Minimising school disruption under high incidence conditions due to the Omicron variant in France, Switzerland, Italy, in January 2022

Background As record cases of Omicron variant were registered in Europe in early 2022, schools remained a vulnerable setting undergoing large disruption. Aim Through mathematical modelling, we compared school protocols of reactive screening, regular screening, and reactive class closure implemented in France, in Baselland (Switzerland), and in Italy, respectively, and assessed them in terms of case prevention, testing resource demand, and schooldays lost. Methods We used a stochastic agent-based model of SARS-CoV-2 transmission in schools accounting for within- and across-class contacts from empirical contact data. We parameterised it to the Omicron BA.1 variant to reproduce the French Omicron wave in January 2022. We simulated the three protocols to assess their costs and effectiveness for varying peak incidence rates in the range experienced by European countries. Results We estimated that at the high incidence rates registered in France during the Omicron BA.1 wave in January 2022, the reactive screening protocol applied in France required higher test resources compared with the weekly screening applied in Baselland (0.50 vs 0.45 tests per student-week), but achieved considerably lower control (8% vs 21% reduction of peak incidence). The reactive class closure implemented in Italy was predicted to be very costly, leading to > 20% student-days lost. Conclusions At high incidence conditions, reactive screening protocols generate a large and unplanned demand in testing resources, for marginal control of school transmissions. Comparable or lower resources could be more efficiently used through weekly screening. Our findings can help define incidence levels triggering school protocols and optimise their cost-effectiveness.


Compartmental model and parameters
The progression of the infection for each host in the agent-based model follows the structure illustrated in Figure S1. Susceptible individuals (S) and individuals who were previously infected by other variants but are susceptible to the Omicron variant (S * ) become exposed (E) following infection. After a latent period, exposed individuals enter a prodromic phase (Ip) during which they can transmit the disease without showing symptoms. Following that phase, individuals can develop a subclinical infection (Isc) with probability psc, otherwise they develop clinical symptoms (Ic). We considered individuals in the prodromic and subclinical compartments to be less infectious than clinical individuals, and to remain undocumented unless tested [1][2][3][4]. After the infectious phase, individuals enter the recovery state (R+, R), where they become immune and no longer transmit the infection. This state is divided into two successive states, R+ and R, to isolate a first period (R+) during which the individual is no longer infectious but PCR tests may still detect the presence of the virus in the upper respiratory tract [5]. We assumed the protection against infection from prior variants to be 20% [6]. The E, Ip, Ic, Isc compartments are further split into sub-compartments to capture a non-exponentially distributed duration of stay in each infection stage, following empirical data [7][8][9][10][11][12][13][14][15][16].
The compartmental model is informed with empirical distributions of disease state periods. We modified the distributions specific to the Delta variant [17] (Figure S2) to account for the shorter latent period of the Omicron variant [18,19]. In the main analysis we considered a period shorter of 0.5 days, and for sensitivity we tested a period shorter of one day. .00 days and std=2.03 days (shape=6.00, scale=0.833). Distributions of disease state durations are assumed to be the same for students and teachers. Estimates from [17]. Table S1 summarizes the parameters of the compartmental model and their values. The compartmental model is further stratified to consider vaccination in the population (subsection 1.6). The model is initialized with 40% natural immunity from seroprevalence estimates [29] and accounting for Delta infections during the start of the fifth wave in France, before Omicron became dominant. Omicron infections are generated by the simulations. Vaccination status is based on data (subsection 1.6).
To parametrize the Omicron wave scenarios, we used the per-contact transmissibility previously estimated for the Delta variant in [27] and considered the transmissibility advantage of Omicron compared to Delta [18]. We considered a transmissibility advantage (expressed in multiplicative form) between 30% and 80% of Omicron compared to Delta [18]. We set =30% in the main analyses and explored =80% for sensitivity.

Empirical contact patterns
We used empirical data describing time-resolved face-to-face proximity contacts between individuals collected in a primary school in France using wearable RFID sensors in a pre-pandemic period. The dataset describes the contacts among 232 students (6-11 years old) and 10 teachers in a primary school in Lyon, composed of 5 grades, each of two classes [30].
We built temporal contact networks, composed of nodes representing individuals (classified by class and student/teacher), and links representing empirically measured proximity contacts occurring at a given time ( Figure S3). As the dataset covers only two days, we developed an approach to temporally extend the datasets by generating synthetic networks of contacts that reproduce the main features observed empirically (class structure, within-vs. between-classes links, contact duration heterogeneity, and similarity across days). In Figure S4 and Figure S5 we show that synthetic networks well reproduce the heterogeneity in contact duration between pairs of individuals and the timeline of activity, respectively. More details are provided in Ref. [27].

Within-school transmission
Within-school transmission is modelled with an algorithm based on rejection sampling [31]. In the absence of testing protocols, it proceeds as follows.
At each time step ∆ of 15 minutes, the pairwise interactions described in the contact network are evaluated. If a contact of duration • ∆ happens between an infectious ( , , ) and a susceptible ( ) individual in the time step ∆ , the susceptible individual may become exposed with a probability given by where is the transmission rate, is the susceptibility (which depends on age), is the relative transmissibility (which depends on both age and infectious state). In particular, is proportional to the duration of the interaction recorded in the contact network ( . ∆ ), and to the age-specific epidemiological features of the individuals ( , ).
Then, spontaneous transitions between successive compartments are evaluated. The time spent in each compartment follows the distributions of Figure S2, modified to account for a shorter latent period of the Omicron variant compared to the Delta.
School days include Monday, Tuesday, Thursday and Friday. The simulations run for a total of 90 days, with the distinction between school days and non-school days. In the latter and during off-school hours, only spontaneous transitions are evaluated.
An individual may become exposed ( ) due to community interactions outside the school, thus we included a weekly number of introductions due to out-of-school infections (as explained in the next subsection).

Modelling transmission outside schools: introductions conditions
Contacts outside the school are not explicitly modelled, as the sensor data we use capture interactions within the school setting only. Outside-school contacts (i.e., contacts between individuals of the school population and their family and friends, as well as their casual contacts in the community) are responsible for the introduction of infected individuals in the school, as teachers and students can get infected while in contact with the rest of the community.
Weekly introductions at school were modelled stochastically considering a plausible range of age-specific community incidence, to capture the situations experienced across countries in Europe. For a weekly incidence , the prevalence can be estimated as = , ⁄ , accounting for the probability of detection , and considering 7 days of infectious period [32,33]. The expected number of COVID-19 introductions in a specific age class of size ( =232 students, =10 teachers) can then be modelled with a binomial distribution: As we are interested in modelling Omicron epidemic waves of different peak incidence levels (corresponding, for example, to country-specific incidence rates), we explored average weekly introductions ranging from about 0.8 to 23 per week, corresponding to initial incidence levels in the range 100-3,000 per 100,000. These conditions correspond to peak incidence rates between 4,000 and 10,100 cases per 100,000, in absence of interventions. Results are evaluated with respect to peak incidence rates.
Results of Figure 1A of the main text are obtained from fitting the model to the observed incidence rates in 6-10 years old children to infer the weekly introductions (see Section 2).
For these reasons, for test sensitivity on RT-PCR saliva samples, we considered: • the time-varying test sensitivity of RT-PCR naso-pharyngeal samples from symptomatic cases [55], [56], interpolating data before the onset of symptoms with data after the onset of symptoms [55,56] ( Figure S6a). The peak value of sensitivity is 96% [55]. • the time-varying test sensitivity of RT-PCR saliva samples from asymptomatic cases [57] (Figure S6b).
Sensitivity values are defined in terms of days since the first matched positive viral culture from an anterior nasal sample, commonly used to align the time axis to symptom onset [13,58]. For the time-varying sensitivity of LFD tests, we used data obtained from samples collected in asymptomatic adults for which data over time are available [57] (Figure S7a). Sensitivity was shown to vary between asymptomatic and symptomatic cases, and between age classes [59][60][61][62][63]. In absence of time-varying data for all these stratifications, we assumed the time dependence from [57] and rescaled it to match the peak sensitivity values for symptomatic and asymptomatic cases in adults and children obtained from Ref. [64]. Peak values are in accordance with the literature [60,65,66].
Sensitivity over time was then adjusted to the sensitivity of the RT-PCR anterior nasal tests, as the sensitivity of the LFD tests was measured with respect to the latter [57,64]. We fixed the sensitivity of the RT-PCR anterior nasal tests at 88%, the upper bound of the estimate provided by the review of Ref. [67] relative to the sensitivity of the RT-PCR naso-pharyngeal test, in agreement with other estimates [42,[68][69][70][71][72]. Once adjusted, the peak value of the absolute sensitivity of the LFD test for a symptomatic adult was 81%, considering the peak value of the RT-PCR naso-pharyngeal samples being equal to 96% [55]. Results are shown in Figure S7b.
Finally, we explored a lower peak sensitivity of 55% for asymptomatic children, for both test types (Figure S7c). Figure S7. Time-varying test sensitivity of lateral flow device nasal antigen tests. (a) Test sensitivity is relative to the test sensitivity of PCR nasal tests, from adult asymptomatic cases [57]. The peak value of sensitivity is 95%. Data from [57] was fitted with a polynomial of degree 4 minimizing the mean squared error. (b) Absolute test sensitivity considering the sensitivity of the RT-PCR anterior nasal tests at 88% [67] and the sensitivity of the RT-PCR nasopharyngeal test 96% [55]. The time dependence measured in [57] is adjusted to match the peak sensitivity values from [64] for symptomatic and asymptomatic cases in adults and children. (c) Absolute test sensitivity considering the peak sensitivity of the LDF test for asymptomatic children at 55%. Value explored in the absence of empirical estimates on test sensitivity against Omicron infection.
The probability of detection of COVID-19 infection based on symptoms is age-dependent and informed from the literature [73,74] (Table S3). We further explored a range for sensitivity analysis.
All detected cases (identified on the basis of their symptoms or following a screening) are put in isolation for a duration of 7 days. The only exception is the Italian protocol of reactive class closure which required 10 days of isolation for cases and students in their class. At the end of the isolation period, students return to school without further testing, following current recommendations. We consider that teachers are required to show a negative PCR test before returning to school, accounting that the virus can still be detectable by a PCR test after the infectious period [5]. In our model, every time a teacher is detected, she is replaced by a susceptible substitute.
We considered a frequency for regular screening of once per week, and twice per week. We explored adherence in the range from 50% to 100%. We considered a turnaround time of 15 minutes for LFD tests, and of 12h and 24h for PCR tests on saliva samples. We fixed test specificity to 100% for both tests [75].  50%, 100%

Vaccination
The compartmental model illustrated in Figure S1 is further stratified to consider vaccination in the population, as shown in Figure S8. As we are interested in assessing the role of vaccination coverage in the school population within a relatively short timeframe, we do not consider a dynamic vaccination rollout, and assume that vaccination coverage is fixed throughout the simulation. The impact of different coverage levels is assessed by exploring a range of values in both teachers and student populations. Vaccination coverage in children in European countries at different dates is reported in Figure S9.
We considered values for vaccine effectiveness against infection from the Omicron variant from available estimates for children [77] and adults [78] (Table S4). We assumed vaccine effectiveness against transmission to be 20% in both children and adults.  [79] for age class 5-11, data for France is from [80] for age class 5-9, data for other European countries from [81] for age class 5-9. The countries represented are: Austria, Cyprus, Czech Republic, Denmark, France, Greece, Spain, Finland, Croatia, Ireland, Iceland, Italy, Liechtenstein, Lithuania, Luxembourg, Latvia, Netherlands, Poland, Portugal, Slovakia.

Vaccine effectiveness against infection
Value Source Adults At 6 months after the second dose

15%
In line with [78] Within the first 4 weeks after booster

70%
In line with [78] Children Within the first 4 weeks after second dose 50% In line with [77] Lower VE 20% Assumed to account for a strong waning of immunity

Inference framework
To infer weekly introductions at school in France, we used the incidence surveillance data [80] collected during the Omicron peak wave (10/01/2022 -03/02/2022). We fit the weekly introductions and the starting date 0 of the simulation. The model fit is performed with a maximum likelihood approach on the observed 7-day rolling incidence rate in the age class 6-10 years old.
The likelihood function is of the form    Figure S10. The horizontal dashed lines indicate the theoretical values of the demands in number of tests per student in the once and twice per week screening (i.e. imposed by 75% adherence and by frequency). Results are obtained considering the use of nasal LFD tests in both reactive and regular screenings. Shaded areas around the curves correspond to IQR ranges.

Test needs and schooldays lost vs. percentage of case reduction at varying incidence rates.
Figure S12. Test needs and schooldays lost vs. percentage case reduction at varying incidence rates. (a) Demand in the number of tests per student-week at peak as a function of the percentage of case reduction achieved by each protocol compared to symptomatic testing (i.e. in absence of interventions). The horizontal dashed lines indicate the theoretical values of the number of tests per student in the once and twice per week screening (i.e. imposed by 75% adherence and the frequency). Dots reduce their transparency for increasing incidence. (b) Percentage of student-days lost as a function of the percentage of case reduction achieved by each protocol. The percentage of case reduction is computed with respect to symptomatic testing. The reactive quarantine of the class is shown as an additional protocol. In panel (b) incidence values in the legend refer to peak incidence of symptomatic testing (i.e. in absence of interventions); the corresponding values for each protocol are plotted in Figure 2A Simulated weekly incidence expressed in number of cases in students per 100,000 over time for different protocols, vaccination coverage in children varies between 0 and 60%. Figure S14. Impact of vaccination coverage with booster for teachers. Percentage of peak reduction achieved by each protocol compared to symptomatic testing (i.e. in absence of interventions) as a function of vaccination coverage in teachers for lower (a) and higher (b) introduction conditions. In panels (a) and (b), peak incidence values in the absence of interventions are 7,500 and 10,100 cases per 100,000 respectively.

Sensitivity analysis on advantage in transmission rate of Omicron relative to Delta
Figure S15. Impact of advantage in transmission rate of Omicron relative to Delta. (a,d) Demand in the number of tests per student-week at peak as a function of the peak incidence (cases in students per 100,000) for the reactive, once per week, and twice per week protocols. The horizontal dashed lines indicate the theoretical values of the number of tests per student in the once and twice per week screening (i.e. imposed by 75% adherence and the frequency). Dots reduce their transparency for increasing incidence. (b,e) Demand in the number of tests per student-week at peak as a function of the percentage of peak reduction achieved by each protocol compared to symptomatic testing (i.e. in absence of interventions). The horizontal dashed lines are as in panels (a,d). Dots transparency code is the same as in panels (a,d). (c,f) Peak percentage of studentdays lost as a function of the percentage of peak reduction achieved by each protocol; both quantities are computed with respect to symptomatic testing. The reactive quarantine of the class is shown as an additional protocol. In panels (b,c,e,f) incidence values in the legend refer to peak incidence of symptomatic testing (i.e. in absence of interventions); the corresponding values for each protocol are plotted in panels (a,d). In all panels, peak incidence values in the absence of interventions range between 7,000 and 9,600 cases per 100,000.

Sensitivity analysis on latent period of Omicron
We considered a latent period of the Omicron with respect to the Delta variant 0.5 days shorter (subsection 1.1). We explored for sensitivity a latent period of the Omicron with respect to the Delta variant of the same length and 1 day shorter. Figure S16. Impact of latent period of Omicron. (a) Percentage of peak reduction achieved by each protocol compared to symptomatic testing (i.e. in absence of interventions) as a function of the latent period when latent period is either as for Delta or 1 day shorter. (b) Demand in the number of tests per student-week at peak as a function of the latent period. The horizontal dashed lines indicate the theoretical values of the number of tests per student in the once and twice per week screening (i.e. imposed by 75% adherence and the frequency). In all panels, peak incidence value in the absence of interventions ranges from 7,400 to 7,800 cases per 100,000. Figure S17. Impact of detection probability. (a) Percentage of peak reduction achieved by each protocol compared to symptomatic testing (i.e. in absence of interventions) as a function of detection probability. (b) Demand in the number of tests per student-week at peak as a function of the detection probability. The horizontal dashed lines indicate the theoretical values of the number of tests per student in the once and twice per week screening (i.e. imposed by 75% adherence and the frequency). Peak incidence values in the absence of interventions range from 5,100 to 12,300 cases per 100,000.

Sensitivity analysis on control screening
We considered the reactive protocol applied in France in January 2022, requesting an LFD test at days D0, D2, and D4 to the class of the detected case, following case identification. We explored for sensitivity an LFD test at days D0, D3, and D7 and an LFD test at days D0, D4. Figure S18. Impact of control screening. (a) Percentage of peak reduction achieved by each protocol compared to symptomatic testing (i.e. in absence of interventions) as a function of number and delays of control screenings. (b) Demand in the number of tests per student-week at peak as a function of number and delays of control screenings. The horizontal dashed lines indicate the theoretical values of the number of tests per student in the once per week screening (i.e. imposed by 75% adherence and the frequency). Peak incidence value in the absence of interventions is around 7,500 cases per 100,000.