Dear Dr. Liu,

Thank you very much for submitting your manuscript "Using a multi-strain infectious disease model with physical information neural networks to study the time dependence of SARS-CoV-2 variants of concern" 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.

Please also ensure that you are in compliance with our code-sharing policy at this stage.

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.

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[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,

Roger Dimitri Kouyos

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: Based on the limitations in quantifying intervention strategies and using static parameters in SIR models, authors propose a new technique — VOCs-INN — by informing NNs with the mechanisms of SIR models. I find the study very interesting but I have several major points,

1. Given how authors mention the superiority of their method to the previous fitting procedures, I think it is essential to include certain comparisons of simpler approaches in this paper. For example, how would the dummest SIR model would perform with static infection parameters? The next logical step is to compare this with an SIR model that assumes time-dependent variables but does not use NNs for fitting, as well as only NNs what do not have any information from an SIR model. Finally, we reach to the most complex scenario, which is what authors demonstrate with their informed NN model. An easier comparison here can be achieved by playing with the weight of the LOSS_ode relative to LOSS_data and compare the goodness of fit as the weight is increasing from 0 (not informed NN at all) to 1. To make their case, authors should show that informing the NNs with the SIR model (hence increasing this weight) should make significant contributions to the output as it is increasing.

2. This brings me to my second major point, where I couldn’t find any definitions of the goodness of fit in the manuscript. In lines 212-213, authors write :”It can be seen from the figure that VOCs-INN can fit the 212 real data very well. “. This is a computational study, I expect here a mathematical expression that is coherent with the rest of the manuscript. What is the quantification of “fitting well”? Which metric do you use the assess the goodness of fit? The y axis in Fig. 6 is scaled with 1e3, which means very small differences in the plot can map to considerable differences in absolute numbers. A metric to asses the goodness of the fit is necessary here.

3. And the next major point, I think it is also imperative to present the details of computational complexity of these different approaches (for example the dummest SIR versus authors’ method) since this is a trade-off in predictive power versus computational complexity and authors also mention this as a selling point for their method In Lines 21-24. Honestly, I find it hard to believe that fitting NNs is computationally less expensive than a least squares method? I can understand the benefits about the temporal aspect of certain parameters (and most methods assuming them constant over time) but the differences in computational complexity has to be justified if the authors are making this claim.

4. Another major point is about the short-term predictions. Predictions that authors provide in Figs. 9 and 10 correspond to a time where the population is mostly stabilized. Is this really the right time window to demonstrate the capabilities of this model? For example, shouldn’t we test for the short-term predictions of the model right after an intervention that will alter Re? Wouldn’t that be more consistent with the narrative of the paper since it emphasizes this in the authors summary?

5. And finally, reproducibility. I see that there is no repository of the code that is shared? Moreover, hyperparameters and the number of hidden layers is painful to adjust and specific to the question at hand. Authors should mention the processes that led to the results they mention in lines 183-186. What is the learning rate, batch size, etc.? How did the authors experiment with these?

Some of my other minor comments are below.

- I would generally suggest authors to have a more modest language throughout the manuscript, and avoid phrases like “fascinating aspect”.

- As I am at line 72 in the introduction, I am having a hard time understanding what exactly makes this paper novel. Author summary focuses on quantifying the control interventions, then authors mention the inclusion of time dependent parameters, then we read about computational complexity, and then finally incorporating the mechanisms into a black box model and making it more gray-like. What is really the benefit of the method authors developed? All of these? If so, revise writing to make this more clear.

Reviewer #2: Review comments are uploaded as an attachment.

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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: No: There is no repository of the code?

Reviewer #2: No: No code is shared. The epidemiological data used is named and referenced (ref 35), but the URL in the reference points to example.com. No data underlying the plots is shared. No code or data sharing is discussed.

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Reviewer #1: No

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.

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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

Attachments

Attachment

Submitted filename: review_comments.docx

PCOMPBIOL-D-24-01438R1

Using a multi-strain infectious disease model with physical information neural networks to study the time dependence of SARS-CoV-2 variants of concern

PLOS Computational Biology

Dear Dr. Liu,

Thank you for submitting your manuscript to PLOS Computational Biology. After careful consideration, we feel that it has merit but does not fully meet PLOS Computational Biology's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript within 30 days Feb 25 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at ploscompbiol@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcompbiol/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

* A rebuttal letter that responds to each point raised by the editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to formatting updates and technical items listed in the 'Journal Requirements' section below.

* A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

* An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Roger Dimitri Kouyos

Section Editor

PLOS Computational Biology

Roger Kouyos

Section Editor

PLOS Computational Biology

Journal Requirements:

1) We have noticed that you have uploaded Supporting Information files, but you have not included a complete list of legends. Please add a full list of legends for your Supporting Information files after the references list.

2) Please ensure that the funders and grant numbers match between the Financial Disclosure field and the Funding Information tab in your submission form. Note that the funders must be provided in the same order in both places as well. State what role the funders took in the study. If the funders had no role in your study, please state: "The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.".

If you did not receive any funding for this study, please simply state: u201cThe authors received no specific funding for this work.u201d

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: I thank the authors for rigorously addressing all my comments. I believe that the manuscript has improved significantly and ready for publication.

Reviewer #2: Review comments uploaded as an attachment.

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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: Yes

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.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: Yes: Burcu Tepekule

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

Figure resubmission:

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. Registration is free. 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 PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. If there are other versions of figure files still present in your submission file inventory at resubmission, please replace them with the PACE-processed versions.

Reproducibility:

To enhance the reproducibility of your results, we recommend that authors of applicable studies deposit 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

Attachments

Attachment

Submitted filename: review_comments_r1.docx

Dear Dr. Liu,

We are pleased to inform you that your manuscript 'Using a multi-strain infectious disease model with physical information neural networks to study the time dependence of SARS-CoV-2 variants of concern' 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,

Roger Dimitri Kouyos

Section Editor

PLOS Computational Biology

Roger Kouyos

Section Editor

PLOS Computational Biology

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