PONE-D-20-38775

The Social Cost of Contacts:

Theory and Evidence for the first wave of the COVID-19 Pandemic in

Germany

PLOS ONE

Dear Dr. Quaas,

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We look forward to receiving your revised manuscript.

Kind regards,

Martial L Ndeffo Mbah, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments:

There are several points that needs to clarify to improve transparency, readability, and enable an in depth assessment of the results. More details can be found within Reviewer 1 comments. Similar concerns are raised by Reviewer 3. Addressing these issue should greatly improve the quality of the manuscript and make it suitable for publication.

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grant number 01LC1826E."

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data 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 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: Yes

Reviewer #3: Yes

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

PLOS ONE 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: No

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5. 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 #1: This work concerns the epidemic SIR model, which poses social distancing for the COVID 19 pandemic in Germany. Authors try to find the gap between private and social cost of contact theoretically and verify it by using survey data. Although the work seems to contain some meaningful content from a theoretical and application point of view, I believe that several extra details should be introduced before considering the possibility of publishing this manuscript. Below I detail these concerns:

I think it will be significant if authors read and cite the newly established concept of the social efficiency deficit (SED). In the indicator SED, one can easily show the gap between social optimum and Nash equilibrium. They should read and introduce the idea of SED to show the gap (SED). It would be very interesting if the author can suggest how it will minimize this gap. Refer to the following kinds of literature to introduce the idea of dilemma strength,

Kabir, K. A., Tanimoto, J.; The role of advanced and late provisions in a co-evolutionary epidemic game model for assessing the social triple-dilemma aspect, JTB, 503, 110399 (2020).

Arefin, M.R., Kabir, K. M. A., Jusup, M., Ito, H., Tanimoto, J.; Social efficiency deficit deciphers social dilemmas, scientific reports, 10, 16092 (2020).

Kabir, KM. A., Tanimoto, J.; Modeling and analyzing the coexistence of dual dilemmas in the proactive vaccination game and retroactive treatment game in epidemic viral dynamics, Proc. R. Soc. A 475: 20190484 (2019).

The current form of all figures is unclear (axes and legends) and it is very difficult to understand the key point of your figures. I would like to ask you to redraw the figures with more details and give the details explanation in figure captions.

In the abstract, “Altruistic motives substantially increase individual protection efforts, but a substantial gap to the social optimum remains.”. This sentence seems to be very interesting and important to me. But I could not find a precise explanation for this, specifically in the result or conclusion section. Why this gap remains??

Reviewer #2: This model examines an SIR epidemic model of a population composed of multiple demographic groups, e.g. differentiation of age and gender, and dynamic social distancing strategies. The main goal of the analysis is to compare resulting societal welfare performance when distancing strategies are derived from a centralized social planner, versus decentralized selfish players. The model is quite complex with many parameters. The authors have gathered survey data from Germany in order to estimate and calibrate these parameters. The paper stipulates that selfish distancing behavior can stabilize the epidemic, but at a much higher infection cost than the optimal centralized policy. The presence of imperfectly altruistic individuals results in a balance between these two scenarios.

I find the paper is well written and precise. The derived conclusions are quite interesting. The mathematical model seems complex but is still numerically amenable with classic algorithms (dynamic programming). Hence, the model is quite valuable for offering predictions/insights for other scenarios that have not been as successful in containing COVID-19. For example in the U.S., where the rates are much higher than Germany, would the qualitative conclusions made in the paper still hold?

Regarding some technical aspects, it was not clear how the selfish and the semi-altruistic Nash equilibrium is computed. Also, it was not mentioned that there exists a unique equilibrium in both cases. If there are multiple Nash, then one would have to perform worst-case analysis, e.g. by calculating the price of anarchy.

It was also not clear how the the welfare function (eqn. 9) performs at the various Nash equilibria. The main figures 3 and 4 only show the effect on infection levels and contact levels. What would be interesting to see, which is not shown here, is the welfare as imperfect altruism ranges from completely selfish to completely altruistic. Is it obvious that this will be monotonically increasing? Surprising results can be found in other contexts, for example in congestion games:

Caragiannis, Ioannis, et al. "The impact of altruism on the efficiency of atomic congestion games." International Symposium on Trustworthy Global Computing. Springer, Berlin, Heidelberg, 2010.

Reviewer #3: Authors have computed utility functions of being socially distant considering individual vs. social cost using a discrete epidemiological model. They characterize the disparity in the Nash equilibrium and social optimum by quantifying it using Germany survey data on social distancing during COVID. The research is certainly valuable, important, timely and bears journal compatibility. However, I have preservation in presentation of the material in the draft. So, before it goes to publication house, I would like following things to be cleared. These are as follows pointwise:

1. The introduction is way more than expected by the reader. For example, authors have devoted approx. more than one and half page to portray how their work adds value compare to others. Reading these, it may loose some focus in the beginning of a draft. I would say shorten the introduction at least one page. Maybe some information to put in 'discussion' para.

2. The derivation of utility functions (2) - (6) should be explained in parts, better in appendix. Can authors use this reference to compare how they got or arrived those equations: Math Biosci. 2011 Apr; 230(2): 67–78. A general approach for population games with application to vaccination by Timothy Reluga and Alison P. Galvani. This is much more important to increase the audience of the paper.

3. Similarly, it is not clear how authors got the equations (10a-10f). Need more explanations and proper derivations.

4. How they got equation (12)?

5. Can author gives an justification why Bernoulli utility suits here in this epidemiological framework?

6. Parameter Estimation or calibration method is not clear from the text! Did they use some kind of MLE technique?

7. Neither clear how they arrived equation (18) and (19).

So, I mainly observe that paper lacks certain explanations, and derivations of mathematical equations. I encourage authors to revise the paper accordingly, and resubmit.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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The Social Cost of Contacts:

Theory and Evidence for the first wave of the COVID-19 Pandemic in

Germany

PONE-D-20-38775R1

Dear Dr. Quaas,

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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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Martial L Ndeffo Mbah, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

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 #1: (No Response)

Reviewer #3: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #3: Yes

**********

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

Reviewer #1: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data 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 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 #3: Yes

**********

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

PLOS ONE 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 #3: Yes

**********

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 #1: (No Response)

Reviewer #3: The paper looks good now with improved comments and additions. Authors have considered all comments and improved their paper. It is now acceptable for journal publication.

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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.

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 #3: Yes: SAMIT BHATTACHARYYA