When to end a lock down? How fast must vaccination campaigns proceed in order to keep health costs in check?

We propose a simple rule of thumb for countries which have embarked on a vaccination campaign while still facing the need to keep non-pharmaceutical interventions (NPI) in place because of the ongoing spread of SARS-CoV-2. If the aim is to keep the death rate from increasing, NPIs can be loosened when it is possible to vaccinate more than twice the growth rate of new cases. If the aim is to keep the pressure on hospitals under control, the vaccination rate has to be about four times higher. These simple rules can be derived from the observation that the risk of death or a severe course requiring hospitalization from a COVID-19 infection increases exponentially with age and that the sizes of age cohorts decrease linearly at the top of the population pyramid. Protecting the over 60-year-olds, which constitute approximately one-quarter of the population in Europe (and most OECD countries), reduces the potential loss of life by 95 percent.


Comments to the Author(s)
This is a very elegant article focussing on some key relationships of highly topical importance, and can be published as is. However, given its probable utility to policy makers, it would gain by a table of indicative results for different permutations of key parameters associated with different countries; this would serve to illustrate some of the key points and relationships. For the same reason, the discussion could be extended to address explicitly how the results could be affected by the presence of new virus variants.

Decision letter (RSOS-211055.R0)
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Dear Dr Gros
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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. Both of the reviewers comment positively on the relevance and on the presentation of the paper. One reviewer is positive about the paper. However the other reviewer, whilst liking some aspects of the paper, expresses serious concerns about both the context of the paper, in particular the lack of references. They are also concerned that the models are not well described, and that more details need to be given about the derivation of the various formulae used. These are both serious points which I agree with. The authors should therefore carefully revise their paper along these lines.
Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) The paper concerns a relevant topics and is sufficiently well written. It lacks context: reference to related literature and comparison of findings. Also it lacks clarity: often the formulae are introduced without a clear explanations and the symbols used in the equations are often not clarified or confused. There are also a number of English typos. The relevance of the results of the paper suggests a revision that amends the pitfalls.
A revision should be conducted along the following lines: 1. More literature references should be included, especiaily with regards to papers that assess the dynamic of the COVID-19 contagion in Europe should be added, and the results therein made complementary with the findings of the paper. Examples are the papers Agosto, Giudici: Risks, 2020; Agosto, Campmas, Giudici, Renda: Statistics in Medicine, 2021.
2. Each formula should be fully explained, stating exactly what each quantity and symbols represents and possibly adding an interpretational comment and a numerical example.
3. The Authors assume almost full vaccine coverage. As they remark, this is not a realistic assumption, and the coverage does also depends on specific types of vaccines. The authors should extend their work in this direction 4.The incidence rate I/I(hat) is not exogenous but depends on vaccines and NPIs. The authors should extend their model to take this aspect into account. Possibly using a statistical approach to estimate the incidence rate for the aggregate EU countries 5. The paper should be better focused, possibly only on European countries for which more data and evidence is available 6. It is not clear whether and why the authors consider only people aged above 60. This should be clarified. Possibly, younger cohorts should be included in the analysis as further covid variants may change the age incidence distribution Reviewer: 2 Comments to the Author(s) This is a very elegant article focussing on some key relationships of highly topical importance, and can be published as is. However, given its probable utility to policy makers, it would gain by a table of indicative results for different permutations of key parameters associated with different countries; this would serve to illustrate some of the key points and relationships. For the same reason, the discussion could be extended to address explicitly how the results could be affected by the presence of new virus variants.

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Author's Response to Decision Letter for (RSOS-211055.R0) See Appendix A.

RSOS-211055.R1 (Revision)
Review form: Reviewer 1 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

Recommendation?
Accept as is

Comments to the Author(s)
The authors have successfully addressed my remarks. The paper can be accepted Decision letter (RSOS-211055.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 Dr Gros,
It is a pleasure to accept your manuscript entitled "When to end a lock down? How fast must vaccination campaigns proceed in order to keep health costs in check?*" 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.
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