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. 2022 Jan 17;2022(1):CD015029. doi: 10.1002/14651858.CD015029
Preprint ID Full  publication ID Differences
Burns A 2020 Burns A 2021 Title: changed
Methods: more details on model, its validation and parameters
Results: The authors focus on the two outcomes: outbreak duration and attack rate (less outcomes as presented in the preprint); results have been restructured to reduction in attack rate. The results do not seem to correspond to the ones reported in the preprint. The figure axes have been adapted to make the graphs more comparable.
Discussion: in the first paragraph, the results are reported differently now (preprint: "For influenza, a 15% and 25% reduction in the attack rate is expected with one and two days of isolation" versus peer‐reviewed article: "For influenza, requiring isolation for fever is expected to reduce the typical attack rate by 29 (13–59)% and 70 (55–85)% with 1 and 2 days of post‐fever isolation, respectively."); for covid‐19, it is the same (preprint: "For COVID‐19, we find that one day of post‐fever isolation would reduce the attack rate by 8% in the conservative scenario where only 50% of the cases detect fever" versus peer‐reviewed article: "Indeed, we found that a 1‐day post‐fever isolation policy would reduce the attack rate in schools by 7 (5–14)%, and with 14 days of fever isolation we estimated that the attack rate would change by 14 (5–26)%."
Curtius 2020 Curtius 2021 Title: not changed
Methods: one additional section in methods, some sections moved from results (Curtius 2020) to methods (Curtius 2021); number of particles emitted per hour changed from 68.400 to 198.000; estimated risk of one infection in the classroom 70% (Curtius 2021), instead of 33% (Curtius 2020); no implication for results (unless we misunderstood)
Results: few smaller new sections (i.e. p9: "from the average...", "The OPS total number..."; added comparison with venting a room (p.10 and supplements); no change in overall results/conclusion: the overall conclusion "inhaled dose via airborne transmission is reduced by a factor of six when using air purifiers with an air exchange rate of 5.7/h" remains the same but there is one changed measurement in the results section: total aerosol mass (p.9, upper right): "56 mg/m3 at the beginning of the lesson to about 9 mg/m3" instead of reduction from 35 mg/m³ to 6 mg/m³ (Curtius 2020)
Discussion: minor changes
Di Domenico 2020a Di Domenico 2021 Title: not changed
Background/intro: appears to be differences because of additional data that became available after the preprint was written: "This study was conducted in the lockdown phase, before its end in May, and was therefore based on a scenario analysis. Here, we also provide an ex‐post assessment of the epidemic situation reported by data that became available after the initial submission."
Methods: different parameters described in preprint versus peer‐reviewed:
  • Preprint: "Intervention measures are modeled through modifications of the contact matrices, accounting for a reduction of the number of contacts engaged in specific settings. For example, the lockdown matrix is constructed assuming 70% of workers not going to work (because of telework, closure of activity, caring for children not going to school, and other cases), school closure, 90% reduction of contacts established by seniors, and closure of non‐essential activities"

  • Peer‐reviewed: "Intervention measures were modeled through modifications of the contact matrices, accounting for a reduction of the number of contacts engaged in specific settings. The lockdown matrix was constructed assuming a certain fraction of workers not going to work (because of telework, closure of activity, caring for children not going to school, and other cases), school closure, 50% reduction of contacts established by seniors, and closure of non‐essential activities"


Results: major differences in numerical findings, probably because of different dates/parameters used to construct model.
Examples:
  • Preprint: "Calibrating the model in the lockdown phase to ICU admission data up to April 28, 2020, we estimate a drop of the reproductive number from R' =3.0 [2.8, 3.2] (95% confidence interval) prior to lockdown to R+, =0.53 [0.49, 0.58] during lockdown, in agreement with recent estimates."

  • Peer‐reviewed: "Calibrating the model in the lockdown phase to hospital and ICU admission data up to April 26, 2020, we estimated a drop of the reproduction number from R0 = 3.28 [3.20, 3.39] (95% confidence interval) prior to lockdown 4 to RLD = 0.71 [0.69, 0.74] during lockdown, in agreement with prior estimates"

  • Preprint: "model projections indicate that by May 11 the region may experience 350 [268, 421] new clinical cases per day (corresponding to 710 [555, 869] new infections), 18 [10, 28] new admissions in ICUs, with an ICU system occupied at 42% [33, 52]% of currently strengthened capacity (Figure 1). Estimated fluctuations refer to 95% probability ranges from simulations parameterized with R+, =0.53."

