Sarah Tubiana

Charles Burdet

Nadhira Houhou

Michael Thy

Pauline Manchon

François Blanquart

Charlotte Charpentier

Jérémie Guedj

Loubna Alavoine

Sylvie Behillil

Anne Leclercq

Jean-Christophe Lucet

Yazdan Yazdanpanah

Mikaël Attia

Caroline Demeret

Thierry Rose

Julia Anna Bielicki

Patricia Bruijning-Verhagen

Herman Goossens

Diane Descamps

Sylvie Van Der Werf

Bruno Lina

Xavier Duval
email: xavier.duval@aphp.fr

High-risk exposure without personal protective equipment and infection with SARS-CoV-2 in healthcare workers: results of the CoV-CONTACT prospective cohort

Keywords: SARS-CoV-2, healthcare workers, high-risk exposure, personal protective equipment, transmission

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Introduction

Since December 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) which causes COVID-19, rapidly spread around the globe [START_REF] Dong | An interactive web-based dashboard to track COVID-19 in real time[END_REF][START_REF] Guan | Clinical Characteristics of Coronavirus Disease 2019 in China[END_REF]. The difficulty to control its rapid propagation is related to many factors, including the fact that infectiousness can precede the symptoms onset, thereby complicating the identification and isolation of infected individuals before they can transmit the virus [START_REF] Arons | Presymptomatic SARS-CoV-2 Infections and Transmission in a Skilled Nursing Facility[END_REF][START_REF] Cheng | Contact Tracing Assessment of COVID-19 Transmission Dynamics in Taiwan and Risk at Different Exposure Periods Before and After Symptom Onset[END_REF].

Healthcare workers (HCWs) can be infected following a contact with a patient, but also after interactions with colleagues, or in the community [START_REF] Barrett | Prevalence of SARS-CoV-2 infection in previously undiagnosed health care workers at the onset of the U.S. COVID-19 epidemic[END_REF][START_REF] Chou | Epidemiology of and Risk Factors for Coronavirus Infection in Health Care Workers[END_REF][START_REF] Contejean | Comparing dynamics and determinants of SARS-CoV-2 transmissions among health care workers of adult and pediatric settings in central Paris[END_REF][START_REF] Lai | Coronavirus Disease 2019 (COVID-2019) Infection Among Health Care Workers and Implications for Prevention Measures in a Tertiary Hospital in Wuhan, China[END_REF][START_REF] Qian | Fighting against the common enemy of COVID-19: a practice of building a community with a shared future for mankind[END_REF][START_REF] Sikkema | COVID-19 in health-care workers in three hospitals in the south of the Netherlands: a cross-sectional study[END_REF][START_REF] Team | Characteristics of Health Care Personnel with COVID-19 -United States, February 12[END_REF][START_REF] Zheng | Analysis of the infection status of the health care workers in Wuhan during the COVID-19 outbreak: A cross-sectional study[END_REF]. The use of personal protective equipment (PPE) was rapidly implemented in departments hosting suspected or identified SARS-CoV-2-infected subjects. However, the atypical presentation of the infection favors high risk contacts between HCW and unidentified patients in other departments [START_REF] Arons | Presymptomatic SARS-CoV-2 Infections and Transmission in a Skilled Nursing Facility[END_REF], and the large circulation of the virus increases the risk of infection during interactions with colleagues, during which the use of PPE or social distancing may be less strictly followed [START_REF] Bielicki | Monitoring approaches for health-care workers during the COVID-19 pandemic[END_REF].

We conducted a prospective cohort study to estimate the risk of infection in HCWs following highrisk exposure in the hospital, and to evaluate the virological, immunological and clinical outcomes following exposure.

Methods

Study design and participants

The CoV-CONTACT study is an ongoing prospective multicenter cohort study including HCWs with exposure to an "index" SARS-CoV-2-infected person (either a patient or a colleague) whose infection was virologically proven by a nasopharyngeal RT-PCR and whose exposure was considered at highrisk of SARS-CoV-2 transmission. HCWs were included in the study in the 14 days following the last identified high-risk exposure. The present analysis focuses on "contact" subjects enrolled at the >1000 bed Bichat Claude Bernard University Hospital (Paris, France) [START_REF] Lescure | Clinical and virological data of the first cases of COVID-19 in Europe: a case series[END_REF] between March, 3 rd 2020 and April, 27 th 2020.

Ethics and regulatory issues

The study was approved by the French National Data Protection Commission (approval #920102), and the French Ethics committee (CPP-Ile-de-France-6, #2020-A00280-39) and was registered on the Clinicaltrial.gov registry (NCT04259892). All subjects provided written informed consent.

Definition of high-risk exposure

Exposure was considered to be at high-risk of SARS-CoV-2 transmission if it occurred i) face-to-face, within one meter and without protective surgical or FFP2/N95 mask, and ii) during a discussion or while the index had an episode of coughing or sneezing, and iii) in the 72 hours prior to, or following the virological diagnosis, or during the symptomatic period of the index. The collected characteristics of the contacts included medical history, weight, height, current medications, and smoking status. The date of the last high-risk exposure, D0, with the index were also recorded, as well as the cumulative exposure duration.

Contacts were followed up for 30 days following D0. Nasopharyngeal swabs were performed at inclusion, and then at D3, D5, D7 and D12. As inclusion could occur up to 14 days after D0, a maximum of five nasopharyngeal swabs could be collected. Blood samples were drawn at inclusion and D30±7d for SARS-CoV-2 serology.

A set of general symptoms (fever >38°C, fatigue, myalgia, headache) and specific symptoms (cough, breathing difficulties, sore throat, nasal congestion, anosmia, diarrhea) was recorded daily from D0 to D30 using self-administered questionnaires. Results of any additional nasopharyngeal swab were collected, as well as the occurrence of hospitalization, or the existence of household contacts hospitalized for a SARS-CoV-2 infection between D0 and D30.

