PCSY-D-24-00065

Multilayer Graph Attention Networks for COVID-19 Prediction with the Fusion Method and Explainable AI

PLOS Complex Systems

Dear Dr. Fujimoto,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems'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 60 days Sep 07 2024 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 complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. 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,

Anjalika Nande, Ph.D.

Academic Editor

PLOS Complex Systems

Luca Pappalardo

Section Editor

PLOS Complex Systems

Journal Requirements:

1. "Please ensure that you provide a single, cohesive .tex source file for your LaTeX revision. You may upload this file as the item type 'LaTeX Source File.' As stated in the PLOS template, your references should be included in your .tex file (not submitted separately as .bib or .bbl). Please also ensure that you are making any formatting changes to both your .tex file and the PDF of your manuscript. If you have any questions, please contact Latex@plos.org. You can find our LaTeX guidelines here: LINK

https://journals.plos.org/complexsystems/s/latex"

Additional Editor Comments (if provided):

Review summary: All reviewers agree that this is promising work and that integrating machine learning with network science and epidemiology is an important research direction. However, they raise some valid points and make important suggestions to improve the manuscript. Specifically, it would be good if the authors work on comparing the performance of their model with multilayer baseline methods for a more accurate comparison, describe their methodology and ML pipeline in more depth so that it can be appropriately assessed, provide an appropriate overview of the existing research on epidemic spread over real contact networks, and discuss the limitations and biases associated with the data used, along with the generalizability of the model outside their sample population.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria ? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: Partly

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

Reviewer #1: Yes

Reviewer #2: I don't know

Reviewer #3: No

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data 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—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?<br/><br/>PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Review Comments to the Author<br/><br/>Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This is a novel paper which demonstrates the utility of multilayer fusion techniques with graph attention networks for predicting COVID-19 infection. The proposed FGAT-COVID-19 architecture does provide a greater impact COVID-19 prediction. The integration of network science, graph neural networks, and XAI has the potential to significantly enhance the control and mitigation of infectious disease spread.

Please find my reviews below:

1. Data Collection and Network Construction:

The data curation is done carefully. The use of three different types of networks (person-person contact network, intrahousehold co-residence network, and person-person co-location network) is a comprehensive approach that captures various dimensions of social interactions that contribute to COVID-19 spread. The only caveat is that the methodology for constructing the networks, particularly the matching algorithm for intrahousehold co-residence networks, should be validated rigorously to ensure accuracy. The reliance on manually curated contact tracing data might introduce biases if the data is incomplete or inaccurately reported.

2. Experimental Setup

The number of nodes used for training, validation, and inference should be clearly mentioned. Is the training size fixed ? and, would the model performance be the same if different nodes were used in training? Please explain this in results are methods section.

3. Model description

Please use mathematical notations in order to explain the model architecture rather than using emb_dim, or num_of_network etc.

4. Baseline comparisons:

To accurately assess the novelty of the proposed FGAT-COVID19 architecture it is crucial to compared to a number of existing baselines. The selection of Logistic Regression and Random Forest as baseline models is appropriate, as these are commonly used methods for classification tasks and provide a good benchmark for comparison. Additional models such as MNE, PMNE or GrAMME should also be considered for baseline methods. Given that these models are designed for multi-layer graph networks.

[PMNE: Weiyi Liu, Pin-Yu Chen, Sailung Yeung ,Toyotaro Suzumura, and Lingli Chen, “Principled multilayer network embedding,” in 2017 IEEE International Conference on Data Mining Workshops (ICDMW). IEEE, 2017, pp. 134–141.

MNE:Hongming Zhang ,Liwei Qiu, Lingling Yi,and Yangqiu Song, “Scalable multiplex network embedding.,” in IJCAI, 2018, pp. 3082–3088.

GrAMME: U. S. Shanthamallu, J. J. Thiagarajan, H. Song and A. Spanias, "GrAMME: Semisupervised Learning Using Multilayered Graph Attention Models," in IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 10, pp. 3977-3988, Oct. 2020, doi: 10.1109/TNNLS.2019.2948797.]

5. Performance metrics:

The study should ensure that the metrics are not skewed by class imbalance, particularly since COVID-19 positivity is a relatively rare event. Techniques such as stratified sampling or the use of additional metrics like precision-recall curves could provide a more nuanced evaluation.

The difference in performance metrics (e.g., accuracy, AUC) between the baseline models and the proposed model, while notable, should be further analyzed to ensure statistical significance.