  • Peer‐reviewed: "Model projections indicate that by May 11 the region would experience 945 [802, 1076] new clinical cases per day (corresponding to 2391 [2025, 2722] new infections), 18 [11, 29] new admissions in ICUs, with an ICU system occupied at 47% [37, 57]% of strengthened capacity"


Discussion: no major changes
Head 2020 Head 2021 Title: changed
Abstract: While the results remain the same, the authors add one important sentence: "However, we found that reopening policies for elementary schools that combine universal masking with classroom cohorts could result in few within school transmissions, while high schools may require masking plus a staggered hybrid schedule."
Methods: no major changes
Results: no major changes
Discussion: stronger focus on effectiveness of reopening strategies "Some reopening strategies can result in few in‐school transmissions among students and teachers alike, according to our findings. Most notably, our model found that reducing in‐school mixing via classroom cohorts or hybrid scheduling is an effective means of reducing the risk of school‐attributable illness across all levels of education, especially when combined with universal masking. These findings concur with observations of schools that reopened with universal masking, social distancing and a hybrid or cohort approach and avoided large outbreaks"
Kaiser 2020 Kaiser 2021 Title: changed
Abstract: substantially condensed
Background: substantially shortened
Methods: mean of out‐of‐school student contacts as per CILS4EU data cited 3.58 in preprint and 3.15 in peer‐reviewed version; no implications for model as average number of out‐of‐school interactions still 4.2 in both preprint and peer‐reviewed version (daily/weekly contact probabilities)
Model parameters: baseline probabilities of infection: same (modelled for 5%, 15%, 25%); proportion of subclinical infections modelled for 20%, 40%, 60% and 80% in preprint and 20%, 50%, 80% in peer‐reviewed version
Results: section on the superiority of cohorting versus not cohorting shortened (fig 3 adapted, fig 4 removed in the peer‐reviewed version); reductions of cross‐cohort ties for different cohorting strategies: same (preprint versus peer‐reviewed); figure 6 (preprint) simplified (= fig 5 in peer‐reviewed version); performance of different cohorting strategies: same in preprint versus peer‐reviewed version, however, the numbers cited in the example on page 7, line 6 onwards differ slightly in peer‐reviewed version; sensitivity analyses reported in supplements; short section added that reports on performance of the gender‐split versus other models in individual classrooms (as opposed to aggregated results) – while network‐chain cohorting performs better than gender‐split cohorting in the majority of classrooms, gender‐split cohorting performs better in a minority of classrooms (e.g. in very gender‐segregated in‐school and out‐of‐school cohorts); short section added reporting on another cohorting model: attendance for one cohort on Monday/Tuesday and for the other on Wednesday/Thursday – more effective when overall transmission is low (due to less time spent in school overall), less effective compared to weekly rotation when transmission is high (less “cool‐down”/natural quarantine time)
Discussion: minor changes
Keeling 2020 Keeling 2021 Title: not changed
Abstract: not changed 
Methods: no major changes (just rearrangement of presentation of figures)
Results: no major changes
Discussion: no changes to the Discussion but the authors have added an 'In context' section which puts the paper into context of simulated versus actual reopening. The authors acknowledge that the Delta variant has changed the context in which schools have reopened. The authors state that in their simulations, return to schools was unlikely to push R above 1, but that the Delta variant may cause R to go above 1 upon reopening. The authors also conducted a retrospective analysis and found that in many regions, there was a positive correlation between cases in the community and cases in schools, with weak evidence suggesting that cases in schools lag behind cases in the surrounding community. Ultimately, the authors conclude that reopening schools (especially secondary schools) is associated with an increased risk of transmission both within the school‐aged pupils and in the wider community. The scale of this increase will inherently depend on the strength of control measures within the classroom and the compliance with mass testing as well as measures in the local community.
Landeros 2020 Landeros 2021 Title: not changed
Abstract: slightly changed, more details on methods, results and implications
Methods: method section more detailed, e.g. more details on the simulation of prevalence tresholds; they also conduct an analysis of different test sensitivities
Results: the way the results are presented graphically was revised; the assessment of test sensititivity which was only a parameter in the preprint is now specifically reported ("Compared to this ideal scenario, an imperfect test with 50% detection leads to a slightly later stopping time owing to infections spread by undetected cases and greater overall paediatric infections. The effect is less pronounced in the adult population due to high adult‐adult transmission."
They adapted the natural transmission rates and reran the model, resulting in different results for the reproduction number:
  • Preprint: "The combined impacts of these risk reduction strategies are modeled as 20%, 40%, 60%, and 80% reductions in the transmission rates β11 and β12 relative to reference values. We particularly examine the changes in infection levels under each scenario, taking care in selecting the adult values β21 and β22 to account for simultaneous risk reduction strategies among adults. Specifically, we take β11 = 0.1 and β12 = β21 = β22 = 0.5 as natural rates. Under a baseline model reducing transmission rates in adults to β21 = β22 = 0.2, we achieve an R0 ≈ 1.8 when schools remain closed. We choose to model increased contact rates β11(t) = c × 0.1 by taking c = 10, which corresponds to R0 ≈ 3.3 under the full capacity reopening scenario. This necessarily represents an extreme that illustrates effects in a poor situation."