Virology

The SARS-CoV-2 RT-PCR was performed blinded to contact characteristics and reported symptoms (see Supplementary appendix).

In contacts with clinical signs suggestive of COVID-19 but a negative SARS-CoV-2 RT-PCR and a negative SARS-CoV-2 serology at D30, a multiplex RT-PCR (QIAstat-Dx Respiratory Panel; Qiagen, Germany) was retrospectively performed on available aliquots to detect other respiratory pathogens (see Supplementary appendix).

Serology SARS-CoV-2 serology was performed blinded to contacts' characteristics and reported symptoms. We used two methods targeting different SARS-CoV-2 antigens: LuLISA N, an in-house Luciferase-Linked Immunosorbent assay designed to detect IgG targeted toward SARS-CoV-2 N antigen (unpublished results) and EuroIMMUN, a commercial immunoassay used for the detection of IgG targeted toward the SARS-CoV-2 recombinant Spike protein subunit (S1) [START_REF] Theel | Performance Characteristics of Four High-Throughput Immunoassays for Detection of IgG Antibodies against SARS-CoV-2[END_REF]. A serum was considered as positive for SARS-CoV-2 antibodies when the signal exceeded the threshold set at 13,402 relative light units per second (RLU/s) for LuLISA or a 1.1 ratio for EuroIMMUN.

For each method, we defined SARS-CoV-2 seroconversion as the apparition of a positive SARS-CoV-2 serology at the D30 visit, or as an at least two-fold increase of the LuLISA signal or EuroIMMUN ratio between inclusion and D30, in the case of a positive serology at inclusion.

Definition of SARS-CoV-2 infection

Three definitions of SARS-CoV-2 infection were used: (i) "clinically-suspected infection", when the contact reported at least one general symptom and one specific symptom during two consecutive days during the 30-day follow-up; (ii) "virologically-proven infection", if the contact had at least one SARS-CoV-2-positive nasopharyngeal swab during the 30-day follow-up; (iii) "immunologically-proven infection" if the contact exhibited a SARS-CoV-2 seroconversion in any of the two methods. SARS-CoV-2 infection was considered as confirmed if it was virologically or immunologically-proven, and considered as possible in case of clinically-suspected infection only.

The primary endpoint was confirmed or possible SARS-CoV-2 infection, thereafter referred to as SARS-CoV-2 infection.

Statistical methods

Categorical variables are expressed as counts (percentage) and continuous variables are expressed as median (IQR). We first estimated the prevalence of SARS-CoV-2 infection among HCWs, with its 95% confidence intervals computed using the binomial distribution. For the primary endpoint, in case of missing data for one of the components, the subject was considered as infected if one of the available components of the endpoint fulfilled the definition of infection, and considered missing otherwise.

We searched for risk factors associated with SARS-CoV-2 infection among HCWs. Variables achieving a p-value <0.20 in univariate logistic regression analysis were entered into a multivariate logistic regression analysis. Using a backward selection method, we obtained a final model in which all risk factors had a p-value <0.05.. A sensitivity analysis was performed after exclusion of the subpopulation who only met the definition of a possible SARS-CoV-2 infection.

We then studied the kinetics of the SARS-CoV-2 infection in participants with virologically-proven and clinically-suspected infection. We analyzed the SARS-CoV-2 viral load as a function of time from symptom onset using a quadratic regression model.. Analyses were performed with R v3.5 (R Foundation for Statistical Computing, Vienna, Austria). All tests were two-sided with a type-I error fixed to 0.05.

Results

Contacts characteristics and type of exposure

Overall, 154 HCWs exposed to 44 COVID-19 index subjects were included. The median age of these contacts was 35 years (IQR 29.0; 46.8), 35/154 were male (22.7 %). High-risk exposure occurred prior to the widespread use of masks in the hospital (on March, 18 th ) in 88/154 contacts (57%). In contrast, the exposure to colleagues increased from 31.8% (28/88) before March, 18 th to 88.2% (60/68) after March, 18 th (2 contacts with combined exposures). Overall 28/154 contacts (18.2%) had a high-risk exposure with more than one index subject.

The median duration of the high-risk exposure period was two days (IQR 0; 3.8), and contacts were enrolled at a median time of 6.5 days (IQR 4; 8) after D0. Table 1 S1.

Based on self-administered questionnaires, 61/151 (40.4%, 95%CI [32.5%; 48.7%]) contacts met the definition of a clinical infection (see details in supplementary appendix). The median duration of symptoms was 5.5 days (IQR 3; 9.2).

The Figure 1 presents the combination of virological, immunological and clinical outcomes; 28 contacts fulfilled only the clinical definition of infection. In these subjects, the prevalence of symptoms dropped at day 10, whereas it persisted elevated until day 30 in those with confirmed infection (Figure 2).

Proportion of contacts with SARS-CoV-2 infection

At D30, among the 148 contacts with available data, 65 met the criteria of confirmed or possible SARS-CoV-2 infection (43.9%, 95%CI [35.9%; 52.3%]), confirmed in 37 (25.0%, 95%CI [18.4%; 32.9%]), and possible (i.e., only clinically-suspected) in 28 (18.9%, 95%CI [13.2%; 26.5%]). Figure S1 presents the different clusters of exposure from the 44 index subjects. Among the 28 contacts with possible SARS-CoV-2 infection, multiplex RT-PCR for other respiratory viruses could be performed in 21 and was negative for 19 patients and positive for two (one bocavirus and one rhinovirus). During followup, one contact with confirmed SARS-CoV-2 infection was hospitalized. There was no hospitalization for SARS-CoV-2 infection reported in their household contacts.

Factors associated with SARS-CoV-2 infection

In the multivariable analysis, the variables associated with SARS-CoV-2 infection were being a pharmacist or administrative assistant (OR=3.8, CI95%=1.3; 11.2, p=0.01) and having a contact with a SARS-CoV-2-infected patient (OR=2.6, CI95%=1.23; 5.9, p=0.02).

The results of the sensitivity analysis excluding contacts having only a possible SARS-CoV-2 infection provided similar results except for pharmacist or administrative assistants' function (Table S2).

Viral dynamics in infected contacts

The viral load as a function of time since symptom onset reached a maximum at 8.8 log 10 copies/ml 4 days after symptom onset followed by a decline afterwards (Figure 3). Of note, 7/25 subjects had a positive SARS-CoV-2 nasopharyngeal swab before the symptoms onset and the first positive nasopharyngeal swab was observed as early as six days before symptoms onset. In eight subjects, the positive swab was preceded by one negative swab and in two of them, the negative swab was done after the symptom onset.

Discussion

In this prospective cohort of high-risk exposed HCWs, between 25% and 44% of subjects acquired SARS-CoV-2 infection at day 30, depending on the definition used to assess infection. Viral shedding occurred before symptoms onset in 27% of the SARS-CoV-2-positive subjects. The majority of HCWs were exposed to a SARS-CoV-2-infected colleague (62.5%), and a substantial proportion had a highrisk contact with a patient (46.1%). Exposure with a SARS-CoV-2-infected patient was significantly associated with SARS-CoV-2 infection (p=0.023).

The HCWs included in our analysis reflected the diversity of the hospital workers, [START_REF] Sakurai | Natural History of Asymptomatic SARS-CoV-2 Infection[END_REF] offering an ideal perspective to analyze the risks of infections encountered in a hospital. Following universal masking for HCWs on March, 18 th in our hospital, high-risk exposure to SARS-CoV-2-positive patients dropped from 68.2% to 11.8%, and high-risk exposure to SARS-CoV-2-positive colleagues became predominant, increasing from 31.8% to 88.2% and making colleagues-to-colleagues transmission a potentially major route of infection [START_REF] Contejean | Comparing dynamics and determinants of SARS-CoV-2 transmissions among health care workers of adult and pediatric settings in central Paris[END_REF]. The profession of the contact subject was associated with infection, but we did not find any association with the type of activities of the HCWs. Although it is likely that activities involving a close contact with patients favor infection, such association might have been masked as HCWs could also be infected by colleagues.

One of the strengths of our study is its prospective design, with daily self-questionnaire to characterize symptoms onset and evolution, as well as repeated nasopharyngeal swabs to capture the time of infection after exposure, and serological assessments at inclusion and at day 30. The 10% seropositivity of HCWs at inclusion corresponds to the seroprevalence reported in the Paris area in the general population during this period, [18] and it is plausible that these subjects had been infected prior to the high-risk exposure identified in the study. Seroconversion was observed in about a third of exposed HCWs classified as infected, while their nasopharyngeal swabs were negative; most of these HCWs were symptomatic. Inversely a quarter of the HCWs with a SARS-CoV-2-positive nasopharyngeal swabs had no detectable antibodies at day 30, despite the use of two serological techniques. The prospective nature of our analysis allowed us to characterize the time to viral positivity in the 26 subjects with SARS-CoV-2-positive nasopharyngeal swabs and the relationship between the viral load and the time since symptom onset. Nasopharyngeal viral load could be positive before symptom onset, with the first positive viral load obtained as early as six days before symptom onset, consistent with the estimated 6-day incubation period previously reported [START_REF] Lauer | The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application[END_REF][START_REF] Nie | Epidemiological Characteristics and Incubation Period of 7015 Confirmed Cases With Coronavirus Disease 2019 Outside Hubei Province in China[END_REF].

In addition to these confirmed infections, we also considered possible infections, as defined by the presence of one general and one specific symptoms for two consecutive days in subjects with neither a positive PCR nor seroconversion. Our definition is stricter than what was done in other studies [START_REF] Sakurai | Natural History of Asymptomatic SARS-CoV-2 Infection[END_REF][START_REF]standardized surveillance case definition and national notification for 2019 novel coronavirus disease (COVID-19)[END_REF][START_REF] Boulware | A Randomized Trial of Hydroxychloroquine as Postexposure Prophylaxis for Covid-19[END_REF][23]]. Interestingly we found that the kinetics of symptom onset was very similar in confirmed and possibly infected subjects, with 20-35% of subjects presenting symptom between day 4 and day 15 after their last high-risk exposure. The possibly infected patients had a lower prevalence of symptoms as time went by, with a rapid reduction of prevalence around day 15, while subjects with confirmed infection had a prevalence of symptoms that remained larger than 20% until day 30. The faster clearance of symptoms in possible infections suggests that these patients had a milder disease, which would be consistent with the fact that their nasopharyngeal swabs remained negative and that they did not exhibit detectable antibodies. Future analyses, that will include the probabilistic analysis of their serial negative nasopharyngeal swab results, as well as the study of the immune cellular response, will provide more conclusive evidence on their infection status [24].

A major limitation of our study is the absence of whole genome sequencing comparing the virus of the index subject and SARS-CoV-2-infected HCW. Therefore, the network of exposures and infection only suggests that the infection in a subject is the consequence of a high-risk exposure. However, sequencing would be restricted to RT-PCR positive subjects, which only represent 40% (26/65) of our population of confirmed and possible infections. Another limitation was that the type of contacts observed in the study has been modified by universal masking implemented on March, 18 th , 2020.

After this date, most at risk contacts were between two HCWs, which were less likely, but not unlikely, to result in SARS-CoV-2 transmission.

All together, the rate of transmission observed in HCWs after high-risk exposure, which could be as large as 44%, and close to a recent report [25], strengthens the conclusion that universal masking of HCW, both during contacts with patients and colleagues, and at all times, is essential to prevent preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this this version posted September 18, 2020. ; https://doi.org/10.1101/2020.09.17.20194860 doi: medRxiv preprint The first day when a specific symptom and a general symptom had been reported for two consecutive days was considered as the time of symptom onset.

