Dear Dr. Kühn,

Thank you very much for submitting your manuscript "Novel travel time aware metapopulation models: A combination with multi-layer waning immunity to assess late-phase epidemic and endemic scenarios" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

Associate editor

The paper has been read by two experts in the field, and to a lesser extent by me. All of us find the paper potentially interesting but having some issues needing attention. Both referees make many important points, the overall most critical point probably being the fitting and evaluation of the model given its complexity. Please address all questions/comment raised by the referees. I would also consider modifying the current title which is quite long and not very informative.

Kind regards, Tom Britton

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

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Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Tom Britton

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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Associate editor

The paper has been read by two experts in the field, and to a lesser extent by me. All of us find the paper potentially interesting but having some issues needing attention. Both referees make many important points, the overall most critical point probably being the fitting and evaluation of the model given its complexity. Please address all questions/comment raised by the referees. I would also consider modifying the current title which is quite long and not very informative.

Kind regards, Tom Britton

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The review is uploaded as an attachment.

Reviewer #2: The authors present a new epidemiological model that introduces novelty in two fronts: a/ travel time in a graph-ODE metapop model (including passing explicitly through multiple districts), b/ a multi-layer waning immunity model that support different paces for protection against various degrees of disease severity. The authors combine these advancements to investigate the impact of mobility (more specifically the use of mitigation measures such as masks during mobility) in a late-phase epidemic scenario.

Overall, I believe the authors present interesting modelling frameworks, that cover important aspects related to the modelling of infectious diseases. I studied the proposed frameworks which appears to be sound, and I could not find any immediate errors or mistakes. However, such a complex model requires many choices, both regarding model structures and the selected parameters. I think it would be appropriate to discuss the limitations and uncertainties regarding these choices properly in the discussion section, which currently seems to be quite limited.

My main remarks regarding this paper concern the evaluation of the model frameworks, the presentation, some assumptions made about the impact of mitigation strategies while travelling, and reproducibility.

The authors present important advances regarding metapop modelling (time-aware and passing through multiple districts) and immunity waning. However, while these components are not necessarily connected, they are evaluated in combination, which makes it hard to assess how these components match their individual goals. I would expect an evaluation on the SECIRS compartment model and an evaluation that compares the graph-ODE model from [Kuhn, 2021] with the methodological extensions presented in this paper (so, without the SECIRS model). In my opinion the comparison between the graph-ODE and the method presented in this paper can be performed on an early-phase pandemic scenario, when waning is not a concern.

Next, I appreciate the combined setting of a late-phase epidemic, which is interesting. However, at this point, I find it hard to assess how this model is able to capture reality. I tried to make this assessment by interpreting Figure 11, which shows the green model curve (which should be close to the German reality during the time frame that was modelled, if I'm not mistaken) and 2 data curves (red and orange, where red corresponds to the DigiHero reports). Based on this Figure, I find it hard to see how well the red curve and the green curve match. Perhaps a rescaling of the DigiHero curve could help here, but perhaps it would be better to try to capture the DigiHero reporting dynamics in the model to allow for curves that are easier to compare? That being said, I understand that comparing symptomatic curves is not an easy thing to do (due to underreporting, as mentioned by the authors), in that regard, did the authors consider taking hospitalisations into account for evaluating the models (I would argue hospitalisation data has proven more stable during the course of the course of the pandemic)?

Regarding the presentation of the methods. It was not always easy to identify the authors' contributions given that the background and the novel methods are quite intertwined. I think it would be good to explicitly emphasise the contributions and add some more structure to the method section to help the reader. Perhaps it could help to split this section in a background section and a methods section, to make this more clear?

Unless I missed it, the authors consider the type of travel contacts the same as contacts made at home, work, school. I would argue that contacts made during a travel (on the train/bus etc) are more distant, as individuals might not talk to each other. Earlier work in the context of influenza distinguished between conversational and physical contacts (https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002425), but the types of contacts made at public transport might be considered to be of a different type? Can the authors comment on this, as assumptions in this regard could have an impact on some of the conclusions (e.g., Fig 11).

Regarding reproducibility, the authors state "The total number of produced simulation data sums up to 200 GB and cannot be uploaded easily.". I would argue that the simulation results are not that important, but the code and data sources needed to reproduce these results are key. Can the authors explain whether this is possible with the material that is available on GitHub?

Some minor remarks:

- although fighting infectious diseases -> sounds strange, consider rephrase

- situations of high transmission (risk) -> situations of high transmission

- Over the last years, to predict SARS-CoV-2 development in 19 Germany, contributions have been made by a variety of different approaches. -> Rephrase: Over the last years, contributions have been made by a variety of different approaches, to predict SARS-CoV-2 development in 19 Germany."