  • Peer‐reviewed article: "Combined impacts of these strategies are modeled as 20%, 40%, 60%, and 80% reductions in the transmission rates β11 and β22 relative to reference values. Specifically, we take β11 = 0.12, β12 = 0.3, β21 = 0.18, and β22 = 0.6 as natural rates and apply a 40% reduction factor to adults by setting β21 = 0.072 and β22 = 0.24. This implies R0 ≈ 1.7 prior to reopening. Increased contact is modeled by taking c = 10 so that β11 = 1.2, which corresponds to R0 ≈ 2.2 under the full capacity reopening scenario."


Discussion: in the conclusion, the authors now conclude: "We find that measures reducing class density by rotating cohorts between in‐person and remote schooling are likely to have greater impact in reducing the spread of SARS‐CoV‐2 than policies such as mask wearing, handwashing, and physical distancing in the classroom. Nevertheless, the latter policies combined with a reduction in class density are still quite effective in reducing effective transmission" versus "As already mentioned, our simulations suggest that measures that reduce class density by rotating cohorts between in‐person and online schooling are likely to have the greatest impact in reducing the spread of SARS‐CoV‐2 brought on by the resumption of in‐person instruction."
Lazebnik 2020 Lazebnik 2021 Title: not changed
Abstract: shortened; message remains the same
Methods: minor changes
Results: 3.3. Lockdown policies ‐ added paragraph: "The lockdown policy is similar to the schooling‐working hours policy in the manner that both modify the spatial dynamics of the population. Nevertheless, the schooling‐working hours policy defined the number of hours all the children and working adults populations go to school and work, respectively, while the lockdown policy keeps part (or all) the population at home all day long alongside the remain part of the population keeps the regular working and schooling hours. In addition, the lockdown policy isolates individuals at home, which is expressed by the fact that individuals can contact with them but they can not initial an contact with other individuals while this constraint does not take place in the working‐schooling hours policy."
Discussion: minor changes
Lyng 2020 Lyng 2021 Title: not changed
Methods: refer more specifically to classical epidemiological susceptible, infectious‐asymptomatic, infectious‐symptomatic, removed (SIR) model in their peer‐reviewed version. In the peer‐reviewed version, they justify why they did not add the exposed category to the model ("We do not include an “exposed” category as is often done for compartmental models but account for the shorter time a person is infectious rather than the longer period of time they are infected."); add justification about choice of Miami‐Dade as one scenario for their forcing ("It should be noted that the case counts in Miami‐Dade County over this time period are outliers compared to case counts in other counties across the US over the past ten months. These cases are chosen for illustration to show the widest array of possible scenarios.")
Results: peer‐reviewed paper: "At the most lenient frequency considered, every 14 days, the number of infections is reduced approximately 21‐56% (versus 31% to 98% in preprint) compared to no testing at all."
  • "For example, at a test sensitivity of 80%, testing every day reduces the number of cumulative infections relative to no testing by 95.9–99.9% while testing every 14 days reduced the number of cumulative infections at day 100 relative to no testing by only 26.0–27.1% (versus preprint: for example, at a test sensitivity of 80%, the effect of testing every day in a population of 1500 compared to testing every 14 days reduced the number of cumulative infections at day 100 by 364 in the low prevalence community and by 958 in the high prevalence community)"

  • "Importantly, at sensitivities of 98% our models predict that a two‐day delay in results (by send‐out PCR, for example) will result in just a 31% reduction (versus 59% in preprint) in infections experienced at a 14‐day testing frequency; however, as the testing frequency is increased, even with the two‐day delay, the number of missed infections goes down rapidly to a 99% reduction from no testing at all to a daily testing frequency."


Discussion: peer‐reviewed paper: additional information: "Even with a highly specific (99.5%) test such as a PCR, in a low prevalence community with large pools, false positives may still become an issue. The previous example results in 253 false positives over 100 days, highlighting the importance of confirmatory testing."
Munday 2020 Munday 2021 Title: not changed
Methods: minor changes
Results: peer‐reviewed paper ‐ added information: 
  • Networks of household‐based contact between schools. “We constructed a set of seven networks of schools using individual‐level de‐identified data of pupils attending state‐funded schools in England. Links between schools were defined by the number of unique contact opportunities (pupil to pupil) formed through shared households. First, we constructed a network with schools fully open (all pupils attending school) and included 21,583 schools, attended by 4.6 million primary school children and 3.4 million secondary school children in attendance, living at 4.9 million unique addresses (Fig. 1). The remaining six networks each represented a reopening scenario relevant to policy in England, illustrated in Fig. 2. In each scenario different combinations of year‐groups return to school: early‐years education (Reception and Year 1, i.e. 4–6‐year‐olds) and time‐sensitive groups in transition, e.g. through exam certifications or transitional years (Year 6, i.e. 10–11‐year‐olds, Year 10, i.e. 14–15‐year‐olds and Year 12, i.e. 16–17‐year‐olds). These contained between 21 and 100% of all schools and between 35 and 66% of all households (Table 2).” (reported numerical data did not change)Degree distributions of the transmission probability network: “From the contact networks, we estimated the probability of transmission between each pair of schools to assign as edge weights in a transmission probability network for each reopening scenario.”

  • Connected components of binary outbreak networks: “Using the transmission probability networks, we generated 1000 realisations of binary outbreak networks for each scenario, where the edges between schools were weighted either 1, with probability equal to the transmission network, or 0. If schools were linked by an edge of weight 1, transmission occurred between the schools in that realisation, edges of weight 0 indicated no transmission between the schools they linked. Connected components on these net‐ works formed groups of schools that would be infected in an outbreak initiated in the same group, for that realisation.”


Discussion: peer‐reviewed paper ‐ added paragraphs: 
  • “Since reopening in September there has been mixed evidence of transmission of SARS‐CoV‐2 in schools. However, because evidence of school outbreaks is largely based on passive case detection, the true risk of school transmission may be substantially underreported as children have a lower risk of developing symptoms after infection. Moreover, UK prevalence surveys show 11–18‐year‐olds routinely have the second‐highest prevalence after 18–29‐year‐olds. Further, school children are estimated to be several times more likely to introduce infection into the household than adults—a rate which has increased since schools reopened in September, suggesting that transmission in schools may have been an important factor in driving the outbreak since school reopening. Consensus on this matter remains elusive, and our results should therefore be considered in light of the most recent available evidence to the reader.” (versus preprint: “Scientific consensus on this matter remains elusive, and our results should therefore be considered in light of the most recent available evidence to the reader.”)

  • “Our model presupposes that the expected outbreak risk within the school network is closely related to the risk within the wider community. That is, the risk of an infectious pupil seeding a school outbreak is proportional to the prevalence of infection in the community. Therefore, the transmission risks associated with opening schools would be expected to increase as prevalence in the surrounding community increases.”

  • “This framework also implies a well‐mixed contact network within each school, final sizes are likely to be smaller due to preferential mixing within school years, classes and by gender. In addition, if schools implement social bubbles to introduce community structure in the contact network and therefore reduce the probability of a school‐wide outbreak. This is partly reflected in the low values of R that have been chosen relative to those estimated early in the outbreak of 2.0–3.1) but our estimates of the number of households impacted may still be an overestimate compared to any real situation which would include mitigation measures (e.g., improved hand hygiene and use of face masks) and reactive interventions in response to cases detected in schools.” (versus preprint: “This framework also implies a well‐mixed contact network within each school, final sizes are likely to be smaller if schools implement social bubbles to introduce community structure in the contact network and therefore reduce the probability of a school wide outbreak. The reproduction number was assumed to be invariant between schools, this approach was chosen to maintain the parsimony of the approach, as modelling internal transmission dynamics of individual schools would increase complexity considerably.”)

  • “Our framework assumes no presence of immunity, however, there is evidence of immunity to SARS‐COV‐2 in children. The true immunity in schools is likely to vary both by region and between schools, however, the resolution of data on immunity in England is poor and certainly cannot be resolved at a school level. Similarly, the reproduction number was assumed to be invariant between schools, this approach was chosen to maintain the parsimony of the approach, as modelling internal transmission dynamics of individual schools would considerably increase the complexity. In light of these simplifications, our results should be interpreted as the maximal risk posed by transmission within and between schools. We assumed child‐to‐child transmission within households occurs with probability q = 0.15, which is consistent with estimates of the household secondary attack rate. To assess the robustness of the results to this assumption, we re‐ran the analysis with q = 0.3 and q = 0.08 (Supplementary Figs. 2–5), and although the sizes of the connected components changed, the relative impact of scenarios remained comparable to the main analysis. In the absence of more robust evidence, however, we cannot rule out that transmission between children might be different from general transmission patterns to a degree that would fundamentally affect our results.” (versus preprint: “We assumed transmission between members of the same household to occur with probability q = 0.15, which is consistent with estimates of the household secondary attack rate. To assess the robustness of the results to this assumption, we re‐ran the analysis with q = 0.3 and q = 0.08 (supplementary material), where although the sizes of the connected components changed, the relative impact of scenarios remained comparable to the main analysis.”)

  • “Furthermore, such restrictions may be essential for suppressing transmission. While our results should not be considered as realistic epidemiological projections, our simulations provide an indication of the relative impact of each scenario, using highly resolved schools data.” (versus preprint: “Furthermore, such restrictions will be essential for suppressing transmission in the event that all secondary schools are opened.”)

  • “If detailed projections were desired, the framework could be extended to include within‐school contact structure, however, this would greatly increase the network size and therefore computational effort required. The principles highlighted in our analyses are not constrained to SARS‐CoV‐2 and may be considered when evaluating interventions for any epidemic in which children are known to transmit infection.”

Naimark 2020 Naimark 2021 Title: changed
Abstract: no major changes
Methods: no major changes
Results: authors have added a paragraph about a sensitivity analysis stating that when NPIs were implemented and their effectiveness held at the base case value, as the
effectiveness of mitigation efforts within schools diminished, the difference in mean estimated cumulative case numbers by October 31, 2020, between keeping schools closed or reopening them increased. When school mitigation effectiveness was held at the base case value, as the effectiveness of community‐based NPIs decreased, the difference in mean estimated cumulative case numbers between keeping schools closed vs reopening them did not increase.
Discussion: no major changes ‐ authors add a bit more detail about how their study compares to other similar studies and what it adds to the evidence base
Panovska‐Griffiths 2020b Panovska‐Griffiths 2021 Title: not changed
Abstract: slightly changed 
Methods: not changed
Results: no major changes
Discussion: no major changes
Phillips 2020 Phillips 2021 Title: not changed
Methods: minor changes
Results: peer‐reviewed paper: the maximum mean level of exposure (E) is 5.03% in the 15:2 RA scenario (on average) 12 days into the the simulation, with peak 3.18% presymptomatic (P) and 1.63% asympto‐matic (A) proportions of attendees at days 12 and 19 respectively. Meanwhile, peak mean exposure in scenario 7:3 ST occurs on day 2, with 2% attendees exposed to the disease and presymptomatic cases never exceeding that of the start of any simulation; very detailed sensitivity analyses added to main paper (suppose that was in supplementary material before parameter a is now αC (foot c)
Discussion: peer‐reviewed paper: In the most unfavorable scenario (15:2 RA), there were cumulatively 539 and 324 student‐days missed in high versus low‐transmission settings, respectively. Conversely, in the best scenario (7:3, siblings together), there were only 62 and 51 student‐days missed. 
  • More information on bias and limitations added to discussion

  • Simplifying assumptions added to model description

Rozhnova 2020 Rozhnova 2021 Title: not changed
Methods: minor changes
Results: peer‐reviewed paper:
  • Epidemic dynamics ‐ added paragraph: "The joint posterior density of the estimated parameters reveals strong positive and negative correlations between some of the parameters (Supplementary Fig. 5). For instance, the initial fraction of infected individuals is negatively correlated with the probability of transmission per contact and the hospitalization rate, as a small initial density can be compensated by a faster growth rate or a larger hospitalization rate. For that reason, the age‐specific hospitalization rates are all positively correlated. These correlations highlight the necessity of complementing the hospitalization time series data with seroprevalence data, even if the sample size of the latter is small. Without the seroprevalence data many parameters would be difficult to identify."

  • School and non‐school‐based measures ‐ rephrased paragraph: "For other (non‐school‐related) contacts in society in general we assumed that (1) the number of contacts increased after April 2020 (full lockdown) but was lower than before the pandemic, and that (2) reduction in probability of transmission per contact due to mask wearing and hygiene measures was lower in August as compared to April (due to decreased adherence to measures. The starting point of our analyses is an effective reproduction number of 1.31 (95% CrI 1.15–2.07) in accordance with the state of the Dutch pandemic in August 2020 (Supplementary Fig. 4c). Figure 6a demonstrates that in August 2020 other contacts in society in general would have to be reduced by at about 60% to bring the effective reproduction number to 1 (if school‐related contacts do not change))." (versus "For the non‐school related contacts we assumed that 1) the number of contacts increased after April 2020 (full lockdown) but was lower than before the pandemic, and that 2) the transmission probability per contact was lower due to general physical distancing and hygiene measures. The starting point of our analyses is an effective reproduction number of 1.31 (95% CrI 1.15—2.07) in accordance with the situation in August 2020 (Figure S4 C). Specifically, to achieve Re = 1.31 we fixed ζ2 at 0.67 (decrease in adherence to contact‐reduction measures in August as compared to April, when ζ1 is estimated at 0.51) and g at 0.5 (half‐way in the relaxation of non‐school contacts). Assuming the state of the Dutch pandemic in August 2020, Figure 6a demonstrates that non‐school related contacts would have to be reduced by at least 50% to bring the effective reproduction number to 1 (if school related contacts do not change.")


Discussion: peer‐reviewed paper:
  • Added paragaph: "To our knowledge, our modeling study is the first that uses this method to address the role of school‐based contacts in the transmission of SARS‐CoV‐2. Previous studies (e.g. refs. 21–25) used individual‐based or network models that were not fit to epidemiological data using formal statistical procedures. Due to uncertainties in key model parameters, predictions of these models vary widely."

  • Added paragaph: "Therefore, more children may have had an infection than indicated by the seroprevalence survey because the proportion of asymptomatic in children is believed to be high. As a consequence, our study potentially underestimates the role of children in transmission."

Vlachos 2020 Vlachos 2021 Title: changed
Methods: minor changes
Results:
  • Robustness: "Excluding covariates (except age and sex) in SI Appendix, Table S3 leads to a reduction in the esti‐ mates for parents [OLS 1.01, SE 0.43]." (versus OLS 0.91, SE 0.43 in preprint)

  • Robustness: "The OLS estimates with controls [1.09, SE 0.42] and when only controlling for age and sex [1.02, SE 0.42] are similar to those for the main sample. ORs for both samples of parents are similar when only controlling for age and when excluding all controls (SI Appendix, Fig. S4). SI Appendix, Fig. S5 shows the ORs including all controls for the main sample (SI Appendix, Fig. S5A) as well as when non‐EU migrants are included (SI Appendix, Fig. S5B). 2)" (versus "The OLS estimates with controls [1.09, se 0.42] and without controls [0.90, se 0.42] are similar to those for the main sample" in preprint)


Discussion: minor changes
Zhang 2020 Zhang 2021 Title: not changed
Abstract: minor changes
Methods: minor changes
Results: more info added here but no change to numerical results
Discussion: they added some limitations to their modelling approach ("In particular, it is possible that the difference in mixing patterns observed in the prepandemic, outbreak, and post‐lockdown phase would be less marked for symptomatic individuals (especially for severe ones). Therefore, our estimates of SARS‐CoV‐2 transmission in the post‐lockdown phase may be slightly underestimated.")