The black dots show the viral loads at the first positive RT-PCR for each subject. The red dots show the time of the previous negative RT-PCR when present (8 subjects). The black curve is the best fitting second-order polynomial for viral load as a function of time since symptom onset, and the shaded area is the 95% confidence interval.

  Data collection Collected characteristics of the index included age, date of the diagnostic nasopharyngeal RT-PCR and the SARS-CoV-2 viral load [15].

Figure 1 Venn

 1 Figure 1 Venn diagram of the clinical, virological and immunological outcomes among the 154 contacts included in the CoV-CONTACT cohort. SARS-CoV-2 infection could be determined for 148/154 contacts (missing data for immunological and clinical outcomes (n=2), missing data for clinical outcome (n=1), missing data for immunological outcome (n=3).

Figure 2 Proportions

 2 Figure 2 Proportions of symptomatic contact subjects among the 154 contacts included in the CoV-CONTACT cohort.The orange curve corresponds to contacts subjects with confirmed SARS-CoV-2 infection (i.e., virologically-or immunologically-proven, n=37). The green curve corresponds to contacts subjects with possible SARS-CoV-2 infection (i.e., clinically-suspected without viro-immunological confirmation, n=28).

Figure 3 SARS

 3 Figure 3 SARS-CoV-2 viral load in the first positive SARS-CoV-2 nasopharyngeal swab as a function of time since symptom onset, in the 25 healthcare workers with a positive RT-PCR and who met the definition of clinical infection.

  presents the characteristics of the included contacts; 51/154 (33.1%) were medical doctors, midwifes, or residents; 77/154 (50.0%) were nurses, nursing assistant, physiotherapists or hospital students.Contacts were exposed to patients (70/152, 46.1%) or colleagues (95/152, 62.5 %) of whom 13/152 (8.6%) were exposed to both patients and colleagues.While the exposure to patients represented 68.2% (60/88) of high-risk exposure before March 18 th , this number dropped to only 11.8% (8/68) after March 18 th . Most contacts had a cumulated exposure of more than 30 minutes (102/151, 67.5%). In the 95 contacts exposed to an index colleague, exposure was related to face-to-face discussion (89/95, 93.7%), meetings (26/95, 27.4%), lunch sharing (20/95, 21.1%), and other (10/95, 10.5%). CoV-2 viral load was 8.7 log 10 copies/ml (IQR 6.5; 9.4).Overall, 147 of the 154 contacts had both inclusion and D30 sera samples. At inclusion, 15/147 (10%) contacts had a positive serology by one of the two methods. At D30, 31/147 (21.1%, 95%CI [14.8%; 28.6%]) contacts exhibited a seroconversion. Results obtained by the two serological methods are presented in Table

	Virological, immunological and clinical outcomes
	Overall, 26/154 contact subjects (16.9%, 95%CI [11.3%;23.8%]) had at least one SARS-CoV-2-positive
	nasopharyngeal swab (see details in supplementary appendix). When positive, the median
	nasopharyngeal SARS-

  HCWs infection and maintain hospital capacities during outbreaks [26]. Desan Vristi, Doute Jean Michel, Esperou Hélène, Hendou Samia, Kouakam Christelle, Le Meut Guillaume, Lemestre Soizic, Leturque Nicolas, Marcoul Emmanuelle, Nguefang Solange, Roufai Layidé Genetic: Laurent Abel, Sophie Caillat-Zucman ClinicalTrial. Gov identification number: NCT04259892 23. Kluytmans-van den Bergh MFQ, Buiting AGM, Pas SD, et al. Prevalence and Clinical Presentation of Health Care Workers With Symptoms of Coronavirus Disease 2019 in 2 Dutch Hospitals During an Early Phase of the Pandemic. JAMA Netw Open 2020;3:e209673 24. Gallais F, Velay A, Wendling MJ, et al. Intrafamilial Exposure to SARS-CoV-2 Induces Cellular

	Immune	Response	without	Seroconversion.
	https://www.medrxiv.org/content/10.1101/2020.06.21.20132449v1 2020
	25. Houlihan CF, Vora N, Byrne T, et al. Pandemic peak SARS-CoV-2 infection and seroconversion
	rates in London frontline health-care workers. Lancet 2020;396:e6-e7
	26. Houghton C, Meskell P, Delaney H, et al. Barriers and facilitators to healthcare workers'
	adherence with infection prevention and control (IPC) guidelines for respiratory infectious
	diseases: a rapid qualitative evidence synthesis. Cochrane Database Syst Rev 2020;4:CD013582

All rights reserved. No reuse allowed without permission.

Acknowledgments CoVCONTACT study group Principal investigator: Duval Xavier Steering Committee: Burdet Charles, Duval Xavier, Lina Bruno, Tubiana Sarah, Van Der Werf Sylvie CoV-CONTACT Clinical Centers: Abad Fanny, Abry Dominique, Alavoine Loubna, Allain Jean- Sébastien, Amiel-Taieb Karline, Audoin Pierre, Augustin Shana, Ayala Sandrine, Bansard Hélène, Bertholon Fréderique,Boissel Nolwenn, Botelho-Nevers Elisabeth, Bouiller Kévin, Bourgeon Marilou, Boutrou Mathilde, Brick Lysiane, Bruneau Léa, Caumes Eric, Chabouis Agnès, Chan Thien Eric, Chirouze Catherine, Coignard Bruno, Costa Yolande, Costenoble Virginie, Cour Sylvie, Cracowski Claire, Cracowski Jean Luc, Deplanque Dominique, Dequand Stéphane, Desille-Dugast Mireille, Desmarets Maxime, Detoc Maelle, Dewitte Marie, Djossou Felix, Ecobichon Jean-Luc, Elrezzi Elise,

Funding

The study was founded by Reacting, the French Ministry of Health (PHRC-N COVID-19, project PHRC-20-0242) and the European Commission (RECoVer, grant agreement 101003589). Some authors received financial support of the national research agency (ANR) through the ANR-Flash calls for COVID-19 (TheraCoV ANR-20-COVI-0018)

Contributors

ST, CB, XD, YY, JCL, JB, PB and BL designed the experiments. ST, MT, LA, AL and XD included subjects. NH, CC, DD, SvW and BL performed the biological analyses. ST, CB, PM, FB, JG and XD analyzed the data. ST, CB, PM, FB, JG CC, DD, SvW, BL and XD interpreted the results. ST, CB, FB, and XD wrote the Article. All authors reviewed and approved the manuscript before submission.