Reviewer #2: I will comment on three criteria for publications in PLOS Complex Systems.

https://journals.plos.org/complexsystems/s/journal-information#loc-criteria-for-publication

"High importance and broad interest to the transdisciplinary community of researchers who seek to understand complex relationships through a lens of networks, nonlinear relationships, and the use of data, and computational analysis"

This is a nice application of machine learning to an important health problem. It uses the network, machine learning, and epidemiology lenses, so I would argue that it meets the transdisciplinarity criterion of PLOS Complex Systems.

"Follow appropriate standards and practice of open science."

Yes and no. The data is not shared, but that's acceptable since health data is private and protected. However, the experimental code is not shared, and this would have been helpful to better understand the methods.

"High methodological rigor and ethical standards"

I can't say the manuscript is methodologically rigorous.

First, the description of the graph attention architecture is incomplete.

1. As described in the previous literature, graph attention transforms feature vectors, but there is conflicting information about precisely what these vectors are throughout the text. In some sections, a number of features are described: age (coded "continuously" in years--- but maybe as integers, i.e., discretly), sex, race (coded one-hot), three network features, and virus exposure. So, presumably, the feature vectors are ~10 dimensionals. Previously cited work also mentions augmentation with random features. At the same time, a later section of the paper describes the embedding dimension as being 2. Is this after the features have been projected with a linear transformation?

2. Multiple transformations are possible once the attention weights are defined. In the classical GAT architecture, the attention weights parametrize a weighted sum of feature vectors (also projected with a linear transformation), fed through a non-linearity, and only then used as the logits for a loss function. No such things are described here. But one thing is clear: The attention weights are not sufficient to reach a prediction. So, something must have been done with them in the code.

3. Minor note: the vectors "h" in the equations are not defined.

4. The number of attention heads (if any) is not described.

4. The fusion layer is not described. Is it an MLP? An average? Something else?

5. It not clear exactly what parameters is the L1 penalty regularizing. All the model parameters?

Second, constructing a network from indexed COVID cases means that the network structure itself is highly biased: We only get to sample connections in the vicinity of recorded COVID cases. This means that the findings won't generalize to the general population. The XAI results discussed at the end are thus only applicable to the specific sampled population. This also means that the model is of limited use outside of its sampling frame.

Third, there are a few methodologically confusing points

1. If I understand it correctly, Figure 2D suggests that cases are only colocated at a single outbreak site (since edges can be colored with a single label). Wouldn't it be unusual for two people who have colocated at an outbreak site never to do so again? If anything, I would expect one colocation to be a decent predictor of future colocation. And even if it were true of this particular data set, this is not a very robust data representation.

2. Relatedly: in the text, outbreak size is described as being coded as a weighted matrix. This seems like a strange data transformation to do, since the data is inherently categorical. Is something else actually done, like counting the number of colocations?

4. It is unclear to me why symmetrization is ever needed. All the network information described seems symmetric by definition: Contacts (PP) involve two individuals and are reciprocal; colocation is a projection of presence at an address/house that is also symmetrical.

5. There are no details whatsoever on the GCN architecture

6. The Levenshtein distance is a number of edits, not a fraction. Is there a form of normalization going on?

Reviewer #3: The attention network in the context of COVID-19 forecasting involves understanding how attention mechanisms, a key component in machine learning and artificial intelligence, can be leveraged to improve the accuracy and reliability of predicting the spread and impact of the virus. This paper intertwines concepts from epidemiology, data science, and computational modeling, to offer insights into how advanced techniques can enhance our ability to forecast and mitigate the effects of pandemics. In particular, the authors employ a novel graph attention network architecture merging different layers of contact networks by means of advance fusion techniques.

I agree with the authors that the integration of network science, graph neural network, and xAI is an interesting line of research, with a lot of potential and interesting research question.

Regarding the current version of the paper I see 3 major issues.

1.Premises: The current premises of the work suggests a significant gap in the academic literature. This gap is between theoretical/random network models and deep neural networks, without adequate consideration for a vast body of research that explores epidemic spread as dynamic processes on real contact networks, from [1] to [2].

2. Data. The data curated in the paper are very detailed and offer many important insights on the forecasting of COVID19. However, is not clear if these data may be available in the future, if they are good enough to be used to train a more general model. Collecting those data is expensive and a deeper analysis is necessary to assess the real potential of the dataset. Meaning either use synthetic data that mimic the same initiative or founding similar survey to test the real potential of the model.

3. Model. I found the proposed architecture interesting, but the data used are not-euclidean. This breaks some of the assumptions used in some of the models. In particular, the logistic regression asks the independence of the data, the network features though are dependent (more so, ranking metric like PageRank), at the same time a whole new branch of literature (geometric deep learning) tries to tackle the issues that CNN has with non-euclidean data. Is FGAT compliant with this type of data?

Minor question:

- In the fusion architecture you merge the 3 networks independently, how this structure would perform against an ensemble model that merge the forecasting over the three different network separately?

- Is the model robust against delay, that seems to be an important issue with this type of data?

- Line 436-441 are not super clear to me since the number of users seems 2264 (as said in the abstract).

Overall, I would suggest commenting the 3 points, and maybe reinforce some of the analysis.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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PCSY-D-24-00065R1

Critical Brokerage in Multilayer Modular Networks and Epidemic Dynamics

PLOS Complex Systems

Dear Dr. Fujimoto,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems'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 60 days Jun 20 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 complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ 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 any 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,

Anjalika Nande, Ph.D.

Academic Editor

PLOS Complex Systems

Anjalika Nande

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

Journal Requirements:

Additional Editor Comments (if provided):

Thank you for submitting the revised version of this manuscript that addresses a lot of the comments provided by the reviewers for the first submission. Particularly, all the reviewers agree that the methods are now more clearly and thoroughly explained and the review provided in Section 2 on the effect of network structure on disease dynamics is very useful in providing context and will make the manuscript accessible to a larger interdisciplinary audience. However, reviewers 1 and 4 raise valid points regarding some of the conclusions drawn from the analysis that are not supported by the results/data which still need to be addressed. Of particular note, given the sampling scheme used, it is not possible to claim that the observed relationship between node degree and infection status is a true epidemiological finding as opposed to a sampling artifact. The current framing of the manuscript does not align with this limitation of the dataset so a reframing that focuses more on the utility of this method in operational settings (for e.g., as a prediction tool) rather than as a way to unearth fundamental patterns of disease transmission may be more appropriate.

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Reviewers' Comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: (No Response)

Reviewer #3: All comments have been addressed

Reviewer #4: All comments have been addressed

Reviewer #5: (No Response)

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2. Does this manuscript meet PLOS Complex Systems's publication criteria ? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #2: Partly

Reviewer #3: Yes

Reviewer #4: Yes

Reviewer #5: Partly

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

Reviewer #2: I don't know

Reviewer #3: Yes

Reviewer #4: Yes

Reviewer #5: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data 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—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

Reviewer #5: No

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

Reviewer #5: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: The authors have addressed the clarity issues around the methodology.

* Variables are better explained, with details in the appendix

* There are more details about the GAT architecture, number of heads, hyperparameters, etc. I still cannot check the code, but it will be released on publication

* Fusion layer is described

* Regularization strategy is described

* More robust description of co-location data

* Weighted coding explained

* Matrix normalization is clarified

* GCN was described.

Unfortunatly, the biggest issue with the manuscript, which had motivated my initial recommendation, is still present. (And it would be hard to work around, given the data): The sampling design.

A network sampled via tests can introduce enormous biases, invalidating all attempts at generalizing and leading to the conclusion that "Number of contacts increases risk." This might well be true, but the present dataset cannot support it.

A simple simulation should show why.

1. Create a random social network, and simulate a spreading process on that network.

2. Then, pick nodes at random and trace around them (in doing so, pick some uninfected nodes as sources, simulating tracing around negative tests).

3. Register all the edges seen in this way as "traced edges".

4. Create the subgraph induced by traced edges and compute the average degree of COVID-positive and -negative nodes.

The average degree will be higher for positive cases as long as we're more likely to pick traces around infected nodes than uninfected ones.

This effect is robust. You'll see similar results in iterated tracing (following the contacts of contacts) and for a wide range of network structures. A decent machine learning model will, in turn, pick up on this feature and very easily classify nodes as negative or positive based mainly on the degree. This is precisely what the results show, with degree being the most important feature.

Hence, my claim is that the results are an artifact of sampling, not a fact about COVID-19 in Houston, let alone a generalizable fact about infectious disease. (Again, it's probably true, for example, that a higher degree leads to more infections, but this specific dataset cannot show it. One would need a uniform sample of the contact network.)

As a prediction algorithm, the novel GAT architecture is an interesting exercise.

One might even imagine using it in situation where lots of data are available and what matters is a prediction, not a scientific understanding of contagions.

For example, it could be used to help contact tracing efforts.

That's unfortunately not how the methods and results are presented here.

(On a side note, I'm also worried that confounding effects might show up in the analysis. For example, the degree should be correlated with being present at big outbreak sites like schools since tracing asks about the number of close contacts in the past 24-48 hours, and being at a school increases that number. But this is just one example. Age group will correlate with presence in assisted living. The size of the household might correlate with age, etc. Things like this make generalization fraught.)

Some typos found while re-reading:

===========================

Figure 1

* Some dotted links go nowhere

* While I get the concepts, I think there are errors versus what is explained. Line 279 says that Person Xa attends a school (so far, so good) but also has friends. But there is no cross-layer ties for that same person. The red box connects person Xa to Xc in the personal contact network. Are they the same person? I.e. is "X" the person and "a" the layer? Probably. It is not clear since a different label is used for the three layers.

Figure 2

* Modell -> Model

Garbled text lines 623-626

668 nhidl -> n_{hidl}

Table 4: Isn't the Delong test defined only for AUC and PRAUC? What test was used for Accuracy and F1?

Reviewer #3: The authors comprehensively addressed the feedback provided by the reviewers, enhancing the clarity of the paper contribution and fortifying the analytical framework.

Reviewer #4: See attached.

Reviewer #5: The review is structured in the way to directly address the journal publication criteria. Each criterion is divided into major/minor comments and suggestions.

“ High importance and broad interest to the interdisciplinary community of researchers…”

The current manuscript presents a highly interdisciplinary framework that bridges sociological concepts of brokerage roles, epidemiology, network science and machine learning. The multilayer modular network for epidemiological purposes is a novelty and is of interest for both theoreticians and experimentalists. The use and results of XAI is a methodology that has the potential to interest a broad community focused on mechanistic modeling.

“Originality”

• As already underlined above, the work in this manuscript is definitely original. Beyond the machine learning analysis that is insightful, the very structure of the presented multilayer modular networks is strongly original and has the potential to inspire the network epidemiology community.

• Major comment: However, the novelty of this multilayer modular network must be discussed in regards of other recent works involving multilayer modular networks in the context of disease spreading. In particular, the manuscript should discuss the work of Fügenschuh  and Fu 2023 (https://link.springer.com/article/10.1007/s41109-023-00595-y) and Ma and Wang 2025 (https://www.sciencedirect.com/science/article/pii/S0375960124008934)

• High methodological rigor and ethical standards and substantial evidence for conclusion

Assumption and presentation on the data are clearly set.

• Major comment:

• The discussion from line 937 to line 949 draws conclusion that are not supported by the results and therefore must be amended. Actually the narrative of the discussion focuses on the the prediction value of the network metrics that can be associated with brokerage roles in opposition to demographics factors. However, the interaction between infected coresidents and education center (ranked 9th in Figure 6 – mistake in the current manuscript that indicates ranked 8th) is less predictive than Sex (ranked 8th in Figure 6). From these results, we can also draw the conclusion that Sex,as a demographic factor, has more predictive value that this considered cross-layer boundary spanners component. In conclusion, the claim “structural network-level dynamics contribute more to the prediction of COVID-19 positivity [compared to demographic factor]” must be nuanced based on this consideration.

• The claim on a potential “dilution effect” between line 943-946 must be at least discussed and/or precised with references. Actually, based on the given definition of contacts of HHD( more than 15 minutes at 6 feet) as well as epidemiology and biology, the more exposed to respiratory diseases, the more chance to be infected, the contrary of a potential “dilution effect”. Furthermore, the claim is based on the rank of the metrics in prediction for classification and not on the direction of the correlation (positive and negative). Therefore, only comparison between predictors can be made.

• More broadly, the discussion lacks an a priori criterion threshold that distinguishes the ranks/scores of the explanatory features that really matters from the ones that are more negligible. Since the study has already been performed, this point should be kept in mind for future work and the structure of the current manuscript should not be changed provided that the previous points are addressed.

• Minor comments: In Sec 5.2 on descriptive statistics, the manuscript presents a significant difference between the HH degree of infected and non-infected individuals. It tends to show that infected people tend to have a higher HH degree. However, a negative correlation is obtained in the case of the logistic regression model. Could you discuss this apparent contradiction ?

• PP and HH networks are very sparse as presented in the Descriptive Statistics meaning that probably a significant portion of individuals have HH and/or PP degree of zero or 1. Could you provide in the supplementary, the HH and PP degree distribution for infected and non-infected individuals and potentially the HH+PP overlapping degree one ? This would help visualizing the empirical network and potentially supports the results in case of particular distributions.

• Also, to enrich the claim on the high rank of affiliation to education center and integrate these results in a broader literature, it could be put in perspective with studies evaluating the impact of school closure( https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(22)00138-4/fulltext)

• In line 921, the rank is 5th and not 9th.

• In line 110, closure is mentioned but never used in the study.

“Clearly outlined utility and accessibility for the broader community”

The current version of the manuscript provides a significant effort to bridge different communities (e.g. sociology and network science), in particular in Sec.2, Sec.3 and in the discussion. This effort is greatly appreciated.

• Minor comment: Table 1, the test to assess significant difference needs to be named.

◦ Line 796: “indicate that one model consistently performs…”, assess which one for readability.

◦ Line 178: put (23) instead of Friedman et al. to stay consistent with the reference system.

◦ Line 624-625: Sentence “including...level” should be removed.

• Major suggestion: Since it is a interdisciplinary journal, the first figure is of the utmost importance to carry the main concept to the broad readership. Here Fig.1 does not follow the broadly used convention in the representation of multiplex network. This can lead to misinterpretation of the nature of the representation at stake and ultimately to make the article less accessible. https://arxiv.org/pdf/2401.04589 (Fig4 for example) for how to represent your structure. Also, the global readability of Fig1 could be enhanced by passing most of the details (about person Xa,Xb,Xc) in Sec3.2 into its caption.

• For the sake of readability, make sure that the data structure is associated with the term network and the term graph for the AI structure (ex line 622,664,683).

• Minor suggestion: In the Sec.2.3, I miss a reference from the work of Gross and Havlin (https://appliednetsci.springeropen.com/articles/10.1007/s41109-020-00337-4). Adding such reference can help rallying theoretical network scientist around your work.

Provided the major and minor comments are correctly adressed, the manuscript could be deemed suitable for publication. Althought suggestions could improve the general quality of the manuscript, it is left to the Authors to adress them or not.

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7. 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.

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Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

Reviewer #5: No

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Attachments

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Submitted filename: Review.pdf

Multilayer Modular Fusion Graph Attention Networks (MMF-GAT) for Epidemic Prediction

PCSY-D-24-00065R2

Dear Dr. Fujimoto,

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.

Within one week, you'll receive an e-mail detailing the required amendments. When these have been addressed, you'll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Anjalika Nande, Ph.D.

Academic Editor

PLOS Complex Systems

Additional Editor Comments (optional):

All the reviewers are now happy with the manuscript and recommend it for publication. Please also address the few minor comments/typos noted by Reviewers 2 & 5 in the final submission.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

Reviewer #4: All comments have been addressed

Reviewer #5: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria ? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #2: Yes

Reviewer #4: Yes

Reviewer #5: Yes

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

Reviewer #2: I don't know

Reviewer #4: Yes

Reviewer #5: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data 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—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #4: Yes

Reviewer #5: No

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5. Is the manuscript presented in an intelligible fashion and written in standard English?<br/><br/>PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #4: Yes

Reviewer #5: Yes

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6. Review Comments to the Author<br/><br/>Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: The manuscript now acknowledges the limitation of the sampling design and avoids making broad generalizations.

It meets the standard for publication in PLOS Complex Systems.

All minor comments have been addressed.

Some additional typos:

- line 214 "My first contribution" should presumably be "Our first contribution" given that there are 9 authors

- line 319 "persona network"

- line 758 "retention center"

Reviewer #4: All my comments have been sufficiently addressed.

Reviewer #5: The authors thoroughly addressed my concerns and comments. The interdisciplinary aspects of the current manuscript is reinforced by:

- the integration of the study in a multidisciplinary literature (sociology, network science). The Part 3.6.1 on the tensorial formalism is of great use in setting the multidisciplinary readership on the same standard ground.

- the Figure 1 is now standard in regards of the multilayer network visualization norms and help to understand at glance the multilayer framework used in the study.

In terms of methods, the network analysis in the supplementary material would help the interested reader to understand the sparsity of the networks.

The conclusion centered on MMF-GAT as a public health tool and limitations are now aligned with the results.

Minor comments:

Line 214. “My” should be changed by “We” or “The”

Line 214-215. The phrasing is misleading as it suggests the study provide a “tensorial formalism” that is already pre-existing (cf part 3.6.1 of the article).

Line 509-513. The claim that the MMF-GAT could target allocations of testing resources during outbreak is in contradiction with the fact that computational requirements limit the use of real-time data. I believe the Authors shoudl reframe it as a perspective.

Supplementary – The axes legends are too small.

I believe that the current manuscript is now aligned with the scope of the journal and I am therefore happy to recommend publication. Congratulations to the authors for their work.

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Reviewer #2: No

Reviewer #4: No

Reviewer #5: No

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