- In the introduction, the authors provide a list of different types of models. I have two comments. First, I would split between agent-based and individual-based models. Second, the authors only seem to mention German models, but I think for the individual-based models, models like COVASIM and "STRIDE COVID-19" should also be mentioned? Same remark for the other model categories.

- Mathematical models based on systems of ordinary differential equations (ODE) -> Mathematical models based on systems of ODEs (abbreviation was already introduced)

- When first reading through equation (1), I was confused that there was a patch notation (k), which it concerns a definition that does not consider a metapop approach yet. I think it would be more clear to first introduce a normal SIR model.

- "although the model is a pure infection dynamics model, just parameterized for mobility settings." -> During the first read, this was hard to understand, consider a rephrase.

- "while only a portion p(k) tr ∈ [0, 1] also has contacts in traffic locations (which is nontrivial as people might not" -> don't see why this is nontrivial, I believe it is trivial that only a portion has contacts during travelling? Or do I misunderstand the point of the authors?

- we need to determine who is commuting at all. -> not clear, rephrase

- A important challenge

- where neither infection nor vaccination promises lasting protection -> where neither infection nor vaccination *establishes* lasting protection

- "larger numbers of infected" -> "larger numbers of infected individuals" (this way of writing is also used in the rest of the manuscript, so I would consider changing it there as well)

- The authors indicate that one variable was fitted (Table 3), but I did not find any additional explanation, unless I missed it.

- number is ridiculously large, -> rephrase

- (here denoted Existing method, -> missing a closing )

- "Existing method" -> perhaps a more descriptive name of the original model would be more clear

References:

Kuhn MJ, Abele D, Mitra T, Koslow W, Abedi M, Rack K, et al. Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution. Mathematical Biosciences. 2021;

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: None

Reviewer #2: No: I chose "No" because this was not clear yet to me. I address this in my detailed comments. Based on the feedback of the authors I will reconsider this choice.

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Reviewer #1: No

Reviewer #2: No

Figure Files:

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Attachments

Attachment

Submitted filename: review.pdf

Dear Dr. Kühn,

Thank you very much for submitting your manuscript "Novel travel time aware metapopulation models and multi-layer waning immunity for late-phase epidemic and endemic scenarios" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

Both reviewers were happy with the revision, and so am I. Reviewer 2 just have some very minor issues which you should be able to deal with quickly.

Kind regards, Tom Britton, Academic editor

Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Tom Britton

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

***********************

A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact ploscompbiol@plos.org immediately:

Both reviewers were happy with the revision, and so am I. Reviewer 2 just have some very minor issues which you should be able to deal with quickly.

Kind regards, Tom Britton, Academic editor

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: All comments were addressed. Thank you!

Reviewer #2: I thank the authors for a very thorough and detailed revision, and congratulate them on this nice work.

This revision addresses my comments and I only have a couple of minor remarks:

- "We use wastewater data as an unbiased estimator" -> A bit strange to refer to data as an estimator? Moreover, I would not state that it is unbiased, cause that would be hard to show (also not convinced that it is). Perhaps rephrase as "We use wastewater as a proxy"?

- In Figure 4, the authors state "Spatial distribution of symptomatic infections in Bavaria". Given the revision that was done, perhaps it is better to show ICU cases her as well? And if this adjustment is made, perhaps give some information on how well these predictions follow the reported ICU data from a spatially perspective?

- The authors state "In Fig. 5 (right), we see that our model is able to capture the reported ICU occupancy for the second part of the simulation very well while discharges on initially admitted are overestimated." Can the authors add some discussion on the mismatch (reported vs model) between initially admitted ICU cases.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: None

Reviewer #2: Yes

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Reviewer #1: Yes: Mohamed El Khalifi

Reviewer #2: No

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

References:

Review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript.

If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Dear Dr. Kühn,

We are pleased to inform you that your manuscript 'Novel travel time aware metapopulation models and multi-layer waning immunity for late-phase epidemic and endemic scenarios' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

Tom Britton

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

Feilim Mac Gabhann

Editor-in-Chief

PLOS Computational Biology

Jason Papin

Editor-in-Chief

PLOS Computational Biology

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Now also the 2nd reviewer is satisfied with the revision, and so am I. I am hence happy to propose that the manuscript is accepted for publication.

Kind regards, Tom Britton

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #2: I thank the authors for their reply and this nice manuscript. I have no more comments. A final suggestion is that a short summary of their response to the second question could be added to the manuscript, as this might also interest the readers.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

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PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

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Reviewer #2: No