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SARS-CoV-2 Omicron VOC Transmission in Danish

Households

Frederik Plesner Lyngse1,2,3,∗, Laust Hvas Mortensen4,5, Matthew J. Denwood6,

Lasse Engbo Christiansen7, Camilla Holten Møller3, Robert Leo Skov3,

Katja Spiess3, Anders Fomsgaard3, Maria Magdalena Lassaunière3,

Morten Rasmussen3, Marc Stegger8, Claus Nielsen3,

Raphael Niklaus Sieber8, Arieh Sierra Cohen3, Frederik Trier Møller3,

Maria Overvad3, Kåre Mølbak3, Tyra Grove Krause3, Carsten Thure Kirkeby6

December 22, 2021

∗Correspondence to Frederik Plesner Lyngse, [email protected]. Affiliations: 1Department of Economics & Center for Economic Behaviour and Inequality, University of Copenhagen, Copenhagen, Denmark; 2Danish Ministry of Health, Copenhagen, Denmark; 3Statens Serum Institut, Copenhagen, Denmark; 4Statistics Denmark; 5Department of Public Health, Faculty of Health and Medical Sciences, University of Copenhagen; 6Department of Veterinary and Animal Sciences, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark. 7Department of Applied Mathematics and Computer Science, Dynamical Systems, Technical University of Denmark, Kgs. Lyngby, Denmark.; 8Department of Bacteria, Parasites and Fungi, Statens Serum Institut, Copenhagen, Denmark

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1 Abstract

The Omicron variant of concern (VOC) is a rapidly spreading variant of SARS-CoV-2

that is likely to overtake the previously dominant Delta VOC in many countries by the

end of 2021.

We estimated the transmission dynamics following the spread of Omicron VOC within

Danish households during December 2021. We used data from Danish registers to estimate

the household secondary attack rate (SAR).

Among 11,937 households (2,225 with the Omicron VOC), we identified 6,397 secondary

infections during a 1-7 day follow-up period. The SAR was 31% and 21% in households

with the Omicron and Delta VOC, respectively. We found an increased transmission

for unvaccinated individuals, and a reduced transmission for booster-vaccinated individ-

uals, compared to fully vaccinated individuals. Comparing households infected with the

Omicron to Delta VOC, we found an 1.17 (95%-CI: 0.99-1.38) times higher SAR for un-

vaccinated, 2.61 times (95%-CI: 2.34-2.90) higher for fully vaccinated and 3.66 (95%-CI:

2.65-5.05) times higher for booster-vaccinated individuals, demonstrating strong evidence

of immune evasiveness of the Omicron VOC.

Our findings confirm that the rapid spread of the Omicron VOC primarily can be ascribed

to the immune evasiveness rather than an inherent increase in the basic transmissibil-

ity.

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2 Introduction

The SARS-CoV-2 variant B.1.1.529, which is referred to as the Omicron variant of concern

(VOC), has overtaken the Delta VOC in South Africa and has spread rapidly to at least 28

countries countries in Europe (7), Asia, the Middle East and South America (9; 17). The

Omicron VOC has been reported to be three to six times as infectious as previous variants

(4), with a short doubling time (11), including early estimates from countries with a high

vaccination coverage indicating doubling times of 1.8 days (UK), 1.6 days (Denmark), 2.4

days (Scotland) and 2.0 days (United States) (26). Transmission of the Omicron VOC

has been high among individuals being fully vaccinated against SARS-CoV-2 infection as

well as among individuals with a history of COVID-19 infection (19).

A current concern worldwide is that the Omicron VOC is able to evade immunity induced

by the currently used vaccines, and a preliminary meta-analysis of neutralization studies

indicated that the vaccine effectiveness is reduced to around 40% against symptoms and

to 80% against severe disease, but that the effect for booster vaccinations is at 86% and

98%, respectively (12). These results are supported by laboratory studies establishing a

markedly reduced elimination of the Omicron VOC by neutralizing antibodies, indicating

that the vaccination effectiveness with Pfizer-Biontech against infection is only at 35%

for the Omicron VOC (5). This was corroborated by another in vitro study reporting an

8.4-fold reduction in neutralization for the Omicron VOC vs. the PV-D614G reference

strain, whereas there was only a 1.6-fold reduction in neutralization for the Delta VOC

(27). Therefore, the advantage of the Omicron VOC seems to be a combination of high

transmissibility and increased immune evading abilities.

Studies on the transmission of the Omicron VOC are yet sparse and a critical prerequisite

for effective control of this variant worldwide (3). In particular, it is important to clarify

whether the growth advantage can be ascribed to immune evasiveness, i.e., a higher pro-

portion of vaccinated or previously infected individuals being susceptible to infection, an

increased inherent transmissibility for this variant, or both.

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The aim of the present study is to investigate the household transmission of the Omicron

VOC. Specifically, we address the following questions: 1) Is the secondary attack rate

higher for the Omicron VOC than for the Delta VOC? 2) Does the Omicron VOC show a

higher immune evasiveness relative to the Delta VOC? 3) Is booster vaccination effective

for reducing transmission?

3 Data and Methods

3.1 Study design and participants

Since July 2021, the Delta VOC has been the dominant variant in Denmark. The

first Danish case infected with the Omicron VOC was detected on 22nd November 2021

(Danish Covid-19 Genome Consortium, DCC), and community transmission was deter-

mined to be present by late November 2021. On 8th December, Danish authorities dis-

continued intensive contact tracing of close contacts for cases specifically infected with the

Omicron VOC. We therefore started the study period on 9th December 2021 when cases

of both variants were treated approximately equally, thus reducing bias from intensified

contact tracing and active case finding of the Omicron VOC that was implemented shortly

after it’s discovery in Denmark (24). The end of the inclusion period for primary cases

was set at 12th December to balance the inclusion of enough cases for proper estimation

and early dissemination of the results. Potential secondary cases were followed up to 7

days after, i.e., until 19th December 2021 to allow for test results to be obtained. We

obtained the last test results on 21st December.

We used Danish register data for this study. All individuals in Denmark have a unique

identification number, enabling cross linking between administrative registers. Using this,

we obtained individual level information on home address, data on all antigen and RT-

PCR tests for SARS-CoV-2 from the Danish Microbiology Database (MiBa; (20)), and

records in the Danish Vaccination Register (13).