Declaration of interests

The authors have no commercial or other associations that might pose a conflict of interest.

Supplementary Methods

Data collection

In the case of exposure between colleagues working together, the beginning of the exposure period was fixed to 72 hours before the diagnosis of the SARS-CoV-2 infection of the index or the onset of the symptoms in the index, whichever occurred first.

SARS-CoV

LuLISA

The LuLISA N assay makes use of a nanobody fused to luciferase for the detection of IgG antibodies binding to the SARS-CoV-2 nucleoprotein (N). Sera were used at a 1:200 dilution. The luciferase signal was measured and expressed in Relative Light Units per second (RLU/s). The threshold of positivity (13,402 RLU/s) was based on the analysis of 231 pre-pandemic sera and defined as the mean + two standard deviations Supplementary Results

Virological, immunological and clinical outcomes

The median number of nasopharyngeal swabs performed per contact was two (IQR 1;3), and the median time between the last high-risk exposure and the first SARS-CoV-2-positive nasopharyngeal swab was 6. The median number of symptoms was 5 (IQR 4; 6) among the 28 contacts with possible SARS-CoV-2 infection and was 6 (IQR 4; 10) among those with confirmed SARS-CoV-2 infection.

Factors associated with SARS-CoV-2 infection

Exposure to a SARS-CoV-2-infected patient was at higher risk of SARS-CoV-2 infection than exposure to a SARS-CoV-2 colleague (p=0.023, Table 1). Nurses, nurse assistants, physiotherapists and hospital students had a higher risk than medical staff (p=0.04), as did pharmacists and administrative assistants (p=0.033). In the multivariable analysis, the c-statistic of this final model was 0.67 (95%CI=0.58; 0.76) and the p-value of the Hosmer-Lemeshow test was 0.99, showing no model misspecification.

All rights reserved. No reuse allowed without permission. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this this version posted September 18, 2020. ; https://doi.org/10.1101/2020.09.17.20194860 doi: medRxiv preprint Supplementary Figure S1 Structure of the contact network between the 44 index subjects and the 154 healthcare workers contact subjects with high-risk exposure to SARS-CoV-2 included in the CoV-CONTACT cohort.

Blue circles are health-care workers (either index or contact subjects), green circles are SARS-CoV-2 infected index patients. Circles with crosses represent the COVID-19 index subjects.

The arrows are the exposures; the red ones are the confirmed infections (i.e., virologically-or immunologicallyproven, n= 37), the orange ones are the possible infections (i.e., clinically-suspected without viroimmunological confirmation, n=28).

Supplementary Table S1

Immunological results obtained by the two serological methods (Lulisa N and EuroIMMUN) in the 147 healthcare workers contact subjects with available data, following a high-risk exposure to SARS-CoV-2 included in the CoV-CONTACT cohort.

Euroimmun technique


Anne-Claire Bennis

Roger Lewandowski
email: roger.lewandowski@univ-rennes1.fr

Edriss S Titi

Simulations de l'écoulement turbulent marin avec un modèle de déconvolution

On introduit une équation de déconvolution qui généralise l'algorithme de Van-Cittert pour des conditions aux limites de type océananique avec vent fixé. On en déduit un modèle de SGE pour lequel on a existence et unicité d'une solution régulière. Nous détaillons un ensemble de simulations numériques qui montrent l'intérêt pratique du modèle.

Abridged English version

A LES model based for the Navier-Stokes equations (NSE), where the convection term is replaced by (H N (u) • ∇)u, was introduced recently in [START_REF] Layton | A high accuracy Leray-deconvolution model of turbulence and its limiting behavior[END_REF]. In this model, H N (u) depends on u in the following way. For a given u, with ∇ • u = 0, we filter u by solving the Stokes (Helmholtz) like elliptic problem -α 2 ∆u+u+∇π = u, ∇•u = 0 subject to the appropriate boundary conditions, and we then set Au = u. We then follow the Van Cittert's algorithm (see [START_REF] Layton | A high accuracy Leray-deconvolution model of turbulence and its limiting behavior[END_REF]), u 0 = u, u n+1 = u n + {u -A -1 u n } and we set u N = H N (u) for some N . This model makes sense in the case of periodic boundary conditions (see [START_REF] Layton | A high accuracy Leray-deconvolution model of turbulence and its limiting behavior[END_REF]). Nevertheless, we cannot use it in the case of realistic nonhomogeneous boundary conditions, such as those satisfied by oceanic flows with a fixed wind stress at the surface under the rigid lid hypothesis. For this reason a substantial modification is necessary. Our contribution starts from observing that the Van Cittert algorithm is in fact nothing but a finite difference scheme of a certain evolution equation. Taking τ as the phony time evolution parameter, this equation for scalar quantities takes the form -α 2 ∆ ∂v ∂τ

+ v = u, v| τ =0 = u.
In this work, we make use of this remark to study the case of an oceanic flow satisfying the boundary conditions (2.1), below. Here

x = (x, y, z) ∈ IR 3 , O ⊂ IR 2 is a bounded smooth domain, Ω = O×[-h, 0], Γ s = O×{0}, Γ l = ∂O×[-h, 0], Γ b = O×{-h}; Γ = Γ s ∪Γ l ∪Γ b . Finally t ∈ [0, T ]
is the real time parameter. We first introduce the system (2.4)- (2.5). This yields the deconvolution model (2.7). In this model, we do not make the hydrostatic balance assumption in order to capture and model the vertical convection.

For the sake of simplicity, we do not consider the Coriolis force, which can be added to (2.7), without causing any difficulties in our analysis. We now give a short description of our results that will be reported in detail in [START_REF] Bennis | A generalized Leray-deconvolution model of turbulence[END_REF]. The space functions are defined in (2.2) below. For a given wind stress V, ψ = ψ(V) is a divergence free vector field which satisfies the boundary conditions (2.1) and is defined by (2.3). Let τ > 0 be given, and

u = u(t, x) with ∇ • u = 0. We set H τ (u)(t, x) = v(τ, t, x) + ψ(V)(x)
where v(τ, t, x) is solution of system (2.4)-(2.5) for a fixed time t (see (2.6) below). Notice that when τ = 0, H 0 (u) = u and therefore our model is precisely the Leray-α model, as considered in [START_REF] Cheskidov | On a Leray-α model of turbulence[END_REF] and [START_REF] Geurts | Regularization modeling for large eddy simulation[END_REF]. When τ = N is an integer, this model remains the same as the one introduced in [START_REF] Layton | A high accuracy Leray-deconvolution model of turbulence and its limiting behavior[END_REF] for the periodic boundary conditions case, and here it is adjusted to satisfy physical boundary conditions. Our main results are

Theorem 0.1 Assume V ∈ H 3 (O) 2 with a compact support, u 0 ∈ IH 1 (see definition (2.2)) and f ∈ C 0 ([0, T ], IH 1 ). Let τ > 0 be given, Problem (2.7) has a unique strong solution (u τ , p τ ) ∈ L 2 ([0, T ], H 2 (Ω) 3 ) × L ∞ ([0, T ], H 1 (Ω)) with u τ ∈ C([0, T ], L 2 (Ω) 3 ), ∂ t u τ ∈ L 2 ([0, T ] × Ω) 3 .
Theorem 0.2 There exists (τ n ) n∈N , which goes to infinity, when n goes to infinity, and such that the sequence (u τn ) n∈IN converges weakly in L 2 ([0, T ], IH 1 ) and strongly in

L 2 ([0, T ], IH 0 ), to a field u = (u h , w) ∈ L 2 ([0, T ], IH 1 ) ∩ L ∞ ([0, T ], L 2 (Ω) 3
), a Leray-Hopf weak solution to the NSE, with

∂ t u ∈ L 4 3 ([0, T ], IH ′ 1 )
and such that for all v = (v h , θ) ∈ L 4 ([0, T ], IH 1 ) (2.8) is satisfied. Moreover, u(t, •) converges weakly to u 0 in L 2 (Ω) 3 as t goes to 0. Moreover, u satisfies the energy inequality. Finally, we display numerical tests by using FreeFem++ [4] in the 2D case. Our code is semi-implicit and makes use of a method of the caracteristics adjusted to the deconvolution. Two cases have been considered. For each case, the wind stress is equal to V(x) = a(x) sin(πx), x = (x, y),

x h = x ∈ Γ s ≈ [0, 1]
, where a(x) has a compact support and it localizes the stress. In the first case, Ω is a square, ∆t = 0.2 s, α = 0.1 m, T = 90 s. The DNS exhibits a good behavior. We compare the cases where the order of deconvolution τ takes for values τ = 0 (Leray-α model), τ = 5 and τ = 20, ∆τ = 1. Vertical profils are displayed in Figure 3.1. They confirm the convergence Theorem and the validity of the code. The second case is the one where Ω has a topography (see Figure 3.2), ∆t = 0.02 s, α = 0.1 m, T = 10 s, τ = 5, ∆τ = 1. Poiseuille Flows have been imposed on the lateral boundaries to enhance turbulence and the DNS converges very slowly. Figure 3.3 displays one profil and underlines the improvement of the computation using the model compared with the Leray-α model. Therefore, our model appears to produce good results and hence could be suggested as a good alternative for simulations in real situations.

Introduction

On a introduit dans [START_REF] Layton | A high accuracy Leray-deconvolution model of turbulence and its limiting behavior[END_REF] un modèle de SGE basé sur les équations de Navier-Stokes, dans lequel le terme de convection vaut (H N (u) • ∇)u, H N (u) étant déduit de la vitesse u (avec ∇ • u = 0) en partant de la filtration -α 2 ∆u + u + ∇π = u, ∇ • u = 0. On pose Au = u, que l'on déconvole à l'aide de l'algorithme de Van Cittert,

u 0 = u, u n+1 = u n + {u -A -1 u n }, u N = H N (u)
. Ceci a un sens dans le cas de conditions aux limites périodiques et permet d'approcher les équations de Navier-Stokes par des problèmes bien posés avec un bon contrôle de l'erreur quand les lois de Kolmogorov sont satisfaites. Il semble difficile d'appliquer cette procédure telle quelle dans le cas de conditions aux limites réalistes, comme par exemple pour l'Océan avec une tension du vent en surface fixée, sous l'hypothèse du to ît rigide. La remarque principale dans ce travail est que l'algorithme de Van Cittert peut être vu comme l'équation aux différences finies d'une équation d'évolution qui s'écrit pour des scalaires sous la forme -α 2 ∆ ∂v ∂τ

+ v = u, u| τ =0 = u,
). Cette note annonce des résultats développés dans l'article en cours de finalisation [START_REF] Bennis | A generalized Leray-deconvolution model of turbulence[END_REF].

2 Resultats théoriques

Géométrie espaces fonctionnels

On note x = (x, y, z) un point de IR 3 , O ⊂ IR 2 un domaine borné régulier de

IR 2 , Ω = O × [-h, 0], où h > 0. Soient Γ s la surface, Γ s = O × {0}, et Γ l et Γ b les frontières latérales et le fond, Γ l = ∂O × [-h, 0], Γ b = O × {-h}. On note enfin Γ = Γ s ∪ Γ l ∪ Γ b .
Soit u = (u h , w) la vitesse de l'eau de mer, u h = (u, v) sa partie horizontale. Les conditions aux limites classiques sont (sous l'hypothèse du to ît rigide)

(2.1)

w| Γ = 0, u h | Γ l ∪Γ b = 0, ∇u h • n| Γs = V,
où n est la normale sortante, V = V(x, y) est le vent (ici fixé) défini sur O. On identifie O et Γ s . Les espaces fonctionnels sont les suivants :

(2.2)

IH 0 = {u = (u h , w) ∈ L 2 (Ω) 3 ; u • n| Γ = 0, ∇ • u = 0}, IH 1 = {u = (u h , w) ∈ H 1 (Ω) 3 , w| Γ = 0, u h | Γ l ∪Γ b = 0, ∇ • u = 0},
Nous montrons dans [START_REF] Bennis | A generalized Leray-deconvolution model of turbulence[END_REF] l'existence d'une base spéciale adaptée, résumé dans ce qui suit.

Lemme 2.1 Il existe une suite de réels strictement positifs

(λ n ) n∈IN des suites (e n ) n∈IN , (π n ) n∈IN où e n ∈ IH 1 ∩H 2 (Ω) 3 , π n ∈ H 1 (Ω) pour chaque n et tels que -∆e n +∇π n = λ n e n .
La démonstration utilise un argument de symétrie pour se ramener un problème de Stokes sur un cylindre avec des conditions aux limites de Dirichlet homogènes. Un résultat analogue avec des équations primitives a déjà été prouvé dans [START_REF] Ziane | Regularity results for a Stokes type system[END_REF] avec la même technique. Nous montrons dans [START_REF] Bennis | A generalized Leray-deconvolution model of turbulence[END_REF] que l'injection IH 1 ⊂ IH 0 est dense. Nous terminons cette section par le relèvement de la condition aux limites. On suppose que V = V(x, y) est à support compact dans Γ s . Soit ψ = ψ(x, y, z) le champ de vecteurs défini dans Ω par

(2.3) ψ(x, y, z) = ψ h ψ v = ρ(z)V(x, y) -κ(z)(∇ h • V)(x, y) = ψ(V), où κ(z) = z -h ρ(z ′ )dz ′ et ρ(z) = 3 4h z 2 + z + h 4 .
Il est facile de vérifier que ψ = ψ(V) est à divergence nulle dans Ω et satisfait les conditions aux limites (2.1).

La Filtration

On suppose que

V ∈ H 3 (O) 2 et est à support compact, α > 0 est fixé, u ∈ IH 1 . Soit (2.4) -α 2 ∆ û + û + ∇r = u -ψ(V), ∇ • û = 0, ŵ| Γ = 0, ûh | Γ l ∪Γ b = 0, ∇ ûh • n| Γs = 0.
En raisonnant par symétrisation on montre dans [START_REF] Bennis | A generalized Leray-deconvolution model of turbulence[END_REF] que (2.4) admet une unique solution ( û, r) avec û ∈ H 3-ε (Ω) 3 pour tout ε > 0. Soit u défini par u = û + ψ(V). On note que u a une trace sur Γ s ainsi que ∇u et donc u satisfait (2.1). Soit u = u(t, x) à divergence nulle. L'équation de déconvolution est, où τ est le paramètre de déconvolution

et v = v(τ, t, x) = (v h , θ), t ∈ [0, T ] est fixé, (2.5)    -α 2 ∆ ∂v ∂τ + v + ∇π = u -ψ(V) = û, ∇ • v = 0, v h | Γ l ∪Γ b = 0, ∇v h • n| Γs = 0, θ| ∂Ω = 0, v(0, x) = u + ψ(V) = û. Soit τ > 0, H τ (u)(t, x) = v(τ, t, x) + ψ(V)(x). Avec la base du Lemme 2.1, on écrit pour u ∈ L 2 ([0, T ], IH 1 ) ∩ L ∞ ([0, T ], IH 0 ), u = ∞ k=1 u k (t)e k et ψ(V) = ∞ k=1 ψ k e k . On a (2.6) H τ (u)(t, x) = u(t, x)+ ∞ k=1 (u k (t)-u k (t)) exp(- τ α 2 λ k ) e k (x), u k (t) = u k (t) + α 2 ψ k 1 + α 2 λ k ,

Le modèle de déconvolution

Le modèle de SGE que nous considérons est le suivant, avec u la vitesse et p la pression :

(2.7)

∂ t u + (H τ (u) • ∇) u -ν△u + ∇p = f , ∇ • u = 0, w| Γ = 0, u h | Γ l ∪Γ b = 0, ∇u h • n| Γs = V, u t=0 = u 0 ,
Notons que quand τ = 0, il s'agit du Leray-α modèle ( [START_REF] Cheskidov | On a Leray-α model of turbulence[END_REF]). Nous prouvons dans [START_REF] Bennis | A generalized Leray-deconvolution model of turbulence[END_REF] :

Théorème 2.1 Soit V ∈ H 3 (O) 2 à support compact, u 0 ∈ IH 1 et f ∈ C 0 ([0, T ], IH 1 ). Pour τ > 0 fixé, le système (2.7) admet une unique solution (u τ , p τ ) ∈ L 2 ([0, T ], H 2 (Ω) 3 ) × L ∞ ([0, T ], H 1 (Ω)) avec u τ = u τ (t, x) ∈ C([0, T ], L 2 (Ω) 3 ), ∂ t u τ ∈ L 2 ([0, T ] × Ω) 3 .
Théorème 2.2 Il existe une suite (τ n ) n∈N qui tend vers l'infini quand n tend vers l'infini, telle que (u τn ) n∈IN converge faiblement dans

L 2 ([0, T ], IH 1 ), fortement dans L 2 ([0, T ], IH 0 ), vers un champ u = (u h , w) ∈ L 2 ([0, T ], IH 1 )∩L ∞ ([0, T ], L 2 (Ω) 3 ) avec ∂ t u ∈ L 4 3 ([0, T ], IH ′ 1 ) et tel que pour chaque v = (v h , θ) ∈ L 4 ([0, T ], IH 1 ) on a (2.8) < ∂ t u, v > - T 0 Ω u ⊗ u : ∇v + ν T 0 Ω ∇u : ∇v - T 0 Γs V • v h = T 0 Ω f • v.
De plus, u(t, •) tend faiblement vers u 0 dans L 2 (Ω) 3 quand t tend vers 0, et vérifie l'inégalité d'énergie.

Résultats numériques

On résoud (2.7) par la méthode des éléments finis en utilisant FreeFem++ [4] dans le cas 2D, pour τ fixé. On détermine la pression et la vitesse par un schéma semi-implicite initialisé avec des solutions d'un problème de Stokes. On a écrit un algorithme de résolution itératif qui adapte la méthode des caractéristiques au cas du transport déconvolé. On arrête la simulation lorsque les algorithmes ont convergé. On présente un premier cas servant à valider notre modèle de déconvolution et un deuxième cas qui montre son intérêt pratique.

Turbulence induite par le vent de surface

On considère Ω = [0, 1] × [-0.5, 0], triangulé avec h max = 0.014 m et h min = 0.006 m. On choisit V(x) = a(x) sin(πx) où a(x) est une fonction de localisation à support compact. On compare les résultats des simulations DNS et LES pour des paramètres de déconvoution successivement égaux à τ = 0, τ = 5 ou τ = 20 grâce à des profils verticaux ; ici ∆τ = 1, α = 0.1 m, ∆t = 0.2 s et on a fait 450 itérations en temps, ce qui nous donne le résultat pour T = 90 s. On trouve une erreur L 2 moyenne de 0.5 % entre les résultats DNS et les résultats du modèle de déconvolution pour τ = 20 et de 1% pour τ = 5, ce qui est satisfaisant et ce qui valide notre modélisation. De plus, on a divisé l'erreur L 2 moyenne d'un facteur 4 entre les résultats du Leray-α modèle (τ = 0) et ceux du modèle de déconvolution pour τ = 20, ce qui montre l'amélioration apportée.

Cas avec bathymétrie

On considère le domaine Ω décrit ci-dessous avec une bosse, triangulé avec h max = 0.010 m et h min = 0.003 m. On observe que notre modèle améliore la solution donnée par le modèle Lerayα, ce qui est en accord avec les conclusions précédentes. Ce profil montre qu'il faut augmenter le nombre de déconvolution qui est égal à 5 comme préconisé par Adams et al [START_REF] Stolz | An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows[END_REF]. Il est aussi nécessaire d'abaisser la valeur du paramètre de filtration α, afin d'avoir un temps de calcul raisonnable par un abaissement du taux de déconvolution. Ce cas montre que notre modèle peut corriger les effets de la filtration et montre aussi que le calage des paramètres de déconvolution et de filtration n'est pas le même selon les cas étudiés.

Aknowledgement. The work of Roger Lewandowski is partially supported by the ANR project 08FA300-01. The work of Edriss S. Titi is partially supported by NSF grant No DMS-0708832 and the ISF Grant No 120/6.

Figure 3 . 1 :

 31 Figure 3.1: Profils verticaux de la vitesse horizontale pour la DNS (DNS), pour le modèle de déconvolution avec τ = 5 (LES-1) et avec τ = 20 (LES-2) et pour le modèle Leray-α (Leray-α)

Figure 3 . 2 :

 32 Figure 3.2: Géométrie du domaine à gauche et Résidus des équations de Navier-Stokes à droite (DNS en rouge, modèle de déconvolution en bleu et modèle Leray-α en noir)

Figure 3 . 3 :

 33 Figure 3.3: Profil vertical de la vitesse horizontale. Modèle de déconvolution en bleu (LES-1), modèle Leray-α en noir (Leray-α) et DNS en rouge

  où τ est le paramètre de déconvolution. Nous exploitons cette remarque de manière rigoureuse pour les conditions aux limites (2.1) satisfaites par la vitesse de l'écoulement marin, en introduisant le système (2.4)-(2.5). Cela nous permet d'introduire le modèle de SGE (2.7). Dans ce modèle, nous ne faisons pas l'hypothèse hydrostatique pour mieux décrire les effets convectifs et capter la couche de mélange. Pour simplifier la présentation, nous n'avons pas pris en compte la force de Coriolis, qui peut être rajoutée dans (2.7) sans changer la nature de notre analyse. Nous montrons que ce modèle conduit à un problème bien posé et nous avons un résultat de convergence vers les équations de Navier-Stokes quand le paramètre de déconvolution tends vers l'infini. Dans une série de tests numériques, nous validons le modèle dans le cas 2D en comparant les résultats obtenus avec ceux d'une DNS convergente. Nous produisons des calculs numériques dans un cas avec topographie, cas pour lequel la DNS a un mauvais comportement. Le modèle donne des bons résultats numériques pour τ = 5 qui affinent ceux donnés par les Leray-α modèles habituels adaptés à nos conditions aux limites avec notre méthode, puisqu'ils correspondent au cas τ = 0 (voir les modèles d'origine dans[START_REF] Cheskidov | On a Leray-α model of turbulence[END_REF], [