# Exposure history shapes SARS-CoV-2 viral dynamics in Non-Human Primates and provides insights into correlates of protection against infection and transmission

Adrien Mitard de Girardier, Cécile Herate, Romain Marlin, Flora Donati, Yannis Rahou, Laëtitia Bossevot, Quentin Sconosciuti, Mariangela Cavarelli, Nathalie Dereuddre-Bosquet, Francis Relouzat, et al.

► To cite this version:

Adrien Mitard de Girardier, Cécile Herate, Romain Marlin, Flora Donati, Yannis Rahou, et al. Exposure history shapes SARS-CoV-2 viral dynamics in Non-Human Primates and provides insights into correlates of protection against infection and transmission. Philosophical Transactions of the Royal Society B: Biological Sciences, In press, 10.1098/rstb.2024.0343. inserm-05291797

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1 Exposure history shapes SARS-CoV-2 viral dynamics in Non-Human Primates and provides

2 insights into correlates of protection against infection and transmission

3 Adrien Mitard de Girardier (1,2), Cécile Herate (3), Romain Marlin (3), Flora Donati (4), Yannis Rahou

4 (4), Laëtitia Bossevot (3), Quentin Sconosciuti (3), Mariangela Cavarelli (3), Nathalie Dereuddre-

5 Bosquet(3), Francis Relouzat (3), Sylvie van der Werf (4), Etienne Simon-Loriere (5), Mélanie Prague

6 (2,6*), Jérémie Guedj (1*), Roger Le Grand (3*)

7 (1) Université de Paris Cité, IAME, INSERM F-75018 Paris, France.

8 (2) Inria Bordeaux Sud-Ouest, Inserm, Bordeaux Population Health Research Center, SISTM Team,

9 UMR 1219, University of Bordeaux, Bordeaux, France.

10 (3) Université Paris-Saclay, Inserm, CEA, Center for Immunology of Viral, Auto-immune,

11 Hematological and Bacterial diseases (IMVA-HB/IDMIT/UMRS1184), Fontenay-aux-Roses & Le

12 Kremlin-Bicêtre, France

13 (4) National Reference Center for Respiratory Viruses, Molecular Genetics of RNA Viruses, CNRS

14 UMR3569, Institut Pasteur, Université Paris Cité, Paris, France.

15 (5) Institut Pasteur, Université Paris Cité, National Reference Center for Respiratory Viruses,

16 Evolutionary Genomics of RNA Viruses Unit, Paris, France.

17 (6) Vaccine Research Institute, Créteil, France.

18 *These authors contributed equally to this work.

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# ABSTRACT

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In the SARS-CoV-2 Omicron-variant era, the efficacy of vaccination in preventing viral replication is poorly understood and is further complicated by heterogeneous and hybrid immunity in the population. Here, we analysed by mathematical models the kinetics of both viral load and antibodies in non-human primates (NHPs) with different exposure histories, conferred by infection or vaccination with mono- or bi-valent vaccines. The model describes the control of viral replication by antibodies that accelerate the clearance and reduce the infectivity of viral particles, and suggests that a previous infection leads to a faster elimination of infected cells, which is not mediated by antibodies.

Finally, we used the model to simulate natural infections and show that both binding, neutralisation and exposure history need to be taken into account to predict risks of infection and transmission.

Protection from infection could be reached at levels of $3×10^4$ AU.mL$^{-1}$ for individuals who received both monovalent and bivalent vaccinations whereas hybrid immunity (infection followed by bivalent vaccination) could provide complete protection irrespective of antibody levels. These findings highlight the importance of exposure history in shaping immune responses and suggest correlates of protection for future vaccine and monoclonal antibodies strategies.

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Large-scale vaccination campaigns have dramatically reduced the risk of severe COVID-19 and prevented a large number of deaths since 2021 (1). However, their efficacy against infection and transmission remains less clear, as shown by the large number of recorded infections by Omicron variants in vaccinated individuals during the years 2021-2022 (2). Today, vulnerable population, such as immuno-compromised individuals, remain at risk of severe disease; therefore, it remains crucial to develop vaccines that can effectively reduce the circulation of the virus in the population.
The development of vaccines has focused on preventing symptomatic and/or severe disease.

Accordingly, correlates of protection (CoP) have rapidly been proposed (3–6) and were then also used to accelerate the development of bivalent vaccines against emerging variants (7–9). No such CoP has been established against infection and/or transmission, as this would require complex study designs to detect asymptomatic infections and reconstruct transmission events. While viral load in the upper respiratory tract is often used as a proxy for infectiousness and risk of transmission (10), there is no clear understanding of how vaccination reduces viral load. The question becomes even more complex today due to the diversity of immune backgrounds, with most individuals having hybrid immunity conferred by both vaccination and infection with different variants (11).

Animal models offer many advantages to study this question in a highly controlled environment (12–15). Here we used cynomolgus macaques to investigate the effects on infection by an Omicron variant of different immune backgrounds resulting from either vaccination with the original mRNA vaccine adapted to pre-Omicron variants (BNT162b2), recall with a bivalent vaccine adapted to Omicron variants, or from hybrid immunity (infection with previous Omicron strains and vaccination with the bivalent vaccine). To explore the effects of exposure history on viral and immune response dynamics, we developed a mathematical model that describes the impact of the immune response on viral replication. Using the model, we predict the effects of exposure history on viral dynamics and discuss the findings to propose CoP against infection and transmission.

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## 65 RESULTS

Previous infection or vaccination with a bivalent mRNA vaccine significantly reduces SARS-CoV-2 replication

We designed a study in which 22 immunologically naïve cynomolgus monkeys were divided into 4 groups: a control group (N), a group that received two doses of the original monovalent vaccine
70 (M/M), a group that received one dose of monovalent vaccine and a dose of bivalent vaccine targeted
71 against Omicron BA.4/BA.5 (M/B), and a group that was infected with Omicron BA.1 and/or BA.2 and
72 then received a dose of bivalent vaccine to generate hybrid immunity (C/B). All animals were
73 subsequently challenged with 10⁵ PFU of Omicron BQ.1.1 (Fig. 1A and S.1.).

74 A second injection with the bivalent vaccine (M/B), but not with the monovalent one (M/M),
75 significantly reduced virus replication compared to control (N, p<0.05 by t-test). The effect was even
76 more striking in animals that were both vaccinated and infected (C/B), with mean peak viral loads equal
77 to 7.4 [95% CI: 6.8 – 8.0], 7.1 [6.6 – 7.5], 4.8 [3.1 – 6.5] and 3.4 [2.5 – 4.3] log₁₀ copies/mL in groups N,
78 M/M, M/B and C/B, respectively (Fig 1B). Similar effects were observed for viral titers (Fig. 1C) and
79 time to viral clearance (Fig. S.2).

80 The effect on viral load was correlated with antibody levels. At the time of challenge, the mean binding
81 levels were 1.6 [1.4 – 1.8], 3.6 [3.3 – 4.0], 4.1 [3.9 – 4.3] and 4.7 [4.5 – 4.9] log₁₀ AU/mL in N, M/M,
82 M/B and C/B, respectively (Fig. 1D). The difference between groups in neutralizing antibody was more
83 visible, with levels above the limit of detection for none, half and all animals in M/M, M/B and C/B,
84 respectively (Fig. 1E). All animals with detectable neutralizing activity at the time of challenge had peak
85 viral load below 5 log₁₀ copies/mL and a viral clearance achieved within 6 days. This suggests that
86 neutralizing activity is linked with viral dynamics and may be a key factor to distinguish mono- and
87 bivalent vaccination.

88 A comprehensive model of immune and viral trajectories after repeated exposure and infection

90 We developed (see Methods) a viro-immunological model that incorporates antibodies (binding and
91 neutralizing levels) to explain the heterogeneity observed in viral dynamics as a function of exposure
92 history (Fig. 2). In the following, we discuss the key components of the model, starting with the immune
93 response dynamics and then how viral dynamics are mediated by antibodies and exposure history. All
parameter estimates can be found in Table 1, individual fits are presented in Figures 3, S.3 and S.4,
visual predictive checks are available in the supplementary (Fig. S.9-12) as well as residuals (Fig. S.13).

Antibody dynamics after different exposure histories

A two-compartment model for the B-cell response well reproduced antibody dynamics during
the whole study from the time of first exposure to the viral challenge (Fig. 3A). In this model, short-
lived plasma cells S (with a half-life, log(2)/δs, equal to 0.50 days [95% CI: 0.26 – 0.88]) were largely
predominant, with a small proportion, ρ (about 2 per 1000 cells), of long-lived L cells (with a half-life,
log(2)/δL of 700 days). Plasma cell recruitment after infection in immunologically naïve NHPs, starts
with a delay, τVL¹, equal to 9.5 days [9.1 – 10.0]. The response of animals with previous exposure to
vaccination or infection, τVL², was faster and estimated to 6.0 days [5.8 – 6.2]. In addition, the
proliferation rate of B-cells, noted r, was more rapid in convalescent animals with a fold-change factor,
eβinf;r, equal to 1.5 [95% CI: 1.2 – 2.1].

Modelling the control of viral replication by antibodies and exposure history

We next investigated how antibody levels shaped viral dynamics via binding and neutralization.
The formation of virus-binding antibody complexes occurred at an estimated rate k_on equal to 4.3*10⁻⁴ mL.AU⁻¹.d⁻¹, and these complexes were rapidly cleared with a clearance rate that was assumed to be three times more rapid than the natural clearance (16). This leads to an increase of the clearance of the virus that can be assessed using the mean antibody levels observed in each group at the time of exposure (see Methods). We estimated that this “effective clearance”, c_off, was increased compared to naïve animals by a factor 1.2 [95% CI: 1.1 – 1.6], 1.6 [1.2 – 2.1] and 2.3 [1.7 – 2.7] in M/M, M/B and C/B groups, respectively. The half-lives of free viruses were thus shorter in previously exposed animals, with values estimated to 1.0 h [0.7 – 1.6], 0.8 h [0.5 – 1.2] and 0.6 h [0.4 – 0.9] in M/M, M/B and C/B groups, respectively, compared to 1.3 h [0.8 – 2.3] in naïve animals.

Antibodies also acted through virus neutralisation preventing cell infection. We introduced a
neutralizing efficacy parameter noted $\gamma$. It represents the proportion of viruses bound by antibodies
(forming then immune complexes) that are completely neutralised and unable to infect new cells,
while the others are still able to infect at the same rate. The model identified that a monovalent
vaccination elicited less neutralizing activity against the variant of infection than a bivalent vaccination
or a previous omicron infection. At the time of challenge, the cumulated exposure to vaccination or
infection led to neutralization efficacies estimated to 15% [95% CI: 5.3 – 31], 41% [24 – 64] and 75%
[54 - 90] in groups M/M, M/B and C/B, respectively (corresponding to γ₀e²*βₘ₄₀, γ₀eβₘ₄₀ and γ₀).

Again, using the mean observed antibody levels and the estimated neutralisation efficacies, we
obtained that the “effective” cell infection rate was reduced compared to control animals by a factor
1.0 [1.0 – 1.1], 1.1 [1.1 – 1.3] and 1.8 [1.3 – 2.8] in M/M, M/B and C/B groups, respectively.

The model finally identified a non-antibody mediated effect of exposure history on the loss rate of
productive infected cells, noted δ₁. The fold increase compared to the naïve state was estimated to 1.3
[1.1 – 1.5], 2.3 [1.9 – 2.7] and 35 [11 – 109] in M/M, M/B and C/B groups, respectively (evolution across
the study described in Fig S.5).

All these mechanisms led to a change in the within-host reproductive number, R₀, with values equal to
4.9 [95% CI: 4.1 – 6.0], 3.3 [2.6 – 4.2], 1.6 [1.3 – 2.0] and 0.06 [0.02 – 0.17] in N, M/M, M/B and C/B,
respectively. Key viral metrics can then be retrieved for the different groups. We found mean peak
viral loads in the nasopharynx equal to 6.0 [5.4 – 6.5], 5.5 [4.8 – 6.1], 5.0 [4.3 – 5.7] and 2.4
log₁₀(copies/mL) [1.5 – 3.5] in N, M/M, M/B and C/B, respectively. These values were lower than what
was observed in animals in N and M/M groups (see discussion). However, the predicted time to viral
clearance was close to those observed, with values of 16.0 [12.2 – 19.7], 12.0 [8.5 – 17.0], 8.1 [5.4 –
11.7] and 1.1 day [0.5 – 3.1] in N, M/M, M/B and C/B, respectively.

## Binding and neutralisation as correlates of protection against infection and transmission

Finally, we used the model to predict the impact of these different immune backgrounds
during a natural infection. In order be more realistic, infections were simulated assuming a lower viral
inoculum of 10 PFU (17). We considered complete protection from infection if the mean peak viral
load was below the limit of detection at all times. With this definition, C/B exposure was associated
with complete protection in all scenarios considered, regardless of the antibody levels at baseline. For
vaccinated and non-previously infected individuals, the peak viral load decreased with higher antibody
binding levels and complete protection from infection was achieved at levels 4x10⁵ and 3x10⁴ AU/mL
for M/M and M/B backgrounds respectively, albeit with large confidence intervals (Fig. 4A). Similar
patterns were observed for viral titers, a proxy of infectiousness (18,19), with complete protection
against transmission (i.e., undetectable mean viral titers at all time) when antibody binding levels reach
about 8x10⁴ and 3x10³ AU/mL for M/M and M/B backgrounds, respectively (Fig. 4B). We then assessed
risks of infection and transmission while varying both antibody binding and neutralizing levels. The last
information needed to simulate viral trajectories is then the loss-rate of infected cells (δᵢ). Complete
protection was found, regardless of the antibody binding level, for antibody neutralizing levels, ID50,
of about 400 and 160 if δᵢ is consistent with M/M (Fig. 4.C,D) or M/B (Fig. 4.E,F) backgrounds
respectively.

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DISCUSSION

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Our experimental study showed that exposure history shapes viral dynamics after an infection
with SARS-CoV-2 Omicron variant. Individuals with a booster of bivalent mRNA vaccine (M/B) had
lower viral load than those with only monovalent vaccination (M/M), and the effect was more dramatic
in individuals with hybrid immunity (C/B). To understand the impact of exposure history, we developed
a mathematical model that describes the host pathogen interaction. We found that antibodies
controlled viral replication through both an increased clearance of the virus and a reduction of viral
infection (neutralization). In addition to antibody-mediated mechanisms, we found that exposure
history had a major effect on the elimination rate of infected cells. Using parameter estimates and the
observed mean binding levels, we estimated the within-host reproductive number, R₀, to 4.9, 3.3, 1.6
and 0.06 in N, M/M, M/B and C/B, respectively. Based on these results, we predicted that infection
169 could be averted at a binding level of 3x10⁴ and 4x10⁵ AU.mL⁻¹ after M/B and M/M vaccination, 170 respectively. Assuming that viral dynamics are similar in saliva and nasopharynx, antibody binding 171 levels about 10-fold lower were sufficient to protect against transmission (i.e., no detectable infectious 172 virus).

173 The study unambiguously demonstrates that exposure history shapes viral replication.
174 Vaccination with original monovalent mRNA vaccine had limited effect on viral load consistent with 175 the substantial neutralisation escape of SARS-CoV-2 BQ.1.1 (20) and with the rapid transmission of 176 Omicron variants in largely vaccinated population. More interesting, vaccination with bivalent vaccine 177 had a large effect on viral load, showing that the higher immunogenicity conferred by updated vaccines 178 is associated with a better control of viral replication (8,21). As expected, hybrid immunity provided 179 the most efficient protection (22) with an enhanced clearance of infected cells found in animals that 180 were previously infected. This effect was not mediated by antibodies and could suggest a stronger 181 cytotoxic T cell response in this population (23,24). It is so large that convalescents are protected from 182 infection irrespectively of antibody levels. Consistent with this prediction, two animals in this group 183 were re-challenged only 2 months after their primary challenge, and none of them were infected, 184 despite low predicted antibody levels (Fig. S.5). It would therefore be of great interest to understand 185 the mechanisms behind this covariate effect and its persistence. It could also simply reflect the fact 186 that convalescent animals were younger and included male animals, although neither age or sex were 187 found significantly associated with parameter values (not shown).

188 These results can inform on protection against infection and transmission. Our model 189 suggested that high levels of antibodies (> 10⁴ AU/mL) were required to prevent viral replication, at 190 least in absence of a previous infection with an Omicron-variant. Validating these results in humans is 191 made difficult by the fact that it would require to prospectively track individuals for both symptomatic 192 and asymptomatic infections as well as following closely their antibodies dynamics. Yet, a prospective 193 study in Japan, which took place in the Omicron era between June 2022 and March 2023, estimated
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that binding antibody levels greater than 10⁴ AU.mL⁻¹ reduced the risk of infection by 33 to 66%
compared to the median risk of 6% (25).

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The main originality of our study was the development of a model that captured the viral and
immunological interplay following infection. To account for the different mechanisms of action of
antibodies, the model distinguished the capability of antibodies to bind to viral particles (leading to
rapid clearance) and their neutralization efficacy, noted γ, to prevent successful cell infection when
bound to virus particles. According to our simulations, neutralisation brings only limited extra
information compared to binding against a strain antigenically close to the infecting variant. It derives
from the assumption that there cannot be neutralisation without binding which is consistent with the
current understanding of antibody mechanisms (26). Overall, the model allows to disentangle the
information brought by binding and neutralisation assays as they both depend on antibody
concentration and affinity. The predictions could be supported by additional experimentations. First,
the clearance of immune complex could be measured by assessing the clearance while increase dose
of monoclonal antibody as previously done in HIV with inactivated virus (16). Second, a proxy of the
neutralisation efficacy could be obtained by diluting serum to hit a specific range of binding level. Using
this "antibody-normalized scale", one could measure how well the antibodies neutralize the virus.

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The second originality of the model is the capability to model antibody dynamics after repeated
exposure (up to 4 per animal in this study). Compared to previous models of the B cell response (27,28)
we did not include a memory compartment – often unidentifiable. The proliferation rate of plasma
cells was assumed to be proportional to the number of long-lived plasma cells *L*. It is coherent to use
*L* as a proxy of the memory because its half-life is 3 times longer than the maximum gap between
exposures (700 against 230 days). In addition to a better identifiability, which is crucial as most datasets
provide little information on circulating B cells and even less on memory cells, this model is also robust
to a complexification of the design. For example, fitting two vaccinations didn't require more
parameters than a single injection.

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The model provides parameter estimates that are consistent with results from the literature.
First the delay in antibody recruitment in naïve animals of 9.5 days is coherent with IgG, IgM and IgA
being detected only 10 days after infection during a human challenge in seronegative adults (29).
Immune response was also characterized by a low ratio between L and S (2.4 for 1000), close to the
value of 4 for 1000 found by Balelli et al in the context of vaccination against Ebola infection (27).
Regarding the viral dynamic part of the model, we estimated the within-host reproductive number of
the naïve group, R₀, to 4.9, in the same range as previous estimates for different SARS-CoV-2 variants
in the same animal model (between 2.8 and 5.4) (15). It is usually higher for human infections with an
estimation of 22, albeit with large uncertainty, in a healthy volunteer challenge (30).

This study nonetheless contains a number of limitations that we discuss below. The binding
levels were not measured against the infecting strain BQ.1.1 but against BA.5, a close ancestor.
However, the impact on the estimation of the immune complex formation rate (k_on) should be minimal
as the antigenic difference is limited (31). Further, we used blood antibodies as a marker of antibody
levels, while the dynamics in site of infection could be different, and possibly more rapid (29). It also
prevented us from investigating the impact of mucosal immunity on viral replication, a question of
great interest as nasal vaccines are expected to offer higher protection than traditional ones against
respiratory viruses (32). There is currently no consensus on the matter, yet, a study on vaccinated
healthcare workers showed that an increase in IgA titer reduces the risk of breakthrough Omicron
infection (33). However, we found no statistical benefit in estimating different parameters for the
nasopharynx and the trachea suggesting a limited effect of mucosal immunity in this experimental
context.

Another model limitation was the overestimation of peak viral load in the nasopharynx for the N and
M/M groups. As this endpoint is well captured in the trachea (Fig. S.2, 3), this could be due to the large
experimental variability observed between nostrils (Fig. S.14). As a different nostril is sampled each
243 day, this is a source of noise that could lead the model to interpret very high values as measurement
244 errors.

245 Finally, a number of parameters had to be fixed to ensure parameter identifiability (Table 1).
246 To address this, a number of sensitivity analyses were made, showing limited impact especially on viral
dynamics (Fig. S.7 and S.8).

248 In summary, we developed a model that explains the impact of exposure history on antibodies
249 and Omicron viral dynamics. It shows that vaccination has an effect on viral replication, and can be
250 used to calculate the level of protection required to reduce the risk of infection and transmission.

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252 MATERIALS AND METHODS

253 Ethics and biosafety statement for NHP experiments

254 20 female and 2 male adult cynomolgus macaques (M. fascicularis), aged 4-15 years at the
255 initiation of the study and originating from Mauritian AAALAC-certified breeding centres were included
256 in this study. All animals were housed at the IDMIT facilities (CEA, Fontenay-aux-roses) under BSL-3
257 conditions (animal housing permit #E92-032-02, Préfecture des Hauts de Seine, France) and in
258 compliance with European Directive 2010/63/EU, French regulations and the Standards for Human
259 Care and Use of Laboratory Animals of the Office for Laboratory Animal Welfare (OLAW, insurance
260 number F22-00556, USA). The protocols were approved by the institutional ethics committee “Comité
d’Ethique en Expérimentation Animale du Commissariat à l’Energie Atomique et aux Energies
261 Alternatives” (CEtEA #44) under statement number A22-006. The study was approved by the Ministry
262 of Research, Innovation and Education under the registration number APAFIS# 36939-
263 2022042217237124v1.
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266 NHP study design
267 **Immunisation phase**

268 22 naïve cynomolgus macaques are included in the study. They are divided into 4 groups:
269 Control (N), Monovalent + Monovalent (M/M), Monovalent + Bivalent (M/B), Convalescent + Bivalent
270 (C/B) (Fig. 1A). The M/M and M/B groups received, on day -130, a first vaccine dose of the mRNA
271 vaccine BNT162b2 (Comirnaty). The NHPs were immunized with 30 µg (in 0.3 mL) by intramuscular
272 injection into the thigh. This corresponds to the human dose administered in the clinic. On day -102,
273 the M/M group received a second dose of the same vaccine by intramuscular route, while the M/B and
274 C/B groups received a dose of the bivalent mRNA Comirnaty vaccine containing 15/15 µg of
275 original/Omicron BA.4-5. Blood samples were collected on days 0, 14 and 28 after each vaccine dose
276 for binding measurements. In terms of demographics (Table S.1), groups N, M/M, and M/B are similar,
277 with only females and a mean age of 15 years. In contrast, the C/B group is younger, with a mean age
278 of 5 years, and included two males and two females.

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280 **SARS-CoV2 challenge**

281 Vaccinated and control animals were challenged on day 0 with SARS-CoV-2 BQ.1.1 (hCoV-
282 19/France/IDF-IPP50823/2022 - EPI_ISL_15195982), provided by the National Reference Center for
283 Respiratory Viruses at the Institut Pasteur, using atropine (0.04 mg/kg) for premedication and
284 ketamine (5 mg/kg) with medetomidine (0.05 mg/kg) for anaesthesia. 90% of the inoculum (10⁵ PFU)
285 was injected intra-tracheally and the remainder intra-nasally, half in each nostril. Nasopharyngeal and
286 tracheal fluids were collected longitudinally on days -6, 2, 3, 4, 6, 7, 10, 14, 21 and 28. Blood samples
287 were collected on days 0, 10 and 21 for binding measurements and on days 0, 14, 28 and 42 for IC50
288 quantification. All samples are taken under anaesthesia (ketamine + medetomidine). Atipamezole is
289 used to shorten anaesthesia's length to less than 30 minutes. The NHPs are put in individual isolation
290 15 days prior to the challenge and until the end of the study (on day 42).
291 Animals in the C/B group were primarily challenged one year earlier (on day -329) using the same
292 protocol with 10⁵ PFU of SARS-CoV-2 BA.2 (hCoV-19/FrancePDL-IPP08031/2022) provided by the
293 National Reference Center for Respiratory Viruses at the Institut Pasteur. It should be noted that two
294 NHPs in this group had also been infected 2 months earlier (on day -385) with 10⁵ TCID₅₀ of SARS-CoV-
295 2 BA.1 (hCoV-19/USA/MD-HP20874/2021) provided by the NIH/BEI (reference: NR-56462). We refer
296 to these as historical challenges.

297 **Experimental measurements**

298 Viral quantification

299 Samples of the upper respiratory tract (nasopharyngeal and tracheal) were collected with swabs (Viral
300 Transport Medium, CDC, DSR-052-01). Tracheal swabs were taken by inserting the swab above the tip
301 of the epiglottis into the upper trachea at a distance of approximately 1.5 cm from the epiglottis.
302 Nasopharyngeal swabs were taken alternately in each nostril to reduce stress to the animal. All
303 samples were frozen at -80°C until analysis by RT-qPCR (13). Viral genomic RNA (gRNA) and subgenomic
304 RNA (sgRNA) were quantified in swabs by RT-qPCR with a standard plasmid reference according to the
305 WHO protocol (34). The limits of detection (LOD) are 2.67 and 2.87 log₁₀(copies/mL) for genomic and
306 subgenomic RNA, respectively. The corresponding limits of quantification are 3.67 and 3.87
307 log₁₀(copies/mL).

308 Viral titers were measured by inoculation of serial two-fold dilutions of the swab specimens on Vero-
309 E6 cells and the presence of a cytopathic effect was determined after 72h of incubation at 37°C
310 essentially as described in a previous study (35). Viral titers are expressed as TCID₅₀/mL (Tissue Culture
311 50% Infectious Dose per mL), they have a LOD of 20 TCID₅₀/mL and an upper limit of quantification
312 (ULOQ) of 2500 TCID₅₀/mL. Viral titers were only measured on nasopharyngeal swabs.
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In two animals from the control group (MF02 and MF06), only one nostril was infected and the other nostril had no detectable viral load at any sampling time. To limit bias in the analysis, only the viral load in the infected nostril was analysed and the viral load in the uninfected nostril was excluded.

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Quantification of IgG concentration by electrochemiluminescence assay

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Cynomolgus macaque blood samples were analysed for spike-specific IgG levels against SARS-CoV-2 wild-type and variants using the V-PLEX SARS-CoV-2 Key Variant Spike Panel 1 (IgG MesoScale Discovery [MSD], Rockville, USA) according to the manufacturer's instructions and as previously described (28). Only antibody binding levels against BA.5 were used in this study.

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Plates were blocked with 150 µL of blocker A (1% BSA in MilliQ water) solution for at least 30 minutes at room temperature and 700 rpm using a digital microplate shaker. During blocking, the heat-inactivated serum samples were diluted 1:500, 1:5,000, 1:50,000 and 1:500,000 in diluent buffer. Each plate contained duplicates of a seven-point calibration curve with a serial dilution of a reference standard and a blank well. The plates were then washed three times with 150 µL of MSD kit wash buffer, blotted dry, and 50 µL of the diluted samples and 50 µL of STD were added to the plates and shaken at 700 rpm at room temperature for 2 hours. The plates were again washed three times, 50 µL of SULFO-Tagged anti-human IgG antibody was added to each well and shaken at 700 rpm for 1h at room temperature. The plates were then washed three times and 150 µL of MSD GOLD Read Buffer B was added to each well. The plates were immediately read on a MESO QuickPlex SQ 120. The electro-chemiluminescence (ECL) signal was recorded. The results were expressed in AU/mL for spike-specific IgG.

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Neutralizing antibody levels, ID50 quantification

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Blood neutralisation levels have been assessed through pseudo-neutralisation with BQ.1.1 lentiviral pseudotypes essentially as previously described (36). The following final dilutions of the serum were tested: 20, 80, 320, 1280, 5120, 20480 and the percentage of neutralisation was determined for each serum dilution.
338

Finally, the LOD of the neutralisation assay is the lowest dilution factor, i.e. 20. The 50% inhibitory dilutions (ID50) are derived from the percentage of neutralisation for the different dilutions of the serum using a sigmoid function with a Hill coefficient of 3.

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## Biological model

343

### Viral kinetic model

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We used a simple Target Cell Limited (TCL) model to analyze the viral load data in the nasopharynx and trachea (15). Following Gonçalves et al and Alexandre et al (12,35), we assumed that there is no viral exchange between the nasopharynx and the trachea. We modelled both regions using the same set of parameters. This assumption was assessed during modelling to determine whether alternative parameter values were needed. The dynamical model is expressed in terms of concentrations, and the nasopharyngeal and tracheal volumes $v_n$ and $v_t$ are used to convert back to absolute values.

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In this model, target cells ($T$) are infected at a rate $\beta$. Infected cells ($I_1$) transition into productive infected cells ($I_2$) at a rate $\kappa$, and subsequently produce virions per cell per day. The virions can either be infectious ($V_I$) or non-infectious ($V_{NI}$), with the infectious ratio denoted by $\mu$. The virions are cleared at a rate $c_V$ and the productive infected cells $I_2$ die at a rate $\delta_I$. The equations written below (Eq. 1) correspond to the nasopharynx (indicated by the subscript $n$). To refer to viral density in the trachea, the subscript $t$ is used (Eq. 2).
357

$$
\begin{equation}
\begin{aligned}
\frac{dT_n}{dt} &= -\beta T V_{I,n} \\
\frac{dI_{1,n}}{dt} &= \beta T_n V_{I,n} - \kappa I_{1,n} \\
\frac{dI_{2,n}}{dt} &= \kappa I_{1,n} - \delta_I I_{2,n} \\
\frac{dV_{I,n}}{dt} &= \mu p I_{2,n} - c_V V_{I,n} - \beta T V_{I,n} \\
\frac{dV_{NI,n}}{dt} &= (1 - \mu) p I_{2,n} - c_V V_{NI,n}
\end{aligned}
\tag{1}
\end{equation}
$$

358 Antibody kinetic model

The model is based on two populations of antibody-secreting cells, namely short-lived **S** and long-lived **L** plasma cells. Both cells produce antibodies (Ab) at the same daily rate noted θ, and differ in their loss rates δ_S and δ_L, respectively. Their recruitment is stimulated by a step function, where the value of vaccine stimulation, **A**<sub>Vac</sub>, is equal to 1 for a period τ<sub>Vac</sub> after an injection and 0 otherwise. Similarly, infection-induced stimulation, **A**<sub>VL</sub>, has a value of 1 if the total viral load is above a certain threshold φ and 0 otherwise (hence the conversion of viral densities using volumes v<sub>n</sub> and v<sub>t</sub> in Eq. 2). Moreover, we considered a delay (τ<sub>VL</sub><sup>1</sup>) in antibody production following infection, as documented in the literature (29). We allow a different delay for naïve primates (τ<sub>VL</sub><sup>1</sup>) and for those that have already been exposed to the virus either through infection or vaccination (τ<sub>VL</sub><sup>2</sup>). Upon stimulation by vaccination or infection, B cells proliferate: r*L* cells are recruited each day. In this context, **L** serves as a proxy for memory B cells. Finally, among the newly produced cells, a fraction ρ differentiates into **L**, while the remaining proportion (1 - ρ) differentiates into **S**.

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371

$$
\begin{equation}
\begin{aligned}
\frac{d\mathbf{L}}{dt} &= \rho r \mathbf{L} (\mathbf{A}_{\text{Vac}} + \mathbf{A}_{\text{VL}}) - \delta_{\text{L}} \mathbf{L} \\
\frac{d\mathbf{S}}{dt} &= (1-\rho) r \mathbf{L} (\mathbf{A}_{\text{Vac}} + \mathbf{A}_{\text{VL}}) - \delta_{\text{S}} \mathbf{S} \\
\frac{d\mathbf{Ab}}{dt} &= \theta(\mathbf{S} + \mathbf{L}) - \delta_{\text{Ab}} \mathbf{Ab} \\
\mathbf{A}_{\text{Vac}}(t) &= \begin{cases} 1, & t - t_{\text{last dose}} \le \tau_{\text{Vac}} \\ 0, & t - t_{\text{last dose}} > \tau_{\text{Vac}} \end{cases} \\
\mathbf{A}_{\text{VL}}(t) &= \begin{cases} 1, & (\mathbf{V}_{I,n}(t - \tau_{\text{VL}}^i) + \mathbf{V}_{NI,n}(t - \tau_{\text{VL}}^i))v_n + (\mathbf{V}_{I,t}(t - \tau_{\text{VL}}^i) + \mathbf{V}_{NI,t}(t - \tau_{\text{VL}}^i))v_t \ge \varphi \\ 0, & (\mathbf{V}_{I,n}(t - \tau_{\text{VL}}^i) + \mathbf{V}_{NI,n}(t - \tau_{\text{VL}}^i))v_n + (\mathbf{V}_{I,t}(t - \tau_{\text{VL}}^i) + \mathbf{V}_{NI,t}(t - \tau_{\text{VL}}^i))v_t < \varphi \end{cases}
\end{aligned}
\tag{2}
\end{equation}
$$
373 Interplay between antibodies and viral replication

374 The models describing viral load (Eq. 1) and antibody dynamics (Eq. 2) were linked based on the main
375 mechanisms of antibody action. The first is their ability to form immune complexes (16,37,38). The
376 complex (C) is formed at a rate $k_{on}$ and then cleared at a rate $c_c$. This complex is infectious or non-
377 infectious, $C_I$ or $C_{NI}$ respectively, depending on the virion that has been bound (infectious or not). $C_I$ is
378 still able to infect cells at the rate $\beta$.

379 Next, to account for the effect of antibody neutralization, we introduced a neutralisation efficacy
380 parameter, denoted $\gamma$ and ranging from 0 to 1, which represents the fraction of infectious virions that
381 have been bound and neutralised and are therefore no longer infectious. We assume that the antibody
382 concentration is high enough so that complex formation does not lead to a local depletion of
383 antibodies. Moreover, their elimination is quickly compensated by diffusion from the blood. The final
384 model is written in Equation 3 and is visually schematized in Figure 2.

385

$$
\begin{equation}
\begin{aligned}
& \frac{dT_n}{dt} = -\beta T_n (V_{I,n} + C_{I,n}) \\
& \frac{dI_{1,n}}{dt} = \beta T_n (V_{I,n} + C_{I,n}) - \kappa I_{1,n} \\
& \frac{dI_{2,n}}{dt} = \kappa I_{1,n} - \delta_I I_{2,n} \\
& \frac{dV_{I,n}}{dt} = \mu p I_{2,n} - (c_V + k_{on} Ab) V_{I,n} - \beta T_n V_{I,n} \\
& \frac{dV_{NI,n}}{dt} = (1 - \mu) p I_{2,n} - (c_V + k_{on} Ab) V_{NI,n} \\
& \frac{dC_{I,n}}{dt} = k_{on} Ab (1 - \gamma) V_{I,n} - \beta T_n C_{I,n} - c_C C_{I,n} \\
& \frac{dC_{NI,n}}{dt} = k_{on} Ab (\gamma V_{I,n} + V_{NI,n}) - c_C C_{NI,n}
\end{aligned}
\tag{3}
\end{equation}
$$

386

387 Initial conditions and assumptions on parameter values
As viral initial conditions, we consider that only a proportion h of the inoculum reaches the target cells, as the majority is rapidly eliminated through the natural downward flow of fluids towards the lungs. This proportion is set at 5%. Since only the product $pT_0$ is identifiable, the initial concentration of target cells $T_0$ is set at 1980 cell.mL$^{-1}$ and the respective volumes of the nasopharynx and trachea to $v_n = 6.3$ mL and $v_t = 1.2$ mL (15,35). The target cell compartments are replenished to their baseline $T_0$ before each challenge. To ensure B cell recruitment, $L(0)$ was set to 1, while $S(0) = 0$ and $Ab(0) = 0$. Although there is no limit of detection in this assay, a minimum baseline binding value is observed and estimated ($Ab_0$). We attribute it to cross-reactivity.

The antibody decay rate is fixed at a plausible value for primates, $\delta_{Ab} = 0.055$ d$^{-1}$, which corresponds to a half-life of 12.6 days estimated for a monoclonal antibody in a similar experimental setup (13). Other fixed parameters are the eclipse phase of 6 hours (which corresponds to $\kappa = 4$ d$^{-1}$) (18) and the clearance of the immune complex, $c_C$, equal to $3*c_V$ (16).

## Observation model

As described in section Experimental procedure, four biomarkers were frequently measured, namely genomic and subgenomic RNA in the nasopharynx and trachea, viral titers in the nasopharynx, binding and neutralizing activity in the blood against BA.5 and BQ.1.1 respectively (Figure S1). Equation (4) describes the observation model, which relates the observation for the individual i at time t to the states of the dynamical model described in Equation 1-3. The subgenomic RNA represents the quantity of virus currently replicating. As in previous modelling work, it is modelled as proportional to the amount of virus daily produced, ie $pl_2$, by introducing a scaling parameter f (15). To obtain viral titers (TCID$_{50}$/mL) from the concentration of infectious particles (PFU/mL), a conversion factor derived from the Poisson distribution is used. By definition, 1 TCID$_{50}$ is the number of viral particles needed to infect half of the cells leading to 1 TCID$_{50}$ = -ln(0.5) = 0.69 (39).
Since no concentration measurements are available in the antibody compartment, the antibody levels are directly observed by binding measurements. Therefore, a linear relationship between antibody concentration and binding is assumed. Neutralisation assays are often misinterpreted as the driving factor is the antibody concentration and not the neutralising ability of a single antibody. To disentangle the two pieces of information, the neutralisation efficacy γ described above is introduced and ID50 is observed as a function of Ab and γ. We found that a sigmoid function described the assay well and defined the parameter K<sub>N</sub> as the neutralisation rate needed to reach 50% of the maximum reading: ID50<sub>max</sub>. Mechanistically, k<sub>on</sub> has to be integrated to the formula as there cannot be neutralisation without binding.

Finally, the error terms e<sub>k</sub> are white noises and represent different error rates, which follow normal distributions.

$$
\left\{
\begin{array}{l}
gRNA_n(i,t) = \log_{10}(V_{I,n}(i,t) + V_{NI,n}(i,t) + C_{I,n}(i,t) + C_{NI,n}(i,t)) + e_1(i,t) \\
gRNA_t(i,t) = \log_{10}(V_{I,t}(i,t) + V_{NI,t}(i,t) + C_{I,t}(i,t) + C_{NI,t}(i,t)) + e_2(i,t) \\
\quad sgRNA_n(i,t) = \log_{10}(fpI_{2,n}(i,t)) + e_3(i,t) \\
\quad sgRNA_t(i,t) = \log_{10}(fpI_{2,t}(i,t)) + e_4(i,t) \\
TCID_{50,n}(i,t) = \log_{10}((V_{I,n}(i,t) + C_{I,n}(i,t)) * 0.69) + e_5(i,t) \\
BAU(i,t) = \log_{10}(Ab(i,t) + 10^{Ab_0}) + e_6(i,t) \\
ID50(i,t) = \log_{10}\left(ID50_{max} \frac{k_{on}\gamma Ab(i,t)}{k_{on}\gamma Ab(i,t) + K_N}\right) + e_7(i,t)
\end{array}
\right.
\qquad (4)
$$

424

425 Statistical model and parameter estimation

To account for interindividual variability and covariates, we use a nonlinear mixed effects framework.

427 All parameters were estimated by computing the maximum likelihood estimator using the stochastic

approximation expectation maximization (SAEM) algorithm implemented in Monolix Software 2023R1

429 (33,34). The likelihood was estimated using importance sampling and we used linearization for the
standard errors. LOD, LOQ and ULOQ are treated by Monolix by left, interval and right censoring, respectively (35).

All parameters follow a lognormal distribution to ensure positivity, except for γ, which follows a logit normal distribution bounded between 0 and 1, and the exposure history covariates effects introduced below (the $β_{exp,a}$), which follow normal distributions.

## Model building methodology

During model building, we use the BICc (corrected Bayesian Information Criterion) to discriminate between competing models, as it is the most appropriate information criterion for nonlinear mixed-effects models (36).

In the first step, model parameters were estimated assuming a random effect for all estimated parameters except those directly related to the observation. This concerns the scaling- or assay-dependent parameters, namely f, Ab0, kon, ID50max and $K_N$.

### Selection of the random effects

The number of random effects is then reduced by downward selection. The random effects are removed one by one by selecting the model with the lowest BICc value. The selection is terminated if any elimination deteriorates the BICc value by more than 10 points (40).

### Fixing parameters through profile likelihood

Fixed effects that remained poorly identified at this stage (relative standard error, RSE > 50%) were then fixed and estimated using the profile likelihood method, assuming no variability (random effect set to 0) and applying a forward selection procedure. The profile likelihood method is a statistical approach that can be used to assess the uncertainty of parameters by systematically varying one parameter while optimizing others to determine the range of plausible values. The lowest minimum of
the likelihood function is selected and the corresponding parameter value is fixed. This process is continued until all fixed effects have an RSE < 50%. The parameter values tested are obtained by multiplying the last estimate by the following vector {0.01, 0.1, 0.5, 0.8, 1, 1.2, 2, 10, 100}. The sensitivity of the model predictions to those values is addressed in the supplementary (Fig. S.7 and S.8).

## Difference between viral kinetics in the nasopharynx and trachea

We then challenged the hypothesis that the parameters in the nasopharynx and trachea are identical. We tested a covariate effect on all estimated parameters by using a forward procedure with a threshold reduction in BICc of 10 points (37).

## Effect of exposure history

We tested whether each exposure (infection, monovalent or bivalent vaccination) led to a change in immune-related parameter values. We assume that such changes are not immediate and will therefore affect the response to the next exposure. For simplicity we also assume that each effect is independent meaning that the change induced by an exposure does not depend on the exposure history. Finally, we assume that infection only has an effect on the quality of immune response if a persistent viral load is detectable. Therefore, the second historical challenge is not included in the exposure history covariate.

For each parameter a, the effect of an exposure is captured by a 3 levels covariate β$_{exp,a}$ taking the values β$_{inf,a}$, β$_{mono,a}$ and β$_{bi,a}$ for the different types of exposures (infection, monovalent or bivalent vaccination). Parameter value is then updated after each exposure. For an individual i having experienced his exposure number k ('exp_k'), the parameter a takes the value a(i,k+1):

$$ \begin{cases} a(i, k + 1) = a(i, k)e^{\beta_{\text{exp},k,a}} \\ a(i, 1) = a_0 \end{cases} $$
475

An example of the values taken by the elimination rate of infected cells for the different groups across time is given in Figure S.6.

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477

Again, we use a forward procedure to test the effects of all 3 types of exposures on every estimated immune related parameter. The selection is done firstly on the lowest BICc score with a minimum benefit of 10 points. The covariate is also included if it improves the visual predictive checks or if it removes potential group effects in the distribution of random effects (tested through ANOVA). If a covariate is selected but some levels cannot be estimated (RSE>50%), they are fixed to 0.

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482

## Predicting the impact of exposure history on viral dynamics during a natural infection

483

With the final model, we simulated human-like infections, assuming different levels of protection at baseline. We assumed that human infections are initiated with 10 infectious particles (17) and to be conservative, we assumed that antibodies are at a steady-state prior to infection. Therefore, for an $Ab_i$ level at t=0, we have as initial conditions for plasma cells: $S_i = 0$ and $L_i = Ab_i \frac{\delta_{Ab}}{\theta}$.

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Simulations were performed with Simulx 2024 R1, using *lixoftConnectors* and *RsSimulx* packages with the R version 4.1.2. Simulations were based on 500 datasets of 500 individuals, with population parameters sampled from a normal distribution of their estimated value and associated standard errors (Fig. 4A,B).

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To investigate more precisely neutralisation as a CoP, in addition to varying the binding level, neutralisation level was chosen by fixing $\gamma$ to the unique value (see Eq. 4) that satisfied the desired pair binding/neutralisation at the time of infection (Fig. 4C-F). For computation reasons, and as the uncertainty is not represented on the heatmaps, the simulations were performed with 1000 individuals sampled from the population parameters.

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496

## Within-host reproductive number $R_0$, effective clearance and infection rate
497 Free virions are either complexed by antibodies or not and are therefore cleared at a rate $c_c$ or $c_v$.

498 According to equations (3), the proportion of virions cleared naturally is $\frac{c_v}{c_v+k_{on}Ab}$ and by neglecting

499 the time needed for the formation of immune complexes we define the effective clearance $c_{eff} =$

500 $\frac{c_v^2+c_Ck_{on}Ab}{c_v+k_{on}Ab}$. Half-lives are obtained by dividing log(2) by the rate of interest. In this case, the half-

501 life of virions is equal to $log(2)/c_{eff}$.

502 Similarly, infectious virions can either infect cells at a rate $\beta$ or are neutralised and cannot infect. The

503 effective infection rate is then defined as $\beta_{eff} = \beta \frac{c_v+(1-\gamma)k_{on}Ab}{c_v+k_{on}Ab}$.

504 The within-host reproductive number is calculated using the next generation matrix method, details

505 can be found in the supplementary (41). We obtained:

$$506 R_0 = \frac{\beta T_0 p \mu}{\delta c_c (c + k_{on} Ab)} (c_c + (1 - \gamma) k_{on} Ab)$$

507 The values of $c_{eff}$, $\beta_{eff}$ and $R_0$ presented in the results part were computed using the mean antibody

508 binding value at the time of inoculation for each group. Confidence intervals for parameters and by-

509 product metrics such as $c_{eff}$ can be obtained by Monte Carlo sampling from the asymptotic distribution

510 of the MLE. It consists in simulating many draws of parameters from a normal distribution centered at

511 the estimated mean with variance equal to the estimated variance, compute the by-product relevant

512 parameter and then take the empirical quantiles of the draws (2.5th and 97.5th percentiles in this case).

513 This simulation-based CI is equivalent to the normal-theory interval but computed through resampling.

514

515
516 ACKNOWLEDGMENT

517 This work has been supported by the SMATCH project (ANR-22-PESN-0003) funded under the
518 Programmes et Equipements Prioritaires de Recherche - Santé Numérique of the Stratégie
519 d'Accélération France 2030.

520 The modelling was part of the research program MODVAR funded by the ANRS-MIE project EMERGEN
521 (ANRS0151).

522 The biological work was supported by the PRI and BIOVAR programs of the ANRS-MIE project
523 EMERGEN (ANRS0151).

524 IDMIT is supported by the "Programme Investissements d'Avenir" (PIA), managed by the ANR under
525 references ANR-11-INBS-0008 and ANR-10-EQPX-02-01. We thank Julien Lemaitre, Audrey Bobillier,
526 Claire-Maëlle Fovet, Benoît Delache, Sébastien Langlois, Emma Burban, Victor Magneron, Maxime
527 Potier, Jean-Marie Robert, Eleana Navarre, Flavie Misplon, Eleonore Sizun, Thierry Prot, Antoine
528 Carlotti, and Mallory Lassance for the NHP experiments; Julie Morin and Laura Junges for reagent
529 preparation and viral load quantification assay; Julien Dinh, Alexandre Baillet, Eloïse Joffroy, and Elodie
530 Guyon for NHP sample processing; Vanessa Contreras for scientific support; Frédéric Ducancel, Alicia
531 Pouget, Sylvie Legendre, and Yann Gorin for their help with the logistics and safety management;
532 Isabelle Mangeot and Salomé Piault for their help with resource management; and Brice Targat and
533 Karl-Stephan Baczowski for their contribution to the data management.