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Households were defined based on residential addresses. We included households with

2-6 members to exclude care facilities and other places, where many individuals share

the same address. If two individuals tested positive on the same day, we excluded these

households from the data, to ensure proper identification of the primary case within each

household.

We defined a primary case as the first individual within a household to test positive

with an RT-PCR test within the study period. We followed all tests of other household

members in the study period. A positive secondary case was defined by either a positive

RT-PCR test or a positive antigen test (10). Almost all samples that tested positive with

RT-PCR were tested with Variant PCR to determine the VOC (21) (see Appendix section

6.2). Based on the variant PCR test result of the primary case, we classified households

into households with either the Omicron or the Delta VOC. The Delta VOC has been

the dominating variant in Denmark since early July 2021, accounting for approximately

100% of all positive RT-PCR samples August-November 2021 (23).

We classified individuals by vaccination status into three groups: i) unvaccinated; ii)

fully vaccinated (defined by the vaccine used, Comirnaty (Pfizer/BioNTech): 7 days after

second dose; Vaxzevria (AstraZeneca): 15 days after second dose; Spikevax (Moderna):

14 days after second dose; Janssen (Johnson & Johnson): 14 days after vaccination, and

14 days after the second dose for cross vaccinated individuals) or 14 days after previous

infection; or iii) booster-vaccinated (defined by 7 days after the booster vaccination, (16;

2)). Partially vaccinated individuals were regarded as unvaccinated in this study. By 22nd

December 2021, of all vaccinated individuals, 85% were vaccinated with Comirnaty, 14%

with Spikevax, 1% with Janssen, and approximately 0% with AstraZeneca (22).

3.2 Statistical analyses

We defined the secondary attack rate (SAR) within households as the proportion of po-

tential secondary cases within the same household that tested positive between 1-7 days

following the positive test of the primary case within the household (15). Adjusted odds

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ratios (OR) were estimated from multivariable logistic regression models fit to the binary

outcome of test status of each potential secondary case, with the primary explanatory

variable reflecting the strain type in the household (Omicron vs. Delta VOC) and po-

tentially confounding variables of age and sex of the primary case, age and sex of the

potential secondary case, and household size (2-6 individuals). To test if vaccine sta-

tus conferred differential protection against the Omicron and Delta VOC, we included

an interaction term between vaccination status of primary and potential secondary cases

and the variant. Standard errors were adjusted to control for clustering at the household

level.

We have conducted a number of supplementary analyses to support the main analysis.

We re-analysed each strata of the data separately using another set of logistic regression

models (see appendix 7.4). To examine the potential mediating role of viral load of

primary cases infected with the Omicron VOC relative to the Delta VOC, we plotted

the distributions of Ct values for each variant (appendix Figure 3). We also examined

the extent to which the Ct value of the primary case could explain the difference in

transmission between the variants (see appendix Table 8). Our study relies on Variant

PCR testing to determine if each primary case was Delta or Omicron. We estimated the

intra-household correlation of variants, i.e., the probability that the positive secondary

case was infected with the same variant as the primary case. To investigate if there

was bias in the selection of samples for Variant PCR, we investigated the probability of

sampling for Variant PCR by sample Ct value and age. Moreover, we tested the robustness

of potential secondary cases being tested and testing positive by only using RT-PCR tests,

which are more sensitive.

3.3 Ethical statement

This study was conducted using data from national registers only. According to Dan-

ish law, ethics approval is not needed for this type of research. All data management

and analyses were carried out on the Danish Health Data Authority’s restricted research

servers with project number FSEID-00004942. The study only contains aggregated results

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and no personal data. The study is, therefore, not covered by the European General Data

Protection Regulation (GDPR).

3.4 Data availability

The data used in this study are available under restricted access due to Danish data

protection legislation. The data are available for research upon reasonable request to The

Danish Health Data Authority and Statens Serum Institut and within the framework of

the Danish data protection legislation and any required permission from Authorities. We

performed no data collection or sequencing specifically for this study.

4 Results

A total of 2,225 primary cases with the Omicron VOC and 9,712 primary cases with the

Delta VOC were included (Table 1). The SAR was 31% in households with the Omicron

VOC and 21% in households with the Delta VOC. Generally, the estimated SAR was

higher for the Omicron VOC than for the Delta VOC, for all age groups. Unvaccinated

potential secondary cases experienced similar attack rates in households with the Omicron

VOC and the Delta VOC (29% and 28%, respectively), while fully vaccinated individuals

experienced secondary attack rates of 32% in household with the Omicron VOC and

19% in households with the Delta VOC. For booster-vaccinated individuals, Omicron

was associated with a SAR of 25%, while the corresponding estimate for Delta was only

11%.

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Table 1: Summary Statistics

Omicron Delta Primary Potential Positive SAR Primary Potential Positive SAR

Cases Secondary Secondary (%) Cases Secondary Secondary (%) Cases Cases Cases Cases

Total 2,225 4,718 1,474 31 9,712 23,156 4,923 21

Sex Male 1,149 2,266 665 29 4,987 11,372 2,317 20 Female 1,076 2,452 809 33 4,725 11,784 2,606 22

Age 0-10 130 709 197 28 2,417 4,615 1,134 25 10-20 454 917 215 23 1,884 4,466 652 15 20-30 723 975 281 29 1,242 2,026 325 16 30-40 298 508 219 43 988 3,867 934 24 40-50 282 780 268 34 1,253 4,893 1,053 22 50-60 238 633 226 36 1,120 2,106 498 24 60-70 78 134 48 36 573 794 256 32 70+ 22 62 20 32 235 389 71 18

Household size 2 865 865 362 42 2,941 2,941 833 28 3 543 1,086 341 31 2,062 4,124 866 21 4 558 1,674 489 29 3,068 9,204 1,933 21 5 202 808 229 28 1,318 5,272 1,033 20 6 57 285 53 19 323 1,615 258 16

Immunity Unvaccinated 368 1,156 340 29 4,629 7,410 2,044 28 Fully vaccinated / previous infection 1,752 3,257 1,057 32 4,797 14,239 2,714 19 Booster-vaccinated 105 305 77 25 286 1,507 165 11

Notes: The secondary attack rate (SAR) is expressed as a percentage (%). Summary statistics based on primary cases are shown separately from summary statistics on potential secondary cases, positive secondary cases and SAR.

We found that the cumulative probability of potential secondary cases to be tested at

least once increased from 33-41% to around 87-89% at 7 days after the primary case

tested positive (Figure 1, panel a). The probability was higher when the primary case

was infected with the Delta VOC compared to the Omicron VOC. The probability of

potential secondary cases being tested twice increased from 9% to 69-74% at 7 days after

the primary case tested positive. The probability of potential secondary cases testing

positive increased from 3-4% on day 1, to 21% and 31% on day 7, when the primary

case was infected with the Delta VOC and Omicron VOC, respectively (Figure 1, panel

b).

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Figure 1: Probability of being tested and testing positive

(a) Probability of testing

81 84

86 87 87

83 86 88 89 89

62 67 69

0 1 2 3 4 5 6 7

Days since primary case

100

P ro

po rt

io n

(% )

Tested twice - Delta Tested twice - Omicron Tested once - Delta Tested once - Omicron

(b) Probability of testing positive

0 1 2 3 4 5 6 7

Days since primary case

S ec

on da

ry A

tta ck

R at

e (%

)

Delta Omicron

Variant

Notes: Panel (a) shows the probability of potential secondary cases being tested after a primary case has been identified within the household. Panel (b) shows the probability of potential secondary cases that test positive subsequently to a primary case being identified within the household. Note that the latter is not conditional on being tested, i.e. the denominator contains test negative individuals and untested individuals. The x axes shows the days since the primary case tested positive, and the y axes shows the proportion of individuals either being tested (a) or testing positive (b) with either antigen or RT-PCR tests, based on the variant of the primary case. The SAR for each day relative to the primary case can be read directly from panel (b). For example, the SAR on day 7 is 31% and 21%, whereas the SAR on day 4 is 24% and 15%. The shaded areas show the 95% confidence bands clustered on the household level. See appendix Figure 5 for the same two panels, only using RT-PCR tests.

The effect of vaccination on susceptibility and transmissibility of SARS-CoV-2 within

households is shown in Table 2. The estimates of susceptibility by vaccine status were

stratified by variant because we observed an interaction between variant and vaccination

status of the potential secondary cases (p < 0.001). After adjustment for confounders,

we found that in households with the Delta VOC, the OR of infection was 2.31 (95%

confidence interval (CI) 2.09-2.55) for unvaccinated individuals and 0.38 (CI: 0.32-0.46)

for booster-vaccinated individuals when compared to fully vaccinated potential secondary

cases. For households with the Omicron VOC, the corresponding OR for infection for

unvaccinated individuals was 1.04 (CI: 0.87-1.24) and 0.54 (CI: 0.40-0.71) for booster-

vaccinated individuals. When considering the vaccine status of primary cases, i.e. trans-

missibility, we observed no difference in the OR of infection between households with the

Omicron and Delta VOC. An unvaccinated primary case was associated with an OR of

1.41 (CI: 1.27-1.57) for potential secondary cases compared to fully vaccinated primary

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cases, while a booster-vaccinated primary case was associated with a decreased OR of

0.72 (CI: 0.56-0.92).

Table 2: Effect of Vaccination

Susceptibility Transmissibility Omicron households Delta households All households

Unvaccinated 1.04 2.31 1.41 (0.87-1.24) (2.09-2.55) (1.27-1.57)

Fully vaccinated ref ref ref (.) (.) (.)

Booster-vaccinated 0.54 0.38 0.72 (0.40-0.71) (0.32-0.46) (0.56-0.92)

Number of observations 27,874 27,874 27,874 Number of households 11,937 11,937 11,937

Notes: This table shows odds ratio estimates for susceptibility and transmissibility by vaccination status. Column 1 shows the susceptibility based on the vaccination status of the potential secondary case, condi- tional on being in a household infected with the Omicron VOC. Column 2 shows the susceptibility based on the vaccination status of the potential secondary case, conditional on being in a household infected with the Delta VOC. Column 3 shows the transmissibility based on the vaccination status of the primary case, unconditional on the variant in the household. Note, all estimates are from the same model, but with a different reference category across column 1-3. The estimates are adjusted for age and sex of the primary case, age and sex of the potential secondary case, and size of the household. The estimates are furthermore adjusted for vaccine status of the potential secondary case interacted with the household variant, and the vaccine status of the primary case. 95% confidence intervals are shown in parentheses. Standard errors are clustered on the household level. The odds ratio estimates for the full model are presented in Appendix Table 8, column I.

The relative difference in transmission between the Omicron and Delta variants when

comparing potential secondary cases with the same vaccine status is shown in Table 3.

For unvaccinated individuals, an OR of 1.17 (CI: 0.99-1.38) was estimated for households

with the Omicron VOC compared to households with the Delta VOC. For fully vaccinated

individuals, the OR was 2.61 (CI: 2.34-2.90) for households with the Omicron VOC, and

for booster-vaccinated individuals the OR was 3.66 (CI: 2.65-5.05). This significant change

in OR for fully vaccinated and booster-vaccinated individuals represents strong evidence

of immune evasion of the Omicron VOC.

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Table 3: Relative effect of the Omicron VOC

Unvaccinated Fully vaccinated Booster-vaccinated Omicron households 1.17 2.61 3.66

(0.99-1.38) (2.34-2.90) (2.65-5.05) Delta households ref ref ref

(.) (.) (.) Number of observations 27,874 27,874 27,874 Number of households 11,937 11,937 11,937

Notes: This table shows odds ratio estimates for the effect of living in a household infected with the Omicron VOC relative to the Delta VOC. Column 1 shows the relative transmission of the Omicron VOC, conditional on being unvaccinated. Column 2 shows the relative transmission of the Omicron VOC, conditional on being fully vaccinated. Column 3 shows the relative transmission of the Omicron VOC, conditional on being booster-vaccinated. Note, all estimates are from the same model, but with a different reference category across column 1-3. The estimates are adjusted for age and sex of the primary case, age and sex of the potential secondary case, and size of the household. The estimates are furthermore adjusted for vaccine status of the potential secondary case interacted with the household variant, and the vaccine status of the primary case. 95% confidence intervals are shown in parentheses. Standard errors are clustered on the household level. The odds ratio estimates for the full model are presented in Appendix Table 8, column I.

