Dear Mrs. Bouman,

Thank you very much for submitting your manuscript "Bayesian workflow for time-varying transmission in stratified compartmental infectious disease transmission models" 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.

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).

Important additional instructions are given below your reviewer comments.

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,

Samuel V. Scarpino

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: # Review PLOS-CB

In their manuscript, Bouman and coauthors present a Bayesian workflow to infer time-varying parameters in stratified compartmental models. They identify four key features within this framework that need to account for i) incomplete case ascertain (a.k.a., case underreporting), ii) adequate sampling for lab-confirmed cases, iii) flexible implementation of the time-varying transmission rate, and iv) age structure. They explore different models for each and variations of the parameters thereof and validate the workflow using both synthetic and real-world data (first two COVID-19 waves in the canton of Geneva, CH). They conclude that the best-performing methods (for the disease considered and dataset quality) are quasi-poisson for sampling and BSplines for the time-varying transmission rate.

Besides providing valuable insights from the dataset they analyze (which, although regional, is novel), the article is very educational and open with the methodologies applied -- the kind of paper one would give their students to explore a new method. While I am a big fan of such papers, we have some reservations (which we list below) on the generality of the approach proposed.

## Major

1. On the generalizability of the proposed approach. While the paper, title and abstract are presented and discussed in a general way, the choice of a SEIR model (and other points listed below) are already assumptions strong enough to constrain its applicability considerably. This goes beyond the choice of parameters, which could help us translate from very similar diseases or variants thereof; it's about mechanisms. Other common respiratory viruses, as e.g. the respiratory Syncytial virus, have markedly different dynamics and thus require markedly different structures (e.g., an SIS model in cascade like that of Zheng and coauthors in JAMA Open 2021). Here, incidence and seroprevalence would have to be re-defined in terms of the new compartments and the timescales involved considered when choosing which functions to use to match the data. Some non-pharmaceutical interventions require extra compartments, and testing could also be thought of as an intervention that reduces transmissibility (as test-trace-quarantine). Vaccination and pharmaceutical interventions might not be relevant when analyzing historic 2020 COVID-19 data, but they should be when analyzing influenza. That being said, the methodology is presented in a way that is general enough to be easily adapted to account for the points I mentioned before -- please expand the methods on how to adapt the workflow to other diseases (i.e., other compartments and transition rules) and rephrase where applicable, acknowledging that the current results for real-world and synthetic data are COVID-specific. Besides, how flexible and intuitive is the R implementation of HETTMO to compartments and mechanisms? [as we are not fluent R users, we couldn't check this point ourselves]

2. On the model's structure and equations to match to observables. The SEIR engine used for simulation and inference is a strong assumption; it says that the disease that spreads is very COVID-19-like. This is not only because of the similarity with the typical disease stages of COVID (well, neglecting asymptomatic individuals), but also because of the way that seroprevalence and incidence are modelled. Defining the cumulative incidence through the compartment $R(t)$ disregards the individuals that are still in the infectious compartment but have been already tested. This works here because of the short infectious period of COVID (and the much lower estimate the authors use for $1/\\gamma$) and the smoothing induced by real-world seroprevalence studies. Furthermore, defining the modelled incidence as the difference between the recovered from one point to the other disregards the newly reported cases, which again average out with the weekly resolution of the data the authors use. While these are valid modelling choices for a COVID-19-like disease, they can be wrong assumptions for other diseases. I recommend expanding the discussions in this regard so that readers are aware of other modelling choices and possibilities.

3. On the selection of parameters. Not to be repetitive with the issue of COVID-19-like parameters (the authors do a good job discussing this in the paper), the definition of parameters in Table S6 is wrong or flipped; $\\tau$ should be the latent period, i.e., from infection to before turning infectious, and be the residence time in E. [side note, as $\\tau$ is typically thought to as with time units, defining it as a rate can be a bit unexpected for some readers and reviewers]. $\\gamma$ is typically the recovery rate, and its inverse is the days that it takes to recover (8--10)? If simulating COVID, the parameters we had in mind were $\\tau$ closer to 4--5 days, and $1/\\gamma - \\tau \\approx 4-8$ days. The definitions are inaccurate on line 78, as $\\tau$ (or its inverse) should be _the latent period_ of the disease. Also note that parameters for the contact matrix might not be available nor represent regional differences, and the mechanisms that cause the quasi-Poisson sampling to be the best might be different in other regions or when analyzing other diseases.

4. On the error function and applicability of the methodology to emerging diseases. In lines 216 and 217, it states that the model fit was performed by computing the RMSE between real and estimated values for the transmission rate $\\rho(t)$. But there can be a catch with this, which is also noted in lines 307 and 308: larger deviations occur when the number of cases is low. If that is the case, then small perturbations to the number of tests will have a drastic effect on the trends of $\\rho$, which will turn erratic. As RMSE is agnostic to the time of the measurements, deviations from these noisy measurements will weigh the same as real errors in times of high case numbers (which should be considered more reliable). For the simulated dataset, where transitions are smooth, and for the data analyzed (where high case numbers and the weekly accumulation of cases do the smoothing part) it is not a problem in general. However, how could this be accounted for in the proposed framework? Perhaps through the introduction of weights or by having a different "goal" variable?

5. On short-term forecasts and real-time surveillance data analysis. Although mentioned, the predictive power of the models is not explored. The authors mention that these models that yield results with increasing variance over time are preferred, but this could be assessed with a leave-future-out analysis of the dataset (not necessary in this case, as it is not the point of the manuscript -- but should be mentioned). However, it is not clear to us how to use this approach in real time to estimate $\\pi_t$; is it necessary to define periods of constant $\\pi$? How do we decide how many of these we need for a new dataset? How much time should we let pass before estimating $\\pi$? Discussing these questions could enlighten readers trying to analyze their datasets in the future.

## Minor

1. Figure and equations do not include stratification

2. Perhaps a demographic-inspired partition of the 18--24 would represent a general case better?

3. The author's summary could be less technical and streamlined towards the methodological/educational approach of the paper.

4. (line 10) COVID-19 pandemic instead of SARS-CoV-2 pandemic? as SARS-CoV-2 was the pathogen causing the pandemic disease.

5. About the HET en HETTMO; We are a bit skeptical about how much heterogeneity is captured here, as the core approach remains mean-field.

6. It is probably a good idea to make the color of the y-axis similar to the line color when using double y-axis (e.g.- Figure 2, the y-axis on the left side will make easier for understand that this axis is for the green line and Grey on the right y-axis for Grey line in the figure)

Reviewer #2: Review is uploaded as an attachment.

**********

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

**********

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

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

Attachments

Attachment

Submitted filename: PCB_Bouman2023.pdf

Dear Mrs. Bouman,

Thank you very much for submitting your manuscript "Bayesian workflow for time-varying transmission in stratified compartmental infectious disease transmission models" 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.

Reviewer 3 has made some suggestions for further clarifications to the approach and motivation for the Bayesian workflow as well as some of the supplementary figures. Reviewer 2 has suggested illustrating the approach using a second dataset on another disease, which may be beyond the scope of the current manuscript, but nevertheless the authors should consider whether this is feasible.

Finally, the Editors feel the manuscript is more appropriately designated as a "Methods" paper rather than a "Benchmarking" paper, since Benchmarking papers have additional requirements that have not been fully met (see https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1006494). If the authors agree to this change, the journal staff should be able ensure it receives the appropriate article type designation.

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,

Samuel V. Scarpino

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:

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 the consideration of our suggestions. We are satisfied with the revisions and have no further observations.

Reviewer #2: I appreciate the fact that the authors responded to comments and further explained their reasoning. However, I still think the authors should potentially perform a second analysis using their R package on a different set of COVID-19 data to further show the robustness of their analytical approach.

Reviewer #3: The authors have provided a careful example of a Bayesian workflow for a complex infectious disease modeling task. That is to say, they have presented a fitted model for a particular data set along with an iterative search of models, some of which may be applicable to related models for other data sets. I think this is a great way to go about presenting modeling results.

The authors seem to have adequately addressed the concerns raised by the initial reviewers. My own suggestion would be for them to further explain what they mean by a Bayesian workflow, as the terms seems relatively uncommon at present. What are they benefits to this approach in general and can they explain some implications of their findings in creating the workflow, such as the relative efficiency of the different ODE solvers and time-varying functions?

A minor correction the authors should make is to provide explanations for the weighed error column in S1 Fig and S2 Fig.

**********

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

Reviewer #3: Yes

**********

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

Reviewer #2: No

Reviewer #3: 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 Mrs. Bouman,

We are pleased to inform you that your manuscript 'Bayesian workflow for time-varying transmission in stratified compartmental infectious disease transmission models' 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,

Samuel V. Scarpino

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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