534 The virus stock used for the NHPs BA.1 challenge was obtained from the Biodefense, Research
535 Resources, and Translational Research branches of the NIH/NIAID/DMID/OBRRTR/RRS (Program
536 Officer, Clint Florence, Ph.D).

537

538
539 REFERENCES

540 1. Meslé MMI, Brown J, Mook P, Katz MA, Hagan J, Pastore R, et al. Estimated number of lives directly saved by COVID-19 vaccination programmes in the WHO European Region from December, 2020, to March, 2023: a retrospective surveillance study. The Lancet Respiratory Medicine. 2024 Sep 1;12(9):714-27.

544 2. Tan ST, Kwan AT, Rodríguez-Barraquer I, Singer BJ, Park HJ, Lewnard JA, et al. Infectiousness of SARS-CoV-2 breakthrough infections and reinfections during the Omicron wave. Nat Med. 2023 Feb;29(2):358-65.

547 3. Gilbert PB, Donis RO, Koup RA, Fong Y, Plotkin SA, Follmann D. A Covid-19 Milestone Attained — A Correlate of Protection for Vaccines. New England Journal of Medicine. 2022 Dec 14;387(24):2203-6.

550 4. Khoury DS, Schlub TE, Cromer D, Steain M, Fong Y, Gilbert PB, et al. Correlates of Protection, Thresholds of Protection, and Immunobridging among Persons with SARS-CoV-2 Infection. Emerg Infect Dis. 2023 Feb;29(2):381-8.

553 5. Koch T, Mellinghoff SC, Shamsrizi P, Addo MM, Dahlke C. Correlates of Vaccine-Induced Protection against SARS-CoV-2. Vaccines. 2021 Mar;9(3):238.

555 6. Bruel T, Pinaud L, Tondeur L, Planas D, Staropoli I, Porrot F, et al. Neutralising antibody responses to SARS-CoV-2 omicron among elderly nursing home residents following a booster dose of BNT162b2 vaccine: A community-based, prospective, longitudinal cohort study. eClinicalMedicine [Internet]. 2022 Sep 1 [cited 2024 Nov 12];51. Available from: https://www.thelancet.com/journals/eclinm/article/PIIS2589-5370(22)00306-6/fulltext

560 7. Chalkias S, Harper C, Vrbicky K, Walsh SR, Essink B, Brosz A, et al. A Bivalent Omicron-Containing Booster Vaccine against Covid-19. New England Journal of Medicine. 2022 Oct 5;387(14):1279-91.

562 8. Cromer D, Reynaldi A, Mitchell A, Schlub TE, Juno JA, Wheatley AK, et al. Predicting COVID-19 booster immunogenicity against future SARS-CoV-2 variants and the benefits of vaccine updates. Nat Commun. 2024 Sep 27;15(1):8395.

565 9. Offit PA. Bivalent Covid-19 Vaccines — A Cautionary Tale. New England Journal of Medicine. 2023 Feb 8;388(6):481-3.

567 10. Marc A, Kerioui M, Blanquart F, Bertrand J, Mitjà O, Corbacho-Monné M, et al. Quantifying the relationship between SARS-CoV-2 viral load and infectiousness. Cobey SE, Van der Meer JW, editors. eLife. 2021 Sep 27;10:e69302.

570 11. Crotty S. Hybrid immunity. Science. 2021 Jun 25;372(6549):1392-3.

571 12. Alexandre M, Marlin R, Prague M, Coleon S, Kahlaoui N, Cardinaud S, et al. Modelling the response to vaccine in non-human primates to define SARS-CoV-2 mechanistic correlates of protection. eLife. 2022 Jul 8;11:e75427.

574 13. Maisonnasse P, Aldon Y, Marc A, Marlin R, Dereuddre-Bosquet N, Kuzmina NA, et al. COVA1-18 neutralizing antibody protects against SARS-CoV-2 in three preclinical models. Nat Commun. 2021 Oct 20;12(1):6097.
577
578

14. Maisonnasse P, Guedj J, Contreras V, Behillil S, Solas C, Marlin R, et al. Hydroxychloroquine use against SARS-CoV-2 infection in non-human primates. Nature. 2020 Sep;585(7826):584-7.

579
580
581

15. Marc A, Marlin R, Donati F, Prague M, Kerioui M, Hérate C, et al. Impact of variants of concern on SARS-CoV-2 viral dynamics in non-human primates. PLOS Computational Biology. 2023 Aug 9;19(8):e1010721.

582
583
584

16. Igarashi T, Brown C, Azadegan A, Haigwood N, Dimitrov D, Martin MA, et al. Human immunodeficiency virus type 1 neutralizing antibodies accelerate clearance of cell-free virions from blood plasma. Nat Med. 1999 Feb;5(2):211-6.

585
586
587

17. Killingley B, Mann AJ, Kalinova M, Boyers A, Goonawardane N, Zhou J, et al. Safety, tolerability and viral kinetics during SARS-CoV-2 human challenge in young adults. Nat Med. 2022 May;28(5):1031-41.

588
589
590

18. Ke R, Zitzmann C, Ho DD, Ribeiro RM, Perelson AS. In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness. Proceedings of the National Academy of Sciences. 2021 Dec 7;118(49):e2111477118.

591
592
593

19. Drain PK, Dalmat RR, Hao L, Bemer MJ, Budiawan E, Morton JF, et al. Duration of viral infectiousness and correlation with symptoms and diagnostic testing in non-hospitalized adults during acute SARS-CoV-2 infection: A longitudinal cohort study. J Clin Virol. 2023 Apr;161:105420.

594
595
596

20. Miller J, Hachmann NP, Collier A ris Y, Lasrado N, Mazurek CR, Patio RC, et al. Substantial Neutralization Escape by SARS-CoV-2 Omicron Variants BQ.1.1 and XBB.1. New England Journal of Medicine. 2023 Feb 16;388(7):662-4.

597
598
599

21. Song S, Madewell ZJ, Liu M, Miao Y, Xiang S, Huo Y, et al. A systematic review and meta-analysis on the effectiveness of bivalent mRNA booster vaccines against Omicron variants. Vaccine. 2024 May 31;42(15):3389-96.

600
601

22. Lasrado N, Barouch DH. SARS-CoV-2 Hybrid Immunity: The Best of Both Worlds. The Journal of Infectious Diseases. 2023 Nov 15;228(10):1311-3.

602
603
604

23. Kent SJ, Khoury DS, Reynaldi A, Juno JA, Wheatley AK, Stadler E, et al. Disentangling the relative importance of T cell responses in COVID-19: leading actors or supporting cast? Nat Rev Immunol. 2022 Jun;22(6):387-97.

605

24. Moss P. The T cell immune response against SARS-CoV-2. Nat Immunol. 2022 Feb;23(2):186-93.

606
607
608

25. Kadowaki T, Sasaki A, Matsumoto N, Mitsuhashi T, Hagiya H, Takao S, et al. Antibody Titers and the Risk of Infection During the SARS-CoV-2 Omicron Phase in Bizen City, Japan. The Journal of Infