Assessing the risk of vaccine-driven virulence evolution in SARS-CoV-2

The evolution of SARS-CoV-2 virulence, or lethality, threatens to exacerbate the burden of COVID-19 on society. How might COVID-19 vaccines alter selection for increased SARS-CoV-2 virulence? Framing current evidence surrounding SARS-CoV-2 biology and COVID-19 vaccines in the context of evolutionary theory indicates that prospects for virulence evolution remain uncertain. However, differential effects of vaccinal immunity on transmission and disease severity between respiratory compartments could select for increased virulence. To bound expectations for this outcome, we analyse an evo-epidemiological model. Synthesizing model predictions with vaccine efficacy data, we conclude that while vaccine-driven virulence remains a theoretical possibility, the risk is low if vaccines provide sustained robust protection against infection. Furthermore, we found that any increases in transmission concomitant with increases in virulence would be unlikely to threaten prospects for herd immunity in a highly immunized population. Given that virulence evolution would nevertheless impact unvaccinated individuals and populations with low vaccination rates, it is important to achieve high vaccination rates worldwide and ensure that vaccinal immunity provides robust protection against both infection and disease, potentially through the use of booster doses.


Recommendation? Major revision is needed (please make suggestions in comments)
Comments to the Author(s) I enjoyed reading Miller and Metcalf's manuscript on assessing the risk of virulence evolution in SARS-CoV-2 as a response to vaccination. It is well written overall, and shows a clear understanding of virulence evolution theory. Given the timeliness of the topic, there is a need for more theory papers addressing evolutionary trajectories of SARS-CoV-2, particularly in light of growing evidence that our most common vaccines are, in fact, more "leaky" than hoped. I enjoyed the attention to detail of the two regions of infection that are linked to transmission (URT) and severe disease (LRT) and appreciate the inclusion of this without having to overly complicate the model. While the methods are sound overall and the model is simple enough to answer the question, the manuscript is considerably outdated in various ways. I understand covid research moves very quickly but any paper to be posted as a preprint this summer and published this fall should include more recent examples, data, and discussion of the most important VOCs currently under investigation.
There are a couple glaring omissions: 1) There is a lack of references to recent papers on SARS-CoV-2 evolution theory or commentaries by important evolutionary biologists in this subfield. Namely: Day et al. 2021 Current Biology, Otto et al. 2021 Current Biology, and in particular Alizon and Sofonea 2021 J. Evo.Bio. As indicated below, there are several places where these (and some of their citations within) should be cited and the authors results be discussed in the context of these works (e.g. in the discussion section). 2) The Delta variant needs to be included. I understand that this manuscript may have been written at a time before Delta had emerged but unfortunately, this variant is too important evolutionarily to omit. It has both increases in transmission and virulence (e.g. Fisman and Tueite 2021 medrxiv) and reductions in vaccine efficacy. The authors consider cases where the optimum virulence is either intermediate between the ancestral strain and B.1.1.7 or greater than B.1.1.7, however, given how delta is sweeping in various geographical regions, it's pretty clear now that the case where the optimum is below B.1.1.7's virulence is not likely. The question in everyone's mind is, how high can virulence get? Please run the model calibrated for the delta variant's parameters (as those done for B.1.1.7 in lines 495-516) and change figures 3 and 4 to include only B.1.1.7, delta and a hypothetical "more virulent than delta" variant, given that the alpha_optim = 1.25*alpha_ansc case is no longer relevant.
Other comments Fig. 1: The first figure should be a schematic of the transmission-virulence trade-off, particularly showing the different shapes it might have. The section "theory of virulence evolution' is nicely written but it's confusing to use a results image as an illustrative image of the concept (e.g. the unknown parameters and how they are related is confusing given the equations/model have not been presented yet). A schematic of the trade-off could be added as the first panel to Fig.1 or have a new stand-alone figure in the introduction.
Paragraph ending in line 120: Delta needs to be added here.
Paragraph starting in line 121: please cite and discuss previous published works mentioned number 1 above.
Line 132: this decoupling of death from the trade-off has been discussed in the worked mentioned in number 1, please cite.
Paragraph starting on line 285: please include real-world data here not just the vaccine trails, since we now have estimates for these in global populations.
A direct analysis of vaccine leakiness (how much infectious viral shedding per vaccinated host) and its potential to drive virulence evolution would require a nested model approach, which is, understandably, beyond the scope of this study. However, given parallels of our current vaccine situation with that of Marek's Disease virus (which the authors briefly mention), the most studied example of vaccine-driven virulence evolution, it would be of use to the reader to understand the authors' results in context of this example (e.g. Read et al. 2015 Plos Biology). Please include this in the discussion section.
Points relating to herd immunity: Vaccine-induced herd immunity is an import part of the results of this paper and given that reaching HIT (herd-immunity threshold) is a moving target for SARS-CoV-2 (e.g. Hodgson et al. 2021 Eurosurveillance), here are some specific points to address about herd immunity.
The underlying R0 of a virus really affects the needed level of coverage to reach HIT and delta has changed this. How does the authors' results of their scenarios in Fig. 4, such as "how likely herd immunity without virulence evolution", change when considering the delta variant?
Line 306: "... 3) existing vaccines …" this is still theoretically true but please cite/add any caveats that have been debated in the modelling literature. For example, the vaccines don't reduce transmission as much as we hoped (especially with &lt; 2 doses and for delta) and the projections for vaccine coverages needed for reaching herd immunity are changing (e.g. Mancuso, Eikenberry and Gumel 2021 medrxiv).
In figures 3 and 4, the 10% vaccinated coverage panels are there for completeness but are not really what we are aiming for globally. It would make more sense to just present two columns of 50 and 90 or have a gradation from 50 to 100%. assume 25% of individuals are already in the C class). At least this is my interpretation of what they are doing. The analysis section is very limited in its explanation. What I believe the authors are doing, is using R_E as a proxy for fitness. R_E acts as the growth rate of a strain (unique alpha) in a population that is smaller than the disease free population. The adaptive dynamics approach works by "competing" strains against one another by calculating invasion fitness. By using R_E, the authors ignore competing existing strains in the population. They then compare the growth rate of a standard B117 strain to that of a different strain (with a different alpha). The issue is, the population is not totally naïve, since 25% have already been infected and are sitting in the C class. This suggests there should be a significant number of infectious individuals in the population, with the B117 infection. Therefore the growth rate of the B117 strain and the novel strain should be calculated with this in mind. I am not convinced that the authors approach represents the dynamics that they claim. Perhaps simulating short term growth rates given the assumptions above is the way to go?
It would be helpful if the authors could provide their analytical expression for R_0, R_E and any other math used in this analysis (including code), either in the SI or in the main text. The analysis section is very short, and primarily a justification for not using adaptive dynamics.
The authors could include waning immunity into their model and leave it as a free parameter. Then they could take an adaptive dynamics approach and see how varying levels of immunity impact virulence evolution.
Minor Suggestions: Only issue is in the caption there is discussion of parameter values, well before the model is introduced. Either make these parameters clear or leave them out.
Some changes in font size (see Line 178 …compartments is known to exist…).
Line 110. Missing "more' transmissible? (see sentence …has been identified as being 43-82% transmissible …) Line 262 "selection for increased virulence decreases…" Does this mean there is still an increase in virulence, but it is less than in other scenarios?' Are you referring to the sign of the second derivative of selection? Sentence is awkward.
Line 296 double period ".." Line 443 "we extend previous work" citation of the previous work please.
Line 456 (Equation 1). define b1 and b2 and any constraints on these parameters. For example, I assume b2&lt;1, if you want this function saturating. Why do both LRT and URT infections contribute equally to transmission (ie have the same b1). Does the b1 parameter need to exist then? Is it important for scaling? What if epsilon is large, then a LRT infection would lead to proportionally more transmission, is this biologically accurate? If alpha&lt;0.0025, then transmission is negative. What does negative transmission mean biologically, how does this impact the model? What is, or is there, a the relationship between r_U and r_L (Equation 1) and (r_{U,C} /r_{U,V}) and (r_{L,C} /r_{L,V}).
Line 508: what do you mean by "more fit" what does this mean mathematically?
Line 510: Just include the bounds in the alpha_optimal range. Listing three values makes it seem like alpha_opt is one of the three options, not bounded between them.

Review form: Reviewer 3
Is the manuscript scientifically sound in its present form? Yes

Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
Overall, very insightful and interesting study, especially considering such limited data on virulence-transmission tradeoffs of SARS-CoV-2 and the long-term effects of immunity from vaccines vs. natural immunity being largely unknown. This is certainly a theoretical model that can be built off of and strengthened into a powerful tool as more data emerges. I have relatively minor clarifying questions and comments that could potentially strengthen the paper (see Appendix A). Since many readers of Royal Society Open Science will not necessarily be experts in virulence evolution terminology, it might be prudent to define some of the terms as they are mentioned (virulence, antigenic evolution, etc.).

Decision letter (RSOS-211021.R0)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Mr Miller
The Editors assigned to your paper RSOS-211021 "Assessing the risk of vaccine-driven virulence evolution in SARS-CoV-2" have now received comments from reviewers and would like you to revise the paper in accordance with the reviewer comments and any comments from the Editors. Please note this decision does not guarantee eventual acceptance.
We invite you to respond to the comments supplied below and revise your manuscript. Below the referees' and Editors' comments (where applicable) we provide additional requirements. Final acceptance of your manuscript is dependent on these requirements being met. We provide guidance below to help you prepare your revision.
We do not generally allow multiple rounds of revision so we urge you to make every effort to fully address all of the comments at this stage. If deemed necessary by the Editors, your manuscript will be sent back to one or more of the original reviewers for assessment. If the original reviewers are not available, we may invite new reviewers.
