Impact of January 2021 curfew measures on SARS-CoV-2 B.1.1.7 circulation in France

Following the spread of the SARS-CoV-2 B.1.1.7 variant, social distancing was strengthened in France in January 2021. Using a two-strain mathematical model calibrated on genomic surveillance, we estimated that curfew measures allowed hospitalisations to plateau by decreasing transmission of the historical strains while B.1.1.7 continued to grow. School holidays appear to have further slowed down progression in February. Without progressively strengthened social distancing, a rapid surge of hospitalisations is expected, despite the foreseen increase in vaccination rhythm.


Hospital surveillance data
Our model was fitted to daily hospital admission data to capture the epidemic trajectory over time (see the Inference section). We use the SIVIC database which lists daily hospitalizations of patients for COVID-19 (cases confirmed by PCR or chest CT) in public or private hospitals in France. They are among the most robust data sources to use in COVID-19 epidemiological studies, as they are not affected by changes in detection and sampling, as it happens for detected cases, and suffer less the delays or uncertainty in classification of the number of deaths. These data have been used throughout 2020 in France to respond to the health crisis 1-3 and are also routinely used by health agencies for their assessments of the epidemiological situations.
Data include admissions to conventional hospitalizations or critical care for COVID-19 by date of event (admission, entry into critical care) and not by date of registration of the event in the database, and are corrected for notification delays. They exclude transfer of patients, follow-ups, rehabilitation care. As such, data may be different from those reported in official statistics.

Virological and genomic surveillance data
Genome sequencing to estimate the frequency of variants of concern at different moments in time was conducted in France through three surveys, called Flash surveys. They adopted different protocols, evolving over time due to the urgency of assessing the circulation of the variants and because of logistical and resource constraints.  7 viruses, corresponding to a PPV equal to 100% 4 . The alternative screening protocol was based on second-line RT-PCR tests with specific primers that allow the detection of the main mutations that characterize the variants of concern. They must include at least the N501Y mutation and allow to distinguish the 20I Figure 2 of the main paper. Their confidence interval is estimated assuming that B.1.1.7 frequency is described by a normal distribution.
Given the heavy load of sequencing, and the need to provide more timely indicators on the circulation of the variants of concern, starting week 6 a new protocol for virological surveillance was implemented to provide estimates on the weekly frequency of detected viruses with specific mutations 7 , using the second-line RT-PCR tests described above. In Table S1 and Figure 2 of the main paper we report the proportion of positive screened samples showing the N501Y mutation specific to B.1.1.7 variant. PPV value was 100% with this type of screening during Flash3 survey, conducted during week 6, making this a reliable proxy to monitor B.1.1.7 frequency over time.

Compartmental model and parameters
We use a stochastic discrete age-stratified transmission model, integrating demographic, age profile, social contact data, mobility data, data on adoption of preventive measures, to account for age-specific behaviors over time and role in COVID-19 transmission. Four age classes are considered: [0-11), [11][12][13][14][15][16][17][18][19], , and 65+ years old (children, adolescents, adults, seniors). Transmission dynamics follows a compartmental scheme specific for COVID-19 ( Figure S1) where individuals are divided into susceptible, exposed, infectious, hospitalized and recovered. The infectious phase is divided into two steps: a prodromic phase (Ip) and a phase where individuals may remain either asymptomatic (Ias, with probability pa=40% 8 ) or develop symptoms. In the latter case, we distinguished between different degrees of severity of symptoms (paucisymptomatic (Ips), individuals with mild symptoms (Ims), or severe symptoms (Iss) requiring hospitalization 3,9,10 ). Prodromic, asymptomatic and paucisymptomatic individuals have a reduced transmissibility 11 . A reduced susceptibility was considered for children and adolescents, along with a reduced relative transmissibility of children based on available evidence [12][13][14][15][16][17] . We assume that infectious individuals with severe symptoms reduce of 75% their number of contacts because of the illness they experience 18 . Parameter values are reported in Table S2.
Sensitivity analysis on the probability of becoming symptomatic and the transmissibility of children was performed in previous work 1, 2,19 .   Relative infectiousness of % , ) , %* 0.25 for children 0.55 for adolescents, adults, seniors 11 Relative susceptibility 0.5 for children, adolescents 1 for adults, seniors 13

Generation time distribution
The generation time distribution was computed based on the approach of Ref. 23 . Let and be the random variables describing the latency period and the infectious period, respectively. Then the distribution of the generation time is the result of the convolution * ℎ * , with being the probability density function of and ℎ * ( ) = 1 − ( ) ( ) where is the cumulative distribution function of , and ( ) is the mean.
In the compartmental model under consideration (Figure S1), we have that is exponentially distributed with rate , and is the sum of two exponentially distributed random variables (prodromic phase and infectious period, with rate % and respectively). Computations show that the corresponding generation time distribution is Given the values of and % informed from the literature (Table S2), we chose so that the mean of the generation time equals to 6.6 days. The shape of the distribution is displayed in Figure S2 and it closely resembles a gamma distribution with mean 6.6 and shape parameter 1.87, estimated in Ref 22 .

Parameterization of contact matrices from empirical data
Social mixing was informed from behavioral data and was modeled through the parametrization of contact matrices. In particular we considered attendance at school 24 , percentage of telework 25 , and adoption of physical distancing over time 26 .
Contacts at school were considered according to the school calendar. In France all schools are in session with 100% physical presence since the start of the school calendar in September. In the period of May-July, after the first lockdown, schools were open but attendance was on a voluntary basis 19 .
Social contacts at work were modified to account for the percentage of workers not going to their place of work over time, following the variation of presence at workplaces based on Google Mobility Trends 25 ( Figure S3).
To account for individuals' risk protection behavior over time, we parametrized contact matrices with the percentage of population avoiding physical contacts from the results of regular large-scale surveys conducted by Santé Publique France (CoviPrev 26 ). From these data, we also estimated that seniors have a higher risk aversion behavior compared to other age classes, leading to an average additional 30% reduction of their physical contacts 1 .
The contacts in leisure and non-essential activities were informed based on implemented restrictions and mobility data in community settings (see e.g. use of transport and visits to retail in Figure S4). A sensitivity analyses on contacts in leisure and non-essential activities was conducted in Ref. 1 .  In prior work 1 , we compared our approach where the contact matrix is parameterized with the various data sources described above with a simplified version of the model that neglects these input data. This version assumes that all changes in the epidemic trajectory are absorbed exclusively by the transmissibility per contact. This is equivalent to normalize the contact matrix to its largest eigenvalue and estimate the reproductive ratio over time, as also done in other works 3 . Results showed that our model better describes the observed trajectories, thus indicating that changes in age-stratified contact patterns are important to capture the epidemic dynamics.
The code for the model is available at the link provided in Ref. 1 .

B.1.1.7 variant
We considered the co-circulation of B.1.1.7 variant together with the historical strain. Complete cross-immunity and 59% (95% CI: 54-65%) 4 increased transmissibility were considered for B.1.1.7 variant compared to the historical strain ( Figure S1). This estimate was obtained from the Flash1 and Flash2 survey in France, and found to be in line with previous estimates 27, 28 . In the results considered in the main paper, we did not consider further differences between the two strains (generation time, hospitalization or severity rate). Recent results confirm that infection with lineage B.1.1.7 was associated with an increased risk of hospitalization compared with other lineages (adjusted OR of 1.64 (95%CI, 1.32-2.04)). We then considered a 64% increase in hospitalization rates if infected with B.1.1.7 and refitted the model to hospitalization data to provide updated projections under this condition. Results are shown in section 4.
B.1.1.7 variant was initialized on January 7, 2021 (in w01) using the estimates of the first large-scale nationwide genomic surveillance survey (Flash1, see section 1 and main text). No other information was assumed, beyond the increased transmissibility advantage (and the increased hospitalization rate, for sensitivity). As such, no specific dynamics on the two strains is imposed a priori, and the trajectories predicted by the model are the result of the fit to hospitalization data (see next section).

Vaccination rollout campaign
Following estimated plans for rolling out the vaccination campaign, we simulated a rollout scenario based on the administration of 100,000 doses per day in France from w04, prioritized to the older age class. This was based on recent data, reporting an average daily rhythm of vaccination of 99,500 doses (including first and second doses) from w04 to w08 29 . We considered 75% vaccine efficacy against susceptibility 30 , 65% vaccine efficacy against transmission 31 , and a range between 40% and 80% for vaccine efficacy against symptoms given infection, computed from the estimated vaccine reduction of symptomatic disease 31,32 , between 85% 30 and 95% 33,34 .
Estimates were found to be similar when evaluated 14 days after the first dose or 1-2 weeks after the second dose 34 , therefore we assumed efficacy to start 14 days after the first injection. We also considered for sensitivity: (i) a reduced efficacy against transmission (50%); (ii) no efficacy against susceptibility and 90% efficacy against symptoms.
Following the announcements by French authorities on March 4 aiming at administering 10 million first doses till mid-April 35 , we considered an acceleration in the daily rhythm in w10 (starting March 8) with 200,000 doses per day (only first doses). For sensitivity, we considered a more optimistic rollout of 300,000 doses/day (only first doses; this latter estimate based on observations that 250,000 doses were administered on March 5 after the announcements 36 ). These rollouts are compared to a stable rhythm of 100,000 doses (used for first and second injections).

Inference framework
Once the model is parameterized with the data described above, we infer the transmission rate per contact by fitting the model to daily hospital admission data through a maximum likelihood procedure in each pandemic phase. More precisely, prior to lockdown and in absence of intervention (period January-March 2020), we Wald confidence intervals for the scaling factor were computed by fitting a quadratic function on the loglikelihood values around the MLE, to estimate Fisher's information.
In prior work 1 we showed that the stochasticity of the model is the main source of uncertainty in the predictions. , assuming 54% increase in transmissibility. A slower (100k, dotted curve) and optimistic (100k-300k, dot-dashed curve) vaccination rhythms are also shown (only median curves of the overall trajectories are shown, for the sake of visualization). The shaded area around the curves corresponds to the 95% probability range obtained from 500 stochastic simulations. Dots correspond to weekly hospital admission data. The model is fit to daily hospital admissions since the start of the epidemic, propagating uncertainty over time; the figure shows weekly data to simplify the visualization. The second wave is shown for reference, together with indications of the timing of social distancing measures; the shaded rectangle around the second wave corresponds to the second lockdown.

Impact of vaccine efficacy on the projected weekly hospitalizations
We note that our results may be an underestimation of the impact of vaccination on the epidemic trajectory as in our model priority is given to 65+ whereas vaccination is currently being rolled out first in the 75+ age class, characterized by a higher hospitalization rate. As our model does not break down further age classes above 65 years of age, vaccination cannot account for the higher advantage in targeting older age classes. On the other hand, we optimistically assume that vaccine efficacy is reached 2 weeks after the first injection, which was observed so far for mRNA-1273 vaccine 34 .

4.5.
Impact of increased hospitalization rates associated to B.1.

infection
The increased hospitalization rate (+64%) after B.1.1.7 infection, recently estimated in Denmark 37 , is expected to lead to a higher peak of hospital admissions starting at the end of April (Figure S12), if curfew measures only are in place. Hospital admission would be however largely higher than the levels of the first and second peak, even with the considered vaccination rhythms. Results are shown for mainland France. Scenario considered after winter school holidays: curfew scenario, estimated in w04 and assuming no additional changes. Curves refer to the overall trajectory, due to the concurrent circulation of the historical strain and of the B.1.1.7 variant, assuming 59% increase in transmissibility and under the accelerated vaccination rollout (100k-200k doses/day). The solid grey curve refers to the median overall trajectory, obtained assuming the same hospitalization rates for infection due to the historical train and B.1.1.7. variant (as in the main paper). The dashed grey curve refers to the median overall trajectory, obtained assuming an increased hospitalization rate (+64%) associated to B.1.1.7 infection 37 .The shaded area around the curves corresponds to the 95% probability range obtained from 500 stochastic simulations. Dots correspond to weekly hospital admission data. The model is fit to daily hospital admissions since the start of the epidemic, propagating uncertainty over time; the figure shows weekly data to simplify the visualization. The second wave is shown for reference, together with indications of the timing of social distancing measures; the shaded rectangle around the second wave corresponds to the second lockdown.