Mathematical Modeling and Simulation of the COVID-19 Pandemic
Round 1
Reviewer 1 Report
The article "Mathematical modeling and simulation of the COVID-19 pandemic" aims to provide better understanding of the dynamics of the COVID-19 pandemic in 6 countries based on data retrieved from the ECDC. Using a SIR simple model the author aims to explain how the pandemic has been progressing over several months initially and the results are forecast for a year from the beginning of the epidemic.
Although SIR models are useful to understand how basic epidemic models evolve, it is misleading to say that this simple SIR model can predict and fit the COVID-19 pandemic. Much more sophisticated models which include other population classes, medical and social interventions are predicting epidemics in different regions more accurately, as these are often based on data from a specific region or country, where population dynamics is specific to that place. The author does not mention a single other model trying to understand the pandemic and compare to this model, which I find disappointing as it is hard then to see what is the contribution of this article among the scientific literature.
There are too many plots which make the reader loose idea of the manuscript scope and the temporal scales are varied from one country to another making it hard to see what is the point of the manuscript and whether the model fitting and assumptions are correct.
However, the section on looking for strategies of a temporary lock-down is an interesting addition that may be worth exploring further or make the main point of an article (keeping the scope of it in focus -e.g. as a generic model that can explain how movement restriction or population shielding can lead to better epidemic control with COVID-19 as a study case).
Please find attached some additional comments I made to the the manuscript.
Comments for author File: 
Comments.pdf
Author Response
Some comments on your remarks
First I have to thank you for your review and your additionanl comments.
You're right that the SIR model is to simple to cover the COVID-19 pandemic
because of his macroscopic character.
This is also true for such models which are extended by outher sub-populations, for
example the SIR-X model (see paper of Maier and Brockmann).
The analysis of the properties of the model with respect to the behavior in the case
of the transfer from normality to a lockdown situation is the main intention of the paper,
also the consequences of temporary lockdowns.
To respect this I rearranged and refocussed the paper (abstract, introduction).
The model parameter evaluation/estimation was another point of my interest.
Based on the date of the early phase of the pandemic the model parameters
could be evaluated with the solution of a non-linear optimzation problem.
I reduced the number of tables and figures to a level which is more acceptable for
the reader. At the end I tried to sum up relevant messages in the conclusional part.
I revised the bibliography (I blanked out selfcitations).
Berlin, June 6th 2020
Guenter Baerwolff
Reviewer 2 Report
In the present article, the author exploits the SIR model to investigate some scenarios that may occur in different countries in consequence of lockdown actions. The effect of the lockdown is modeled in terms of a reduction in the beta coefficient.
The conclusions that are drawn on are interesting and the forecasting scenario sound reasonable. Overall, the article is well written.
However, the quality of the article might be definitely improved by taking into account the following suggestions
- The author exploits the first exponential growth phase in order to obtain a reasonable value for the beta value. This seems reasonable. However, I have not clearly understood whether he uses the parameter obtained from the linearized model or the one estimated with a more rigorous nonlinear regression. In my opinion, it is obvious that the second approach leads to more plausible results. In the former case the error of the measurements is amplified at the beginning of the process as a consequence of the nonlinear transformation of the measured variable. The author should clarify this aspect
- As far as I have understood, figures 1 and 2, figures 3 and 4, figures 5 and 6 etc. refer to the same data plotted together with the corresponding calibrated models but with a different choice of the scales. I suggest the author to put both graphs in the same figure.
- Presentation of the results in the Section is a little confusing. I suggest the author to carefully check the order of the figures.
Other minor aspects to be considered
- The author claims in the abstract that existence and uniqueness of the solutions are discussed in the article. In all honestly, I have not found a rigorous discussion of this aspect in the text.
- The equation on top of the page 13 is immediately repeated in the following with a different choice of the damping factor for the beta coefficient. I suggest the authors to remove it.
Author Response
Some comments on your remarks
First I have to thank you for your review and your additionanl comments.
The model parameter evaluation/estimation was one important point of my interest.
Based on the date of the early phase of the pandemic the model parameters
could be evaluated with the solution of a non-linear optimzation problem.
Because the better results of the estimation of beta with the non-linear minimization
method these results/values are used in the simulation examples.
The analysis of the properties of the model with respect to the behavior in the case
of the transfer from normality to a lockdown situation is the main intention of the paper,
also the consequences of temporary lockdowns and dynamical lockdowns.
To respect your suggestions I rearranged and refocussed the paper (abstract, introduction).
I reduced the number of tables and figures to a level which is more acceptable for
the reader. At the end I tried to sum up relevant messages in the conclusional part.
I revised the bibliography (I blanked out selfcitations).
"In all honestly, I have not found a rigorous discussion of this aspect in the text..."
I canceled these mathematical remarks, they are not of interest in this paper.
Berlin, June 6th 2020
Guenter Baerwolff
Reviewer 3 Report
Please see my comments below:
1) the study was not well-written and lack of important details especially in the introduction. The introduction does not address the topic and highlight previous research done and why this research is needed to be conducted. This leaves the readers to question the meaning of the study.
2) the author use "We" thoroughout the manuscript. But the author list only has 1 author. It is unclear if the author paid attention to details.
3) there have been several modelling studies on COVID-19. What are the advantages and limitation of using the SIR for the modelling? How does this compare with other findings and real scenario?
4) there is a lack of discussion. Please expand this section.
5) too many tables. Can the author only include the important results? Justify why these results are important. Other tables can be labelled as supplementary figures.
6) the author should describe the aim of the study clearly. It is very unclear to the readers when reading the whole manuscript.
7) the author showed some good results. But again, thesre results are not well explained. Please expand.
8) which data did the author use for the assumption and modelling? How good are these data sets?
9) did the author perform any data cleaning on these data sets?
10) how did the author address the "noise" from these data sets? These are all very important questions to be addressed so that these results are not over-intepreted.
Author Response
Some comments on your remarks
First I have to thank you for your review and your additiionanl comments.
I respect your remarks
be rearranging and refocussing abstract, introduction and discussion.
I moved from "we are" to "I am".
I reduced the number of tables and figures to a level which is more acceptable for
the reader.
The actual data of the European Union are used, and I made an alignment with the data
of the Johns-Hopkins university and the German Robert-Koch-Institut.
With the evaluation/estimation of the model data (beta) by the solution of a non-linear
minimization problem a certain kind of "data cleaning" is done, outlier are damped down.
To address noise it is nessecary to move from deterministic to stochastic models,
but this is a subject for another paper.
The analysis of the properties of the model with respect to the behavior in the case
of the transfer from normality to a lockdown situation is the main intention of the paper,
also the consequences of temporary lockdowns.
I used the macroscopic SIR-model for this reason. It is clear that such models
cannot fully cover the COVID-19 pandemic, this is valid for more complex models (for example
the SIR-X model, paper of Maier/Brockmann). But these model are eligible to
investigate the qualitative behavior of social distancing/lockdown.
At the end I tried to sum up relevant messages in the conclusional part and I revised the
bibliography (I blanked out selfcitations).
Berlin, June 6th 2020
Guenter Baerwolff
Reviewer 4 Report
This is an interesting contribution to the pandemic of COVID-19.
The style makes the article sometimes not clear. For example in the Abstract the author writes
“Beside the virology research mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to physicians and 4 politicians for their decisions.”
This means that “virology research mathematical models and simulations” is the subject of the sentence, where the authors means
“Beside the virology research, mathematical models and simulations can be”
The classical SIR is useful, but for this pandemic is too simple. It may be, of course, helpful at the initial stages, but now it would be better to consider some other subpopulations.
What is the role of the asymptomatic population?
Chadi M. Saad-Roy, Ned S. Wingreen, Simon A. Levin, and Bryan T. Grenfell. Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage. PNAS, In Press, first published May 8, 2020 https://doi.org/10.1073/pnas.1920761117
And the role of the super-spreaders?
- Ndaïrou, I. Area, J.J. Nieto, D.F.M. Torres, Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan. Chaos, Solitons and Fractals 135 (2020), 109846.
What about the incubation time?
The estimation of the parameters is reasonable, but it should be compared with other published estimations.
The numerical simulations are for two countries in the section 4.-Some numerical computations for Germany and Spain.
I suggest compare the parameters in Wuhan (see previous reference in Chaos, Solitons and Fractals) and include some figures comparing for example Germany and China.
Revise the style and English.
In the Conclusion,
“The results are pessimistic in total with respect to a successful fight against the COVID-19-virus. Hopefully the reality is a bit more merciful than the mathematical model.”
I cannot agree, the reality is worst.
Author Response
Some comments on your remarks
First I have to thank you for your review and your additionanl comments.
I respect your remarks
by rearranging and refocussing abstract, introduction and discussion.
To your remarks on role of the asymptomatic population
and super-spreading I guess that these phenomenoms can not fully covered
by such macroscopic models like SIR, SIR-X or other lightly modified SIr-type
models.
I revised the bibliography (I blanked out selfcitations), also to indicate to these subjects.
I reduced the number of tables and figures to a level which is more acceptable for
the reader. At the end I tried to sum up relevant messages in the conclusional part.
I canceled "Hopefully the reality is a bit more merciful than the mathematical model", because
you're right.
Berlin, June 6th 2020
Guenter Baerwolff
Round 2
Reviewer 1 Report
Dear author,
Thank you for your revised manuscript. This new version is much improved and the structure of the article is now much easier to follow. I also appreciate that you reformulated the articule so it can reflect the main purpose of your analysis, which was to see how, for how long and when to impose movement restrictions among others. I attach a document with minimal comments for your consideration.
Best wishes.
Comments for author File: Comments.pdf
Author Response
Some comments on your second remarks
I reordered the figures (some of them are subsumed).
I respected your suggestions for the introduction.
Some English changes are made.
Thank you for your suggestions
Berlin, June 26th
Guenter Baerwolff
Reviewer 3 Report
Even after the major revision, the manuscript is still not up to the publisable standards. The author did not seem to address the reviewers' comments adequately.
Author Response
Some comments on your second remarks
The article was in some points refined.
I tried to address the reviewers comments.
I reformulated the introduction,
I reordered the figures (some of them are subsumed).
Some English changes are made.
Thank you for your suggestions
Berlin, June 26th
Guenter Baerwolff
Reviewer 4 Report
At the end of the paper, I am not sure the sentence
But not all measures and interventions can not be described by SIR-type models
should be
But not all measures and interventions can be described by SIR-type models
Please check.
In relation to reference [11] I suggest the following one
N.Moradian et al., The urgent need for integrated science to fight COVID‑19 pandemic and beyond. J Transl Med (2020) 18:205, https://doi.org/10.1186/s12967-020-02364-2
Complete the authors of the references.
Author Response
Some comments on your second remarks
I reordered the figures (some of them are subsumed).
I respected your suggestions to some changes (last sentence, bibliography...)
Some English changes are made.
Thank you for your suggestions
Berlin, June 26th
Guenter Baerwolff