Please submit your revised manuscript and required files (see below) no later than 21 days from today's (ie 04-Oct-2021) date. Note: the ScholarOne system will 'lock' if submission of the revision is attempted 21 or more days after the deadline. If you do not think you will be able to meet this deadline please contact the editorial office immediately.
Please note article processing charges apply to papers accepted for publication in Royal Society Open Science (https://royalsocietypublishing.org/rsos/charges). Charges will also apply to papers transferred to the journal from other Royal Society Publishing journals, as well as papers submitted as part of our collaboration with the Royal Society of Chemistry (https://royalsocietypublishing.org/rsos/chemistry). Fee waivers are available but must be requested when you submit your revision (https://royalsocietypublishing.org/rsos/waivers).
Thank you for submitting your manuscript to Royal Society Open Science and we look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. We apologise for the length of time that this manuscript was in review. We had difficulty securing the required number of reviewers, but have now finally received three review reports.
As you see, the reviewers were broadly very supportive, but do recommend some changes and additional work on the manuscript. One of these changes is to incorporate the Delta variant into the paper, which I know you contacted the Office with a desire to do anyway. If there are requested changes that you do not feel are necessary, then please address this in your point-bypoint response.
I look forward to receiving your revised manuscript. Please note that it might be useful to add additional files to your Github repository to enable others to use the code. The existing files seem to be missing the source code needed to create the supplementary figure files (or this has been renamed). It is, of course, not a requirement of the journal, but was noted by one of the reviewers. There was also a suggestion to include a bit more information in the README file as a guide.
Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) I enjoyed reading Miller and Metcalf's manuscript on assessing the risk of virulence evolution in SARS-CoV-2 as a response to vaccination. It is well written overall, and shows a clear understanding of virulence evolution theory. Given the timeliness of the topic, there is a need for more theory papers addressing evolutionary trajectories of SARS-CoV-2, particularly in light of growing evidence that our most common vaccines are, in fact, more "leaky" than hoped. I enjoyed the attention to detail of the two regions of infection that are linked to transmission (URT) and severe disease (LRT) and appreciate the inclusion of this without having to overly complicate the model. While the methods are sound overall and the model is simple enough to answer the question, the manuscript is considerably outdated in various ways. I understand covid research moves very quickly but any paper to be posted as a preprint this summer and published this fall should include more recent examples, data, and discussion of the most important VOCs currently under investigation.
There are a couple glaring omissions: 1) There is a lack of references to recent papers on SARS-CoV-2 evolution theory or commentaries by important evolutionary biologists in this subfield. Namely: Day et al. 2021 Current Biology, Otto et al. 2021 Current Biology, and in particular Alizon and Sofonea 2021 J. Evo.Bio. As indicated below, there are several places where these (and some of their citations within) should be cited and the authors results be discussed in the context of these works (e.g. in the discussion section).
2) The Delta variant needs to be included. I understand that this manuscript may have been written at a time before Delta had emerged but unfortunately, this variant is too important evolutionarily to omit. It has both increases in transmission and virulence (e.g. Fisman and Tueite 2021 medrxiv) and reductions in vaccine efficacy. The authors consider cases where the optimum virulence is either intermediate between the ancestral strain and B.1.1.7 or greater than B.1.1.7, however, given how delta is sweeping in various geographical regions, it's pretty clear now that the case where the optimum is below B.1.1.7's virulence is not likely. The question in everyone's mind is, how high can virulence get? Please run the model calibrated for the delta variant's parameters (as those done for B.1.1.7 in lines 495-516) and change figures 3 and 4 to include only B.1.1.7, delta and a hypothetical "more virulent than delta" variant, given that the alpha_optim = 1.25*alpha_ansc case is no longer relevant. Fig. 1: The first figure should be a schematic of the transmission-virulence trade-off, particularly showing the different shapes it might have. The section "theory of virulence evolution' is nicely written but it's confusing to use a results image as an illustrative image of the concept (e.g. the unknown parameters and how they are related is confusing given the equations/model have not been presented yet). A schematic of the trade-off could be added as the first panel to Fig.1 or have a new stand-alone figure in the introduction.

Other comments
Paragraph ending in line 120: Delta needs to be added here.
Paragraph starting in line 121: please cite and discuss previous published works mentioned number 1 above.
Line 132: this decoupling of death from the trade-off has been discussed in the worked mentioned in number 1, please cite.
Paragraph starting on line 285: please include real-world data here not just the vaccine trails, since we now have estimates for these in global populations.
A direct analysis of vaccine leakiness (how much infectious viral shedding per vaccinated host) and its potential to drive virulence evolution would require a nested model approach, which is, understandably, beyond the scope of this study. However, given parallels of our current vaccine situation with that of Marek's Disease virus (which the authors briefly mention), the most studied example of vaccine-driven virulence evolution, it would be of use to the reader to understand the authors' results in context of this example (e.g. Read et al. 2015 Plos Biology). Please include this in the discussion section.
Points relating to herd immunity: Vaccine-induced herd immunity is an import part of the results of this paper and given that reaching HIT (herd-immunity threshold) is a moving target for SARS-CoV-2 (e.g. Hodgson et al. 2021 Eurosurveillance), here are some specific points to address about herd immunity.
The underlying R0 of a virus really affects the needed level of coverage to reach HIT and delta has changed this. How does the authors' results of their scenarios in Fig. 4, such as "how likely herd immunity without virulence evolution", change when considering the delta variant?
Line 306: "... 3) existing vaccines …" this is still theoretically true but please cite/add any caveats that have been debated in the modelling literature. For example, the vaccines don't reduce transmission as much as we hoped (especially with < 2 doses and for delta) and the projections for vaccine coverages needed for reaching herd immunity are changing (e.g. Mancuso, Eikenberry and Gumel 2021 medrxiv).
In figures 3 and 4, the 10% vaccinated coverage panels are there for completeness but are not really what we are aiming for globally. It would make more sense to just present two columns of 50 and 90 or have a gradation from 50 to 100%.
Reviewer: 2 Comments to the Author(s) The authors provide a well-written overview of how SARS-CoV-2 might evolve towards greater virulence in response to numerous factors, such as vaccination, naturally inherited immunity, increase transmission etc. The overview (paper intro) is structured well, and reads at a level where one does not need to be an expert in the field.
The authors then present a mathematical model of disease transmission, that includes both vaccinated and unvaccinated hosts. The authors then go on to use this model to study virulence evolution, given assumptions about LRT and URT protection. When analyzing the model, the authors do not take the standard approach to studying virulence evolution, which would be adaptive dynamics. The authors claim this is because long-term immunity is not well understood in this system. Perhaps waning immunity is a parameter that should be incorporated into the deterministic model (#3), if it is a major assumption in the model analysis.
The authors then calculate R_E (the effective reproductive value). This is essentially R0, but not evaluated at the disease-free equilibrium, but at 75% (or less?) of that value (since the authors assume 25% of individuals are already in the C class). At least this is my interpretation of what they are doing. The analysis section is very limited in its explanation. What I believe the authors are doing, is using R_E as a proxy for fitness. R_E acts as the growth rate of a strain (unique alpha) in a population that is smaller than the disease free population. The adaptive dynamics approach works by "competing" strains against one another by calculating invasion fitness. By using R_E, the authors ignore competing existing strains in the population. They then compare the growth rate of a standard B117 strain to that of a different strain (with a different alpha). The issue is, the population is not totally naïve, since 25% have already been infected and are sitting in the C class. This suggests there should be a significant number of infectious individuals in the population, with the B117 infection. Therefore the growth rate of the B117 strain and the novel strain should be calculated with this in mind. I am not convinced that the authors approach represents the dynamics that they claim. Perhaps simulating short term growth rates given the assumptions above is the way to go?
It would be helpful if the authors could provide their analytical expression for R_0, R_E and any other math used in this analysis (including code), either in the SI or in the main text. The analysis section is very short, and primarily a justification for not using adaptive dynamics.
The authors could include waning immunity into their model and leave it as a free parameter. Then they could take an adaptive dynamics approach and see how varying levels of immunity impact virulence evolution.
Minor Suggestions: Some changes in font size (see Line 178 …compartments is known to exist…).
Line 110. Missing "more' transmissible? (see sentence …has been identified as being 43-82% transmissible …) Line 262 "selection for increased virulence decreases…" Does this mean there is still an increase in virulence, but it is less than in other scenarios?' Are you referring to the sign of the second derivative of selection? Sentence is awkward.
Line 296 double period ".." Line 443 "we extend previous work" citation of the previous work please.
Line 456 (Equation 1). define b1 and b2 and any constraints on these parameters. For example, I assume b2<1, if you want this function saturating. Why do both LRT and URT infections contribute equally to transmission (ie have the same b1). Does the b1 parameter need to exist then? Is it important for scaling? What if epsilon is large, then a LRT infection would lead to proportionally more transmission, is this biologically accurate? If alpha<0.0025, then transmission is negative. What does negative transmission mean biologically, how does this impact the model? What is, or is there, a the relationship between r_U and r_L (Equation 1) and (r_{U,C} /r_{U,V}) and (r_{L,C} /r_{L,V}).
Line 508: what do you mean by "more fit" what does this mean mathematically?
Line 510: Just include the bounds in the alpha_optimal range. Listing three values makes it seem like alpha_opt is one of the three options, not bounded between them.
Reviewer: 3 Comments to the Author(s) Overall, very insightful and interesting study, especially considering such limited data on virulence-transmission tradeoffs of SARS-CoV-2 and the long-term effects of immunity from vaccines vs. natural immunity being largely unknown. This is certainly a theoretical model that can be built off of and strengthened into a powerful tool as more data emerges. I have relatively minor clarifying questions and comments that could potentially strengthen the paper. Since many readers of Royal Society Open Science will not necessarily be experts in virulence evolution terminology, it might be prudent to define some of the terms as they are mentioned (virulence, antigenic evolution, etc.) (see attached file: "Miller_Metcalf.pdf").

===PREPARING YOUR MANUSCRIPT===
Your revised paper should include the changes requested by the referees and Editors of your manuscript. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting if your manuscript is accepted.
Please ensure that any equations included in the paper are editable text and not embedded images.
Please ensure that you include an acknowledgements' section before your reference list/bibliography. This should acknowledge anyone who assisted with your work, but does not qualify as an author per the guidelines at https://royalsociety.org/journals/ethicspolicies/openness/.
While not essential, it will speed up the preparation of your manuscript proof if accepted if you format your references/bibliography in Vancouver style (please see https://royalsociety.org/journals/authors/author-guidelines/#formatting). You should include DOIs for as many of the references as possible.
If you have been asked to revise the written English in your submission as a condition of publication, you must do so, and you are expected to provide evidence that you have received language editing support. The journal would prefer that you use a professional language editing service and provide a certificate of editing, but a signed letter from a colleague who is a native speaker of English is acceptable. Note the journal has arranged a number of discounts for authors using professional language editing services (https://royalsociety.org/journals/authors/benefits/language-editing/).

===PREPARING YOUR REVISION IN SCHOLARONE===
To revise your manuscript, log into https://mc.manuscriptcentral.com/rsos and enter your Author Centre -this may be accessed by clicking on "Author" in the dark toolbar at the top of the page (just below the journal name). You will find your manuscript listed under "Manuscripts with Decisions". Under "Actions", click on "Create a Revision".
Attach your point-by-point response to referees and Editors at Step 1 'View and respond to decision letter'. This document should be uploaded in an editable file type (.doc or .docx are preferred). This is essential.
Please ensure that you include a summary of your paper at Step 2 'Type, Title, & Abstract'. This should be no more than 100 words to explain to a non-scientific audience the key findings of your research. This will be included in a weekly highlights email circulated by the Royal Society press office to national UK, international, and scientific news outlets to promote your work.

At
Step 3 'File upload' you should include the following files: --Your revised manuscript in editable file format (.doc, .docx, or .tex preferred). You should upload two versions: 1) One version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); 2) A 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. --If you are requesting a discretionary waiver for the article processing charge, the waiver form must be included at this step.
--If you are providing image files for potential cover images, please upload these at this step, and inform the editorial office you have done so. You must hold the copyright to any image provided.
--A copy of your point-by-point response to referees and Editors. This will expedite the preparation of your proof.

At
Step 6 'Details & comments', you should review and respond to the queries on the electronic submission form. In particular, we would ask that you do the following: --Ensure that your data access statement meets the requirements at https://royalsociety.org/journals/authors/author-guidelines/#data. You should ensure that you cite the dataset in your reference list. If you have deposited data etc in the Dryad repository, please include both the 'For publication' link and 'For review' link at this stage.
--If you are requesting an article processing charge waiver, you must select the relevant waiver option (if requesting a discretionary waiver, the form should have been uploaded at Step 3 'File upload' above).
--If you have uploaded ESM files, please ensure you follow the guidance at https://royalsociety.org/journals/authors/author-guidelines/#supplementary-material to include a suitable title and informative caption. An example of appropriate titling and captioning may be found at https://figshare.com/articles/Table_S2_from_Is_there_a_trade-off_between_peak_performance_and_performance_breadth_across_temperatures_for_aerobic_sc ope_in_teleost_fishes_/3843624.

At
Step 7 'Review & submit', you must view the PDF proof of the manuscript before you will be able to submit the revision. Note: if any parts of the electronic submission form have not been completed, these will be noted by red message boxes.

See Appendix B.
Decision letter (RSOS-211021.R1) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Mr Miller,
It is a pleasure to accept your manuscript entitled "Assessing the risk of vaccine-driven virulence evolution in SARS-CoV-2" in its current form for publication in Royal Society Open Science. The comments of the reviewer(s) who reviewed your manuscript are included at the foot of this letter.
If you have not already done so, please ensure that you send to the editorial office an editable version of your accepted manuscript, and individual files for each figure and table included in your manuscript. You can send these in a zip folder if more convenient. Failure to provide these files may delay the processing of your proof.
Please remember to make any data sets or code libraries 'live' prior to publication, and update any links as needed when you receive a proof to check -for instance, from a private 'for review' URL to a publicly accessible 'for publication' URL. It is good practice to also add data sets, code and other digital materials to your reference list. In particular, we ask that you please archive your GitHub code within the Zenodo repository: https://guides.github.com/activities/citablecode/. By doing this, a formal, citable DOI will be associated with your data record, and an open license (CC-BY preferred) can be applied to your data. We would then ask that you please update your data availability statement to read as: COVID-19 rapid publication process: We are taking steps to expedite the publication of research relevant to the pandemic. If you wish, you can opt to have your paper published as soon as it is ready, rather than waiting for it to be published the scheduled Wednesday. This means your paper will not be included in the weekly media round-up which the Society sends to journalists ahead of publication. However, it will still appear in the COVID-19 Publishing Collection which journalists will be directed to each week (https://royalsocietypublishing.org/topic/special-collections/novel-coronavirus-outbreak).
If you wish to have your paper considered for immediate publication, or to discuss further, please notify openscience_proofs@royalsociety.org and press@royalsociety.org when you respond to this email.
Our payments team will be in touch shortly if you are required to pay a fee for the publication of the paper (if you have any queries regarding fees, please see https://royalsocietypublishing.org/rsos/charges or contact authorfees@royalsociety.org).
The proof of your paper will be available for review using the Royal Society online proofing system and you will receive details of how to access this in the near future from our production office (openscience_proofs@royalsociety.org). We aim to maintain rapid times to publication after acceptance of your manuscript and we would ask you to please contact both the production office and editorial office if you are likely to be away from e-mail contact to minimise delays to publication. If you are going to be away, please nominate a co-author (if available) to manage the proofing process, and ensure they are copied into your email to the journal.
Please see the Royal Society Publishing guidance on how you may share your accepted author manuscript at https://royalsociety.org/journals/ethics-policies/media-embargo/. After publication, some additional ways to effectively promote your article can also be found here https://royalsociety.org/blog/2020/07/promoting-your-latest-paper-and-tracking-yourresults/. The revised version satisfactorily addresses the reviewers' comments including a broader discussion of the picture given the emergence of delta since the original manuscript was submitted. The broadened discussion on waning of immunity is very useful. Overall, this work is a novel contribution to our understanding of the potential for SARS-CoV2 evolution. It is written in an accessible way and the conclusions are supported by the modelling. Overall, very insightful and interesting study, especially considering such limited data on virulence-transmission tradeoffs of SARS-CoV-2 and the long-term effects of immunity from vaccines vs. natural immunity being largely unknown. This is certainly a theoretical model that can be built off of and strengthened into a powerful tool as more data emerges. I have relatively minor clarifying questions and comments that could potentially strengthen the paper, listed below. Since many readers of Royal Society Open Science will not necessarily be experts in virulence evolution terminology, it might be prudent to define some of the terms as they are mentioned (virulence, antigenic evolution, etc.).

22:
In the first sentence, would be good to put "as of September 2021" as a reference, since the number of cases and deaths may increase in time. genotype. (Obviously somewhere in between the 50%-90% plots for the former and between 10-50% for the latter but would still be neat to see the simulation plots for those specific, real-world numbers.) 355: Do you think there is a "deadline" to get to a threshold of vaccinations to ensure herd immunity? I.e., if we still have 60% vaccinated population by this time next year, does that change anything about herd immunity and/or whether a virulent variant may emerge? 395: Switch the words "the" and "both" to "both the effective population…" 398-399: Waning immunity is a very good point and a big unknown that could radically change predicted outcomes. Good point to have here.
405: This data is probably being collected by public health agencies? (I hope) 417: Some readers may think at first you are discussing host resistance, so perhaps to make it clearer, you could state "i.e., viral resistance to the vaccine", or something similar. We appreciate the very thoughtful and detailed comments you have provided us. We have made substantial updates to the paper in light of the emergence of the delta variant. Additionally, we have switched our analysis methods to a more standard adaptive dynamics approach that is aimed more at predicting trajectories of SARS-CoV-2 evolution than at identifying immediate patterns of selection for changes in virulence. These changes have had a minimal impact on our conclusions and closing recommendations.
Please find a point by point response to reviewer comments below.

Sincerely, Ian Miller and Jess Metcalf
Appendix B Reviewer 1: 1. There is a lack of references to recent papers on SARS-CoV-2 evolution theory or commentaries by important evolutionary biologists in this subfield. Namely: Day et al. 2021 Current Biology, Otto et al. 2021 Current Biology, and in particular Alizon and Sofonea 2021 J. Evo.Bio. As indicated below, there are several places where these (and some of their citations within) should be cited and the authors results be discussed in the context of these works (e.g. in the discussion section).
We added citations to these works throughout the paper where appropriate and added a line in the discussion stating: 'This work builds upon the theoretical analyses of SARS-CoV-2 virulence evolution presented in many previous studies by extending the same fundamental concepts to the issue of vaccine-driven evolution." (Line 606) We strongly agree that current evidence surrounding delta necessitates a reconsideration of the optimum virulence scenarios. We changed these to reflect the possibility that optimum virulence could 1) fall between that of alpha and delta, 2) be equal to that of delta, or 3) be greater than that of delta (See methods and new figure S1). We also expanded the introduction and discussion to include details about delta.
3. Fig. 1: The first figure should be a schematic of the transmission-virulence trade-off, particularly showing the different shapes it might have. The section "theory of virulence evolution' is nicely written but it's confusing to use a results image as an illustrative image of the concept (e.g. the unknown parameters and how they are related is confusing given the equations/model have not been presented yet). A schematic of the trade-off could be added as the first panel to Fig.1 or have a new stand-alone figure in the introduction.
We agree that our paper could be improved by a figure more focused on the potential forms of the relationship between virulence and transmission. We created a new figure   (Fig. 1) and moved the original Fig. 1 to the supplement (Fig. S1) while also updating it to reflect the changes detailed in point 2 above.
4. Paragraph ending in line 120: Delta needs to be added here.
We added a discussion of delta to this section (beginning at L140).
5. Paragraph starting in line 121: please cite and discuss previous published works mentioned number 1 above.
We added a discussion of these works to this section (L211-247).
6. Line 132: this decoupling of death from the trade-off has been discussed in the worked mentioned in number 1, please cite.
We added this citation as suggested (L221).
7. Paragraph starting on line 285: please include real-world data here not just the vaccine trails, since we now have estimates for these in global populations.
We have updated these paragraphs with current evidence regarding real-world vaccine efficacy and delta (L457-506).
8. A direct analysis of vaccine leakiness (how much infectious viral shedding per vaccinated host) and its potential to drive virulence evolution would require a nested model approach, which is, understandably, beyond the scope of this study. However, given parallels of our current vaccine situation with that of Marek's Disease virus (which the authors briefly mention), the most studied example of vaccine-driven virulence evolution, it would be of use to the reader to understand the authors' results in context of this example (e.g. Read et al. 2015 Plos Biology). Please include this in the discussion section.
We added context about how the results of the MDV study relate to COVID in lines 272-276: "It is important to note that some factors present in these examples of vaccine-driven virulence evolution are absent in the case of SARS-CoV-2. For instance, in the latter example, viral virulence was extremely high (60-100% infection fatality rate) prior to vaccine-driven evolution, and vaccinal protection against infection was extremely poor." 9. Vaccine-induced herd immunity is an import part of the results of this paper and given that reaching HIT (herd-immunity threshold) is a moving target for SARS-CoV-2 (e.g. Hodgson et al. 2021 Eurosurveillance), here are some specific points to address about herd immunity.
a. The underlying R0 of a virus really affects the needed level of coverage to reach HIT and delta has changed this. How does the authors' results of their scenarios in Fig. 4, such as "how likely herd immunity without virulence evolution", change when considering the delta variant?
We updated the parameterization of b1 and b2 to reflect a reasonable value of R0 for delta (L977).
b. Line 306: "... 3) existing vaccines …" this is still theoretically true but please cite/add any caveats that have been debated in the modelling literature. For example, the vaccines don't reduce transmission as much as we hoped (especially with < 2 doses and for delta) and the projections for vaccine coverages needed for reaching herd immunity are changing (e.g. Mancuso, Eikenberry and Gumel 2021 medrxiv).
We added the caveat "although waning vaccinal protection could jeopardize this outcome" at line 514. We also added a detailed discussion of what herd immunity implies for COVID transmission (i.e. not necessarily a 'COVID-free' world) and how it relates to waning (L609-656).
c. In figures 3 and 4, the 10% vaccinated coverage panels are there for completeness but are not really what we are aiming for globally. It would make more sense to just present two columns of 50 and 90 or have a gradation from 50 to 100%.
We updated the vaccine coverages considered in our analyses to 50%, 75%, and 90%.
Reviewer 2: 1. The authors provide a well-written overview of how SARS-CoV-2 might evolve towards greater virulence in response to numerous factors, such as vaccination, naturally inherited immunity, increase transmission etc. The overview (paper intro) is structured well, and reads at a level where one does not need to be an expert in the field.
The authors then present a mathematical model of disease transmission, that includes both vaccinated and unvaccinated hosts. The authors then go on to use this model to study virulence evolution, given assumptions about LRT and URT protection. When analyzing the model, the authors do not take the standard approach to studying virulence evolution, which would be adaptive dynamics. The authors claim this is because longterm immunity is not well understood in this system. Perhaps waning immunity is a parameter that should be incorporated into the deterministic model (#3), if it is a major assumption in the model analysis.
We changed our methods to a more formal adaptive dynamics approach. Waning immunity will certainly be important for SARS-CoV-2 epidemiological dynamics, and potentially evolutionary dynamics as well. However, as we have witnessed over the past year, significant amounts of virulence evolution can occur in a matter of months. Incorporating waning that leads to a total loss of immunity would mean that epidemiological dynamics would take many years to reach equilibrium, forcing predictions about virulence evolution to fall out of step with the observed pace of virulence evolution. However, we have also witnessed that immunity has waned. Evidence suggests that it weakened rather than disappeared, as protection against severe disease remains robust. Our model formulation can account for this if the r parameters are interpreted as population means, summarizing the variation in immunity across all individuals in each class. We discuss these points in lines 994 to 1010 and elsewhere. To make our model as useful as possible, we have also included waning parameters (set to 0 in our analyses) so that waning can be investigated in the future if appropriate.
2. The authors then calculate R_E (the effective reproductive value). This is essentially R0, but not evaluated at the disease-free equilibrium, but at 75% (or less?) of that value (since the authors assume 25% of individuals are already in the C class). At least this is my interpretation of what they are doing. The analysis section is very limited in its explanation. What I believe the authors are doing, is using R_E as a proxy for fitness. R_E acts as the growth rate of a strain (unique alpha) in a population that is smaller than the disease free population. The adaptive dynamics approach works by "competing" strains against one another by calculating invasion fitness. By using R_E, the authors ignore competing existing strains in the population. They then compare the growth rate of a standard B117 strain to that of a different strain (with a different alpha). The issue is, the population is not totally naïve, since 25% have already been infected and are sitting in the C class. This suggests there should be a significant number of infectious individuals in the population, with the B117 infection. Therefore the growth rate of the B117 strain and the novel strain should be calculated with this in mind. I am not convinced that the authors approach represents the dynamics that they claim. Perhaps simulating short term growth rates given the assumptions above is the way to go?
We have added more details to the explanation of our calculation of basic and effective reproductive numbers and how they relate to the frequencies of individuals in each model class in equation 4 and lines 975 and 1069. Our approach now conforms to a typical adaptive dynamics framework, which resolves the concerns raised here.
3. It would be helpful if the authors could provide their analytical expression for R_0, R_E and any other math used in this analysis (including code), either in the SI or in the main text. The analysis section is very short, and primarily a justification for not using adaptive dynamics.
We added more details about the calculation of these values (see point 2 above). Due to the complexity of the model, a simple closed form expression for R is not available. Code for all analyses can be found in reference 81.
4. The authors could include waning immunity into their model and leave it as a free parameter. Then they could take an adaptive dynamics approach and see how varying levels of immunity impact virulence evolution.
See point 1 above.
5. Figure 1. Nice figure. Only issue is in the caption there is discussion of parameter values, well before the model is introduced. Either make these parameters clear or leave them out.
Thank you. We revised Fig. 1 to illustrate various shapes of the relationship between virulence and transmission. We moved the original Fig. 1 to the supplement (Fig. S1), and made that figure's purpose purely to illustrate assumptions about the optimum value of virulence.
6. Some changes in font size (see Line 178 …compartments is known to exist…).
We were unable to identify any font size discrepancy in the word document version of our manuscript. Perhaps this problem arose during PDF generation. We will keep a look out for this problem moving forward.
8. Line 262 "selection for increased virulence decreases…" Does this mean there is still an increase in virulence, but it is less than in other scenarios?' Are you referring to the sign of the second derivative of selection? Sentence is awkward.
This wording is no longer present in our description of the results of our adaptive dynamics analysis.
10. Line 443 "we extend previous work" citation of the previous work please.
We changed this phrasing to "We separate the impacts…'(L798), as this feature of our analysis is novel.
We prefer to keep our analyses focused on bounding the problem of virulence evolution. Given the amount of uncertainty surrounding potential for virulence evolution, we believe that trying to make pinpoint projections would be more misleading that productive.
17. Line 355: Do you think there is a "deadline" to get to a threshold of vaccinations to ensure herd immunity? I.e., if we still have 60% vaccinated population by this time next year, does that change anything about herd immunity and/or whether a virulent variant may emerge?
Predicting the pace of virulence evolution is even more difficult that predicting the trajectory of evolution, and unfortunately we cannot say anything about a deadline at this time.
18. Line 395: Switch the words "the" and "both" to "both the effective population..." We fixed this error.
19. Lines 398-399: Waning immunity is a very good point and a big unknown that could radically change predicted outcomes. Good point to have here.
Thank you. We added additional discussion of waning immunity throughout the paper in response to points raised by other reviewers.
20. Lines 405: This data is probably being collected by public health agencies? (I hope) Yes, thankfully variants that may be more virulent are monitored carefully. We changed this wording to "continue to be surveilled" (L728). We also removed the need for monitoring from the abstract since this is now happening sufficiently. We now highlight the need for 1) vaccines that provide robust protection against both disease and transmission , and 2) high vaccine coverage rather than monitoring efforts.
21. Line 417: Some readers may think at first you are discussing host resistance, so perhaps to make it clearer, you could state "i.e., viral resistance to the vaccine", or something similar.
We agree that this text was unclear. We removed our discussion of the evolution of vaccine escape because we felt it was no longer adequate given that VOCs that evade immunity have indeed been identified. This is still an extremely important issue, but one that we feel is now outside the scope of this paper. Thank you for pointing out this error. This citation was removed during our switch to an adaptive dynamics approach.