We compared the Ct values of primary cases with the Omicron VOC and the Delta VOC

(Appendix 7, Figure 3). The distribution of Ct values for cases with the Omicron VOC

were slightly skewed to the left compared to cases with the Delta VOC, but the median

values (27.24 and 28.29, respectively) did not differ substantially. Adjustment for Ct

values of the primary cases did not materially alter the findings, suggesting that the

difference between the Omicron and Delta VOC transmission is not due to differences in

viral load in the primary case (appendix Table 8). Similarly, the distribution of time since

last vaccination/booster/infection among positive secondary cases were approximately the

same across the two variants (appendix Figure 4). However, these analyses are limited

by the fact that vaccine roll out in Denmark is largely determined by age, which makes it

difficult to estimate true associations for variables that are also correlated with age.

The probability that a sample was selected for Variant PCR was stable across Ct value,

varying between 97% and 100% (Appendix 7, Figure 2). Selection for Variant PCR

was also similar across age groups, varying between 95% and 99%. The Variant PCR

was validated with high quality whole genome sequencing (WGS) data, and showed an

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estimated false negative rate of 0.06% and a false positive rate of 1.15% (Appendix section

6.3).

We found an intra-household correlation between primary case and secondary case variants

of 98.0% and 97.7% for households with primary cases infected with the Omicron VOC

and the Delta VOC, respectively (Appendix section 7.2). This supports the assumption

that subsequent infections within the same household are likely to be associated with the

same variant as was identified for the primary case.

Finally, misclassification of primary and secondary cases is also a potential concern. It is

not given that the index case is actually also the case with the first positive RT-PCR test.

However, we believe that this potential bias would impact both the Delta and Omicron

VOC transmission estimates equally. Figure 1, panel b, shows the proportion of secondary

cases testing positive on each day after the primary case. One day after, 3% and 4% have

tested positive, two days after, 7% and 12% have tested positive. These cases could

have been misclassified as secondary cases, instead of primary cases. To investigate the

sensitivity of our results for this potential misclassification, we estimated our regression

model including only secondary cases that tested positive on day 2-7 and on day 3-7

(Appendix Table 9).

5 Discussion and Conclusion

Our results show that the Omicron VOC is generally 2.7-3.7 times more infectious than

the Delta VOC among vaccinated individuals (Table 3). This observation is in line with

data from (18), which estimated that 19% of Omicron VOC primary cases in households

in the UK resulted in at least one other infection within the household, compared to only

8.3% of those associated with the Delta VOC. Furthermore, we show that fully vaccinated

and booster-vaccinated individuals are generally less susceptible to infection compared to

unvaccinated individuals (Table 2). We also show that booster-vaccinated individuals

generally had a reduced transmissibility (OR: 0.72, CI: 0.56-0.92), and that unvaccinated

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individuals had a higher transmissibility (OR: 1.41, CI: 1.27-1.57), compared to fully

vaccinated individuals.

Surprisingly, we observed no significant difference between the SAR of Omicron versus

Delta among unvaccinated individuals (Table 3). This indicates that the increased trans-

missibility of the Omicron VOC primarily can be ascribed to immune evasion rather than

an inherent increase in the basic transmissibility. If this observation can be confirmed by

independent studies, it has important ramifications for the understanding of the current

challenges for control of the epidemic. Our data indicate that the non-pharmaceutical in-

terventions that were used to control the previous variants of SARS-CoV-2 are also likely

to be effective against the Omicron VOC. On the other hand, although we showed that

booster vaccines did offer some protection against household transmission, the reduced

level of protection means that vaccination is less likely to be sufficient to curb transmis-

sion within a population. Furthermore, the duration of the protective effect is currently

unknown, and the rapidly waning effectiveness of the second dose against the Omicron

VOC as well as data from neutralization assays (14; 8) do raise some concerns about the

longevity of the booster response. This means that the current vaccines are unlikely to

mitigate the spread of the Omicron VOC to the extent that has been achieved for previ-

ous variants on the long term. We therefore suggest that adapted or improved vaccines

may be necessary to mitigate the spread of the Omicron VOC. However, both a primary

series and a booster dose is likely to play an important role in reducing transmission on a

short term and modifying the outcome of infection by reducing severity. We were unable

to address this question as detailed clinical data were not available in our registries, and

in any case the relatively short follow-up time precludes a thorough investigation of any

subsequent hospitalisations and deaths.

(1) note that the existing circulating immunity within a country is of major importance

in limiting the severity of the epidemic with the Omicron VOC. We found that booster-

vaccinated individuals in Omicron VOC households had an OR of 0.54 (CI: 0.40-0.71)

compared to fully vaccinated individuals (Table 2). This shows that booster vaccination

is effective for reducing household transmission of the Omicron VOC. However, this effect

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is also affected by other factors such as waning immunity for fully vaccinated individuals,

since they were typically vaccinated much earlier compared to the dose received as a

booster vaccination. For the Delta VOC, the booster vaccination had an OR of 0.38

(CI: 0.32-0.46) compared to fully vaccinated individuals, showing the high effectiveness of

booster vaccinations against the Delta VOC. These estimates are important for decision

makers worldwide, as they can inform models for predicting the epidemic and thus for

balancing the most appropriate level of restrictions to control transmission in different

situations.

There are some potential biases in this study. Firstly, in this initial phase, the spread of the

Omicron VOC was characterized by spreading events, and has therefore not yet reached

an even distribution throughout the population (3). We found that a large proportion

of the Omicron VOC cases were aged 20-30 years, and therefore different from the age

distribution of Delta cases (Table 1). Furthermore, the Omicron VOC is mainly found in

households with 2 members, whereas the Delta VOC is mainly found in households with

4 members. This could potentially impact the comparability of our estimates for the two

the variants. However, our results are robust, when we exclude households with a primary

case <10 years and when we only include 2-person households (Appendix Table 8).

Recently, self testing kits have become widely available for purchase in Denmark. This

could influence the results, for instance if individuals that self-test at home refrain from

also being tested in public testing facilities, meaning that their test results are not regis-

tered in the national databases. However, the probability of being tested was very similar

between RT-PCR and any test (Figure 1 and Appendix Figure 5), and consequently most

positive antigen tests were confirmed with a positive RT-PCR test, so we assume that

has likely also been the case for positive self-tests as well. Moreover, we believe that this

potential bias will impact both the Delta and the Omicron VOC transmission estimates

equally.

There are also a number of other confounding variables that might lead to biases within

our study. Vaccines are not randomly distributed within the population, so immunocom-

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promised and other vulnerable individuals are more likely to have had access to a booster

vaccine in particular. To some extent, this has been addressed by including age as an

explanatory variable in the models, but it was not possible to include information on

underlying risk conditions, so this information is incomplete. Similarly, there are likely

underlying behavioural drivers for an individual being unvaccinated, which are likely to

confound with other risky behaviours that might be expected to increase both transmis-

sion and susceptibility to infection (e.g. poor use of face masks, reduced attention to

hygiene). The use of registry data limits our inference to associations between transmis-

sion/susceptibility and vaccination status of individuals, where part of the association is

due to general characteristics of the individuals themselves rather than their vaccination

status. However, a key point of our study is that these biases are non-differential with re-

spect to variant, i.e. they would be expected to affect transmission of both the Delta and

Omicron VOC identically because risky behaviours and/or underlying health concerns

should affect both variants equally. Consequently, although the associations between vac-

cination status and transmission for each variant are likely to each be susceptible to bias,

we believe that any such bias is non-differential with respect to variant. Therefore, our

results concerning the relatively higher transmissibility of the Omicron vs. Delta VOC

for vaccinated individuals should be robust to these potential biases.

The SAR was found to be higher for the Omicron VOC than for the Delta VOC across

all age groups (Table 1). Notably, the SAR for individuals aged 70+ years was 32% for

the Omicron VOC compared to only 18% for the Delta VOC. This has implications for

e.g. care facilities, highlighting the need for increased protection against transmission,

now that the Omicron VOC will likely overtake the Delta VOC in many countries.

To conclude, we found an increased susceptibility for unvaccinated individuals, and a

reduced susceptibility for booster-vaccinated individuals, compared to fully vaccinated

individuals in households infected with the Delta VOC. Additionally, we found a reduced

susceptibility for booster-vaccinated individuals in households infected with the Omicron

VOC. Furthermore, we found an increased transmissibility from unvaccinated individu-

als, and a reduced transmissibility from booster-vaccinated individuals, compared to fully

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vaccinated individuals. Lastly, we we found a general higher transmission in households

infected with the Omicron VOC relative to the Delta for both unvaccinated, fully vacci-

nated and booster-vaccinated individuals. The Omicron VOC showed immune evasiveness

for fully vaccinated and booster-vaccinated individuals. Our results confirm that booster

vaccination has the potential to reduce Omicron VOC transmission in households, al-

though vaccination as a strategy for epidemic control is increasingly challenged by the

immune evasiveness of the Omicron VOC.

Comparing Omicron VOC to Delta VOC, we found an 1.17 (95%-CI: 0.99-1.38) times

higher SAR for unvaccinated, 2.61 times (95%-CI: 2.34-2.90) higher for fully vaccinated

and 3.66 (95%-CI: 2.65-5.05) times higher for booster-vaccinated individuals, demonstrat-

ing strong evidence of immune evasiveness of the Omicron VOC.

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Aknowledgements

We thank Statens Serum Institut and The Danish Health Data Authority for collecting

and providing access to data access. We also thank the rest of the Expert Group for

Mathematical Modelling of COVID-19 at Statens Serum Institut for helpful discussions.

The authors wish to thank the Danish Covid-19 Genome Consortium for genotyping

SARS-CoV-2 positive samples.

Funding

Frederik Plesner Lyngse: Independent Research Fund Denmark (Grant no. 9061-00035B.);

Novo Nordisk Foundation (grant no. NNF17OC0026542); the Danish National Research

Foundation through its grant (DNRF-134) to the Center for Economic Behavior and In-

equality (CEBI) at the University of Copenhagen. Laust Hvas Mortensen is supported

in part by grants from the Novo Nordisk Foundation (grant no. NNF17OC0027594,

NNF17OC0027812). Matthew Denwood, Lasse Christiansen and Carsten Kirkeby receive

funding from Statens Serum Institut as part of the Expert Group for Mathematical Mod-

elling of COVID-19.

Contributions

FPL performed all data analyses. LEC, MD, FPL, LHM and CTK designed the study

and devised the statistical analysis. FPL, CTK and LHM wrote the first draft. All other

authors contributed to the discussion, revised the first draft and approved the submitted

version.

Competing interests

The authors declare no competing interests.

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Supplementary Appendix

6 Background

This section provides some background information in order to better understand the

circumstances underlying our study. The results build on all data available in Denmark,

i.e., not restricted to our study sample.

6.1 Time to test result

Denmark provides free testing with both antigen and RT-PCR tests. Antigen tests provide

a quick test result (positive/negative) with a median time from sample to result of less

than 30 minutes (Table 4). All positive antigen tests are recommended to be confirmed

with an RT-PCR test. RT-PCR tests are more sensitive (25), but also require a longer

time before the result is known. The median time is approximately 24 hours (Table 5).

Only samples from positive RT-PCR tests are selected for Variant PCR and whole genome

sequencing.

Table 4: Time to test results, antigen tests, minutes

Sample Time to test result, minutes Number date P5 Q1 Median Q3 P95 of tests

09DEC21 Thursday 10 16 22 27 33 245,056 10DEC21 Friday 9 19 24 30 37 213,060 11DEC21 Saturday 13 20 24 30 35 155,857 12DEC21 Sunday 11 16 21 26 32 167,670 13DEC21 Monday 8 16 22 27 36 232,659 14DEC21 Tuesday 9 20 25 30 38 225,253 15DEC21 Wednesday 8 21 26 32 41 219,448 16DEC21 Thursday 10 22 29 35 45 258,423 17DEC21 Friday 10 29 34 39 47 236,536 18DEC21 Saturday 17 29 34 38 47 175,514 19DEC21 Sunday 10 27 30 32 35 153,311

Notes: This table provides summary statistics on the time from sampling to the test result (posi- tive/negative). P5 = 5th percentile, Q1 = 1st quartile, Q3 = 3rd quartile, P95 = 95th percentile.

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Table 5: Time to test results, RT-PCR tests, hours

Sample Time to test result, hours Number of date P5 Q1 Median Q3 P95 PCR tests

09DEC21 Thursday 16 20 22 28 41 268,357 10DEC21 Friday 16 20 23 28 41 274,827 11DEC21 Saturday 16 20 24 29 40 178,176 12DEC21 Sunday 16 20 24 28 37 178,066 13DEC21 Monday 16 20 23 28 41 261,215 14DEC21 Tuesday 16 20 22 27 40 254,107 15DEC21 Wednesday 16 20 24 29 42 224,897 16DEC21 Thursday 16 20 24 29 42 255,183 17DEC21 Friday 16 20 24 29 45 273,041 18DEC21 Saturday 16 21 25 29 42 221,572 19DEC21 Sunday 16 20 24 29 39 220,871

Notes: This table provides summary statistics on the time from sampling to the test result (posi- tive/negative). P5 = 5th percentile, Q1 = 1st quartile, Q3 = 3rd quartile, P95 = 95th percentile.

6.2 Probability of sampling for Variant PCR

This subsection provides details on the sampling probability for variant PCR.

Figure 2 shows the proportion of positive RT-PCR samples selected for Variant PCR

testing and the proportion testing positive with the Omicron VOC. There was no clear

selection bias in the probability that a positive RT-PCR sample was selected for Variant

PCR testing (purple)—neither across sample Ct value (panel a) nor across age (panel b).

There was a higher proportion of cases aged 15-30 years that tested positive with the

Omicron VOC (green, panel b).

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Figure 2: Probability of sampling for Variant PCR

(a) Ct value

96 97 100 98

9898 97 98 98 98 96 97 97

99 9797 98 98 100100

17 15

17 20

18 1817 18

16 15 1514 13 12 13

100

P ro

po rt

io n

(% )

18 20 22 24 26 28 30 32 34 36 38

Ct Value

With Omicron Selected for variant PCR

(b) Age

98 97 98 97 97 97 98 97 97 98 98 98 98 99 99 98 98 95

6 5

14 14 15

17 15

13 10 9

5 5

100

P ro

po rt

io n

(% )

0 10 20 30 40 50 60 70 80 90

Age, years

With Omicron Selected for variant PCR

Notes: This figure shows the proportion of positive RT-PCR samples selected (purple) for Variant PCR testing and the proportion testing positive (green) with the Omicron VOC. Panel (a) shows the selection by Ct value; panel (b) by age. Only positive RT-PCR tests from 9th-12th December 2021 performed by TestCenter Denmark are included. The shaded areas show the 95% confidence bands.

6.3 Robustness of Variant PCR results

This subsection provides additional results in order to examine the robustness of the

Variant PCR used to detect the Omicron VOC.

The Variant PCR was validated using the available high quality whole-genome sequencing

(WGS) data. The rate of false positives was estimated to 1.15% (18/1,567) (Table 6, panel

I). The rate of false negative PCR results was estimated to 0.06% (1/1,557) (Table 6, panel

II).

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Table 6: Validation of Variant PCR test using whole genome sequencing (WGS).

I. False positive rate Number of samples %

Confirmed by WGS No (false positive rate) 18 1.15 Yes 1,549 98.85 Total 1,567 100.00

II. False negative rate Number of samples %

Variant PCR result Omicron 1,549 99.49 Inconclusive 7 0.45 Delta (false negative rate) 1 0.06 Total 1,557 100.00

Notes: This table shows the estimates of the false positive rate and the false negative rate of the Variant PCR test, using whole genome sequencing (WGS). Panel I shows the number of Variant PCR tests that were confirmed (Yes) or not confirmed (No) using high quality whole-genome sequencing (WGS). The estimated false positive rate was 1.15% (18/1,567). Panel II shows the number of Variant PCR tests in samples corfirmed as the Omicron VOC using high quality whole-genome sequencing (WGS). The estimated false negative rate was 0.06% (1/1,557).

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7 Additional analyses

This section provides additional analyses in order to better understand our main re-

sults.

7.1 Viral load of primary cases

Figure 3 shows the density of sample Ct values of primary cases stratified by the Omicron

VOC and Delta VOC.

Figure 3: Density of Ct value

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

Ct Value

0.00

0.02

0.04

0.06

0.08

D en

si ty

( %

)

Delta Omicron

Variant

Notes: This figure shows the density of the sample Ct values of primary cases stratified by the Omicron and Delta VOC.

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7.2 Intra-household correlation of variants

In this subsection, we investigate the intra-household correlation of variants, i.e., the

probability that the primary and positive secondary cases are infected with the same

variant.

In households where the primary case was infected with the Omicron VOC, we found

1,160 positive secondary cases that also had a Variant PCR result (Table 7). Of these,

1,137 (98%) were also Omicron VOC and 23 (2%) were Delta VOC. Similarly, in house-

holds where the primary case was infected with the Delta VOC, we found 3,917 positive

secondary cases. Of these, 3,827 (98%) were also Delta and 90 (2%) were Omicron VOC.

The overall intra-household correlation of variants was 97.8 (CI: 97.3-98.3).

Table 7: Intra-household correlation of variants

I. Number of cases Primary case

Omicron Delta All Secondary Case Omicron 1,137 90 1,227 Delta 23 3,827 3,850 All 1,160 3,917 5,077

II. Regression estimates Primary case

Omicron Delta All Intra-household correlation (%) 98.0 97.7 97.8 (95%-CI) (97.2-98.9) (97.8-99.4) (97.3-98.3) Number of observations 1,160 3,917 5,077 Number of households 864 2,866 3,730

Notes: This table provides estimates of the intra-household correlation of variants, i.e., the probability that the primary and positive secondary cases are infected with the same variant. Panel I provides the number of observations. Panel II provides regression estimates. Standard errors are clustered on the household level.

7.3 Time since vaccination for positive secondary cases

Figure 4 shows the distribution of days since last vaccination/infection for positive sec-

ondary cases, stratified by the household VOC. We saw no clear evidence of difference

across the two distributions.

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Figure 4: Time since vaccination for positive secondary cases

0 50 100 150 200 250

Days since vaccination

0.0000

0.0025

0.0050

0.0075

0.0100

0.0125

0.0150

D en

si ty

( %

)

Delta Omicron

Variant

Notes: This figure shows the distribution of days since last vaccination/infection for positive secondary cases, stratified by the household VOC.

7.4 Robustness of main results

This subsection provides additional results in order to validate the robustness of the results

shown in the main paper.

Figure 5 shows the same as Figure 1, but only using RT-PCR tests (i.e. excluding antigen

tests).

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Figure 5: Probability of being tested and testing positive with an RT-PCR test

(a) Probability of testing

71 77

80 81

80 82 83 84

52 55

0 1 2 3 4 5 6 7

Days since primary case

100

P ro

po rt

io n

(% )

Tested twice - Delta Tested twice - Omicron Tested once - Delta Tested once - Omicron

(b) Probability of testing positive

0 1 2 3 4 5 6 7

Days since primary case

S ec

on da

ry A

tta ck

R at

e (%

)

Delta Omicron

Variant

Notes: This figure shows the same as Figure 1, but only including RT-PCR tests. Panel (a) shows the probability of potential secondary cases being tested after a primary case has been identified within the household. Panel (b) shows the probability of potential secondary cases that test positive subsequently to a primary case being identified within the household. Note that the latter is not conditional on being tested, i.e. the denominator contains test negative individuals and untested individuals. The x axes shows the days since the primary case tested positive, and the y axes shows the proportion of individuals either being tested (a) or testing positive (b) with an RT-PCR test, based on the variant of the primary case. The SAR for each day relative to the primary case can be read directly from panel (b). For example, the SAR on day 7 is 30% and 21%, whereas the SAR on day 4 is 23% and 14%. The shaded areas show the 95% confidence bands clustered on the household level.

Tables 8 and 9 show the results of logistic regression models fit to specific strata of the

data.

Column I of Table 8 shows the odds ratio estimates of our main specification, i.e., the

same as used in Table 2 and 3. Column II shows the odds ratio estimates, when excluding

households with a primary case <10 years. Column III shows the odds ratio estimates,

when only including 2-person households. Column IV shows the odds ratio estimates,

while adjusting for Ct value of the primary case.

In Table 9 we show the estimates, while restricting the inclusion criteria for positive

secondary cases. Column I shows the odds ratio estimates, including positive secondary

cases found on day 1-7, i.e, our main specification, also presented in Table 2 and 3.

Column II includes positive secondary cases found on day 2-7. Column III includes

positive secondary cases found on day 3-7.

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Table 8: Effect of Vaccination

I II III IV OR 95%-CI OR 95%-CI OR 95%-CI OR 95%-CI

Potential secondary case vaccination status Delta households Unvaccinated 2.32 (2.10-2.56) 2.27 (2.02-2.56) 2.01 (1.54-2.62) 2.44 (2.12-2.81) Fully vaccinated ref (.) ref (.) ref (.) ref (.) Booster-vaccinated 0.38 (0.32-0.45) 0.40 (0.33-0.50) 0.35 (0.26-0.47) 0.40 (0.32-0.52) Omicron households Unvaccinated 2.73 (2.29-3.26) 2.59 (2.14-3.13) 2.45 (1.50-4.00) 3.16 (2.47-4.05) Fully vaccinated 2.61 (2.34-2.90) 2.55 (2.28-2.86) 2.61 (2.13-3.19) 2.66 (2.29-3.09) Booster-vaccinated 1.39 (1.04-1.84) 1.33 (0.99-1.79) 1.50 (0.95-2.38) 1.11 (0.74-1.67)

Primary case vaccination status Unvaccinated 1.41 (1.27-1.57) 1.43 (1.29-1.59) 1.23 (0.97-1.54) 1.21 (1.05-1.41) Fully vaccinated ref (.) ref (.) ref (.) ref (.) Booster-vaccinated 0.72 (0.56-0.92) 0.71 (0.56-0.91) 0.72 (0.52-1.01) 0.58 (0.41-0.83)

Primary case age 0-10 1.28 (1.10-1.50) - - 0.89 (0.56-1.43) 1.52 (1.23-1.88) 10-20 1.04 (0.90-1.21) 1.09 (0.94-1.26) 1.00 (0.70-1.43) 1.01 (0.83-1.23) 20-30 ref (.) ref (.) ref (.) ref (.) 30-40 1.92 (1.65-2.25) 1.95 (1.66-2.28) 1.66 (1.21-2.27) 1.65 (1.33-2.04) 40-50 2.31 (1.98-2.70) 2.39 (2.05-2.79) 1.96 (1.41-2.75) 2.25 (1.83-2.77) 50-60 2.45 (2.09-2.87) 2.49 (2.13-2.92) 2.25 (1.69-2.98) 2.43 (1.96-3.02) 60-70 3.16 (2.54-3.94) 3.11 (2.50-3.88) 2.68 (1.92-3.74) 2.69 (1.97-3.68) 70+ 3.99 (2.76-5.75) 3.85 (2.67-5.55) 4.11 (2.53-6.68) 4.00 (2.36-6.77)

Potential secondary case age 0-10 0.82 (0.71-0.95) 0.83 (0.71-0.98) 0.38 (0.22-0.66) 0.81 (0.66-0.99) 10-20 0.70 (0.61-0.80) 0.66 (0.57-0.77) 0.50 (0.34-0.74) 0.72 (0.60-0.87) 20-30 ref (.) ref (.) ref (.) ref (.) 30-40 1.64 (1.44-1.88) 1.54 (1.31-1.79) 0.86 (0.63-1.17) 1.77 (1.46-2.13) 40-50 1.60 (1.40-1.82) 1.43 (1.24-1.65) 0.79 (0.56-1.11) 1.74 (1.44-2.09) 50-60 1.48 (1.29-1.71) 1.42 (1.23-1.65) 1.45 (1.10-1.92) 1.55 (1.28-1.89) 60-70 1.53 (1.25-1.87) 1.49 (1.21-1.83) 1.64 (1.18-2.28) 1.73 (1.32-2.28) 70+ 1.01 (0.75-1.37) 0.98 (0.72-1.35) 0.88 (0.56-1.38) 0.92 (0.60-1.42)

Household size 2 2.26 (1.85-2.75) 2.36 (1.86-3.00) - - 2.34 (1.79-3.05) 3 1.53 (1.26-1.86) 1.50 (1.19-1.90) - - 1.51 (1.16-1.95) 4 1.51 (1.25-1.82) 1.53 (1.21-1.94) - - 1.45 (1.13-1.87) 5 1.40 (1.15-1.70) 1.38 (1.08-1.78) - - 1.42 (1.09-1.86) 6 ref (.) ref (.) - - ref (.)

Primary case sex Male ref (.) ref (.) ref (.) ref (.) Female 0.99 (0.92-1.07) 1.03 (0.95-1.13) 1.08 (0.91-1.29) 0.97 (0.88-1.08)

Potential secondary case sex Male ref (.) ref (.) ref (.) ref (.) Female 1.14 (1.07-1.20) 1.15 (1.07-1.22) 1.33 (1.11-1.58) 1.10 (1.01-1.19)

Ct value 14-16 - - - - - - 1.53 (0.30-7.78) 16-18 - - - - - - 3.91 (1.75-8.71) 18-20 - - - - - - 3.16 (2.19-4.56) 20-22 - - - - - - 2.83 (2.09-3.83) 22-24 - - - - - - 2.12 (1.60-2.80) 24-26 - - - - - - 1.91 (1.45-2.52) 26-28 - - - - - - 1.59 (1.20-2.10) 28-30 - - - - - - 1.58 (1.19-2.10) 30-32 - - - - - - 1.28 (0.96-1.71) 32-34 - - - - - - 1.31 (0.98-1.77) 34-36 - - - - - - 1.48 (1.09-2.02) 36-38 - - - - - - ref (.) Number of observations 27,874 20,228 3,806 14,657 Number of households 11,937 9,390 3,806 6,242

Notes: Column I shows the odds ratio estimates of our main specification, i.e., the same as used in Table 2 and 3. Column II shows the odds ratio estimates, when excluding households with a primary case <10 years. Column III shows the odds ratio estimates, when only including 2-person households. Column IV shows the odds ratio estimates, while adjusting for Ct value of the primary case. 95%-Confidence interval in parentheses. Standard errors are clustered on the household level.30

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Table 9: Effect of Vaccination, sensitivity for days for including positive secondary cases

I II III Days including positive secondary cases 1-7 2-7 3-7

OR 95%-CI OR 95%-CI OR 95%-CI Potential secondary case vaccination status Delta households Unvaccinated 2.32 (2.10-2.56) 2.20 (1.99-2.45) 2.13 (1.90-2.38) Fully vaccinated ref (.) ref (.) ref (.) Booster-vaccinated 0.38 (0.32-0.45) 0.39 (0.33-0.47) 0.41 (0.34-0.51) Omicron households Unvaccinated 2.73 (2.29-3.26) 2.80 (2.34-3.35) 2.65 (2.17-3.24) Fully vaccinated 2.61 (2.34-2.90) 2.61 (2.33-2.92) 2.45 (2.17-2.78) Booster-vaccinated 1.39 (1.04-1.84) 1.40 (1.04-1.89) 1.19 (0.83-1.71)

Primary case vaccination status Unvaccinated 1.41 (1.27-1.57) 1.43 (1.28-1.59) 1.38 (1.23-1.55) Fully vaccinated ref (.) ref (.) ref (.) Booster-vaccinated 0.72 (0.56-0.92) 0.71 (0.55-0.93) 0.62 (0.47-0.83)

Primary case age 1.28 (1.10-1.50) 1.44 (1.22-1.69) 1.53 (1.29-1.82) 0-10 1.04 (0.90-1.21) 1.14 (0.98-1.33) 1.19 (1.01-1.41) 10-20 ref (.) ref (.) ref (.) 20-30 1.92 (1.65-2.25) 1.93 (1.64-2.28) 2.02 (1.69-2.42) 30-40 2.31 (1.98-2.70) 2.45 (2.08-2.88) 2.45 (2.05-2.93) 40-50 2.45 (2.09-2.87) 2.64 (2.24-3.11) 2.72 (2.26-3.26) 50-60 3.16 (2.54-3.94) 3.22 (2.56-4.06) 3.13 (2.43-4.02) 60-70 3.99 (2.76-5.75) 4.11 (2.82-6.00) 3.64 (2.40-5.52) 70+

Potential secondary case age 0-10 0.82 (0.71-0.95) 0.89 (0.76-1.03) 0.94 (0.79-1.11) 10-20 0.70 (0.61-0.80) 0.73 (0.63-0.84) 0.75 (0.64-0.88) 20-30 ref (.) ref (.) ref (.) 30-40 1.64 (1.44-1.88) 1.70 (1.47-1.96) 1.77 (1.51-2.08) 40-50 1.60 (1.40-1.82) 1.67 (1.45-1.92) 1.69 (1.45-1.98) 50-60 1.48 (1.29-1.71) 1.48 (1.28-1.72) 1.55 (1.32-1.84) 60-70 1.53 (1.25-1.87) 1.59 (1.29-1.95) 1.58 (1.25-1.99) 70+ 1.01 (0.75-1.37) 1.03 (0.75-1.41) 1.08 (0.76-1.54)

Household size 2 2.26 (1.85-2.75) 2.27 (1.85-2.79) 2.28 (1.82-2.85) 3 1.53 (1.26-1.86) 1.52 (1.24-1.86) 1.57 (1.26-1.96) 4 1.51 (1.25-1.82) 1.52 (1.25-1.84) 1.64 (1.33-2.03) 5 1.40 (1.15-1.70) 1.43 (1.17-1.76) 1.54 (1.23-1.93) 6 ref (.) ref (.) ref (.)

Primary case sex Male ref (.) ref (.) ref (.) Female 0.99 (0.92-1.07) 1.00 (0.93-1.08) 0.97 (0.89-1.06)

Potential secondary case sex Male ref (.) ref (.) ref (.) Female 1.14 (1.07-1.20) 1.14 (1.08-1.21) 1.14 (1.06-1.21) Number of observations 27,874 27,011 25,611 Number of households 11,937 11,709 11,338

Notes: This table shows the sensitivity for the choice of inclusion of positive secondary cases. In Table 9 we show the estimates, while restricting the inclusion criteria for positive secondary cases. Column I shows the odds ratio estimates, including positive secondary cases found on day 1-7, i.e, our main specification, also presented in Table 2 and 3. Column II includes positive secondary cases found on day 2-7. Column III includes positive secondary cases found on day 3-7. 95%-Confidence interval in parentheses. Standard errors are clustered on the household level.

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Abstract
Introduction
Data and Methods

Study design and participants
Statistical analyses
Ethical statement
Data availability

Results
Discussion and Conclusion
References
Background

Time to test result
Probability of sampling for Variant PCR
Robustness of Variant PCR results

Additional analyses

Viral load of primary cases
Intra-household correlation of variants
Time since vaccination for positive secondary cases
Robustness of main results