the effect of not making this simplification on the model predictions?
      12. In Figure 3, the authors refer to the ‘left’ panel, when they should in fact refer to the ‘top’ panel.
      13. On page 11, it would be interesting to see the effect on the model upon addition of another term to Kstep-down that models a reduction in the intervention strength or a reduction in compliance to the intervention measures, which set in after a certain amount of time.


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