PONE-D-20-38562

Characterizing Two Outbreak Waves of COVID-19 in Spain Using Phenomenological Epidemic Modelling

PLOS ONE

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Reviewers' comments:

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Reviewer #1: Partly

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

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Reviewer #1: Yes

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Reviewer #1: Yes

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5. Review Comments to the Author

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Reviewer #1: In general, the topic of the article is important. Several aspects need to be improved to avoid wrong conclusions and public health messages. It is important to remark that media, some researchers and people in general are dissatisfied with the forecasting made by several studies since those have been wrong. The idea is to improve the mathematical process and the validation.

These are the main general aspects that I have found that need to be fixed. The authors need to emphasize that the models presented here are only valid for a very short term, and that they do not take into account changes in social behavior and NPI interventions. Second, since it is a characterization, it is important to see if the parameters are identifiable in a unique way. The algorithm used in this article is a local one, so it would be necessary to use a global optimizer or justify the locality. In addition, the authors need to show the bootstrap correlations plots in the parameter space to address identifiability. Finally, in several parts of the article the authors mention that the model can be used for forecasting and talk about final epidemic size. It is important that the authors mention that the model is valid for a short period and under the current COVID-19 pandemic where there are many changes in social behavior, the models cannot forecast the final epidemic size. In the last table there is an estimation of R0 using final epidemic size, this needs to be modified and explained.

Here particular aspects to improve the paper taking into account previous general comments:

There are few references and the introduction can be improved taking into account previous works.

Line 20. How long? Relative to what?

Line 73. Change the word current. If people look, the current situation in Spain would disagree with the result presented here and specially with the 2nd wave.

Line 87 fix the name

Line 141 add reference and assumptions for this equation. This formula includes final epidemic size, which can't be obtained with the proposed models. Please explain this and the limitations.

Line 213. Is a good comment.

Section 4.1. Explain why and how you chose the specifics early epidemic period? Notice that this would change the values of the estimated parameters.

Section 4.. For the first and second waves, the periods are different. Show in table Co for each wave.

The bootstrapping plots (parameter space) can show correlations between the parameters and asses if the a parameters are identifiable. If this is not true, then there are infinite sets of parameter values such the fit is equally good.

Fig 6. The bootstrapping plots (parameter space) can show correlations between the parameters and asses if the parameters are identifiable. If this is not true, then there are infinite sets of parameter values such the fit is equally good. In this case, it seems that parameters are correlated, please show bootstrap plots in the parameter spaces.

Divide the section in 1st wave and 2nd wave to see the differences more clearly.

For each wave summarize initial condition, parameters, period, results in a Table.

Line 377. I would not use final epidemic size here since as the authors mention this method is only valid for the early period. Moreover, as the authors mention this model does not take into account variation on social behaviors and NPI.

Line 406. This paragraph needs to be changed carefully. The models presented here can't do long term forecast. This has been already mentioned by several studies and the media and people in general are blaming the models and forecasting. Just looking the current data of Spain it can be seen that extrapolation is wrong. However, still models are useful for other aspects. Please emphasize limitations of the study, and focus on what can be done with these limited models.

Lines 415. A deeper discussion would be useful regarding the unreported cases and the effect on the Ro and compare with other studies, Underreporting is a common issue an should be discussed. Authors should add some discussion of the asymptomatic cases and the findings n this study. Finally, discuss about the estimations given in the article and how this is affected by the infectious period, incubation period, proportion of asymptomatic, initial amount of recovered people

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Reviewer #1: No

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Characterizing Two Outbreak Waves of COVID-19 in Spain Using Phenomenological Epidemic Modelling

PONE-D-20-38562R1

Dear Dr. Lopez,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Oscar Millet

Academic Editor

PLOS ONE

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Reviewers' comments: