Dear Dr. Ma,

Thank you very much for submitting your manuscript "The Optimal Spatially-Dependent Control Measures to Effectively and Economically Eliminate Emerging Infectious Diseases" 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.

Note that all three reviewers felt the manuscript needed to do a better job of citing the relevant literature and putting the research in context of recent advances in terms of data-driven metapopulation modeling and the impact of interventions during the COVID-19 pandemic. Some of the modeling assumptions also require better support. Please pay particular attention to addressing Reviewer 3's concerns, as we may not be able to accepted the revised manuscript if these concerns are not sufficiently addressed.

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,

Virginia E. Pitzer, Sc.D.

Section Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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Note that all three reviewers felt the manuscript needed to do a better job of citing the relevant literature and putting the research in context of recent advances in terms of data-driven metapopulation modeling and the impact of interventions during the COVID-19 pandemic. Some of the modeling assumptions also require better support. Please pay particular attention to addressing Reviewer 3's concerns, as we may not be able to accepted the revised manuscript if these concerns are not sufficiently addressed.

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: The paper exhibits commendable writing, delves into an intriguing topic, and demonstrates sound analytical and numerical analyses, rendering the work acceptable. However, I would like to offer some recommendations for improvement. My comments are outlined below:

1. The Introduction and Literature Review sections require a more detailed rewrite. The introduction should furnish a comprehensive summary of relevant prior works, with explicit references pinpointing the gaps in the existing literature.

2. The authors are advised to reconsider or redesign Figures 2 to 6. The red background in each figure appears aesthetically unpleasing and may hinder comprehension. A modification or redraw addressing the visual aspect would enhance the overall clarity of the figures.

To improve, authors can follow the following works.

Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology, Vaccines, 11(9) (2023).

Impact of awareness in metapopulation epidemic model to suppress the infected individuals for different graphs, European Physical Journal B, 92, 199 (2019).

Evolutionary vaccination game approach in metapopulation migration model with information spreading on different graphs, Chaos, Solitons & Fractals 120, 41-55, (2019).

Reviewer #2: The study delves into optimizing the control measures for the Covid-19 Delta variant specifically within Xi’an City. It constructs a compartmental model that also incorporates the geographical distribution of the population. This model is then utilized within an optimal control framework to discern the ideal timing for implementing interventions. Given the dearth of models that integrate both the epidemic and its economic ramifications, this paper contributes to filling the gap. The model is quite complex but well formulated.

The Bayesian parameter estimation model entails the fitting of numerous parameters. A more extensive discussion regarding this process, along with an assessment of the outcomes in relation to existing models or literature, would enhance the comprehensiveness of the paper. While some parameters may not directly correlate with the specific context, it is still worthwhile to explore any relevant comparisons.

The authors acknowledge that the economic costs portrayed in the model are somewhat high-level. Given that this aspect constitutes a significant component of the paper's objectives, providing additional details on the sources of these costs, their units, and any adjustments made would be beneficial. What would be the implications of accounting for costs associated with hospitalisation and deaths?

Minor comments

Several figures could benefit from refinement to enhance clarity and ease of interpretation. For example:

• While most journal readers will likely be able to interpret chunks of the Figure 1 diagram, some may be difficult to interpret without more information, especially as the model is only described later. For example, a few of the states are not easy to interpret without finding where the main text refers to them. I suggest adding sufficient information to understand the diagram. Perhaps moving the diagram down to the model section also helps.

• Figure 5 C3 is difficult to interpret in places. Moving the legends, perhaps to the side or bottom, or adding a white background to the legend could be helpful.

• Fig 6 has a lot going on. Perhaps the figure can be simplified for quicker interpretation. For example, 6A could be separated into multiple pots. Perhaps there’s a clearer way to convey the message about R0, GDP and optimal control cost moving together.

Reviewer #3: This manuscript is about optimal and timely spatial deployment of non-pharmaceutical interventions (NPIs) at the early stages of an outbreak of an infectious disease to prevent it from establishing. The paper would be of great relevance four years ago, but the novelty at this point in time is questionable.

The paper is solid and, as far I as I can tell without access to the code and data, is technically sound.

However, I do not think this paper is suitable for PLOS Comp Bio for several reasons: 1) it is written for a technical audience and not put in a larger applicable context, 2) it covers a very narrow literature, ignoring vast areas of applications in epidemic modelling and 3) therefore missing the novelty and the relevance. What makes a disease easily controllable (Fraser et al Science), relevance of commuters for spreading influenza in the US (Viboud et al, Science), reducing contact rates as an intervention (papers like Prem et al that do that by using contact data) are all seminal papers in the field that would provide relevant context for this work, relate it to a broader set of data and applications, and clarify what exactly this paper adds in terms of novelty.

Authors make a lot of assumptions on flows between patches which are scaled by GDP and distance. The following sentence has a reference to Balcan et al 2009, but these authors use mobility data to capture the flows in their multiscale mobility networks, rather than distance and GDP. There is a vast amount of literature on flows between patches (from mobility data (e.g. cellphone data, and airline traffic data, google mobility), census data (e.g. using postcodes of home and workplaces to infer flows), traffic, work place data) so it is surprising not to see any reflection on that literature in the manuscript and link it with the assumptions about the flows here. Referring to a study that analyses suitability of using GDP in scaling of gravity models would be one way to clarify this.

There are several instances of inappropriate referencing of claims in the paper, for example, citing newspaper article (ref [21]) to support effectiveness of a strategy rather than peer-reviewed analysis of effectiveness of a strategy). “Since contact tracing is only effective if the outbreak is detected early before widespread community transmission [21], ([21] People’s Daily Online. Interpretation of the new policy of epidemic prevention in Shanghai; 2022. Available from: http://health.people.com.cn/n1/2022/0319/c14739-32378995.html.) Instead, the validity of this statement should be supported by a published peer-reviewed paper or shown with own work presented in this manuscript.

There are several technical issues that need clarifying/justifying, for example:

a) lockdown is assumed to have different impact in different locations – is this modelling adherence/ compliance/ or that different locations have different proportions of e.g. keyworkers whose work and commute patterns will be different form non-key workforce? Please elaborate this.

b) Contact trancing is inherently an individual-based process and not straightforward to capture in population-level, compartmental models. Why is a logistic decay function a suitable one for modelling rates of isolation of exposed and infectious individuals? The only reference in this paragraph (lines 147-153) is a newspaper article, which I doubt will inspire readers of Plos Comp Bio with confidence.

c) Whole sections of paper (e.g. Estimation section, Optimal control section) have no references to other literature (e.g. MCMCs, Bayesian inference, modelling over-dispersion, defining a cost function and specifying an optimal control problem, using methods for minimising the cost or utility function should all refer to the relevant literature).

For all of these reasons I think this manuscript is not of sufficient novelty and interest to PLOS Comp Bio audience but I look forward to seeing it published in a specialised, technical journal.

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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: None

Reviewer #3: No: The authors say this will be made available should the paper be accepted, but as far as I am aware it hasn't been made available to reviewers. Or it is not easily accessible.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Dear Dr. Ma,

We are pleased to inform you that your manuscript 'The Optimal Spatially-Dependent Control Measures to Effectively and Economically Eliminate Emerging Infectious Diseases' 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,

Feng Fu

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: Thank you for your efforts.

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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

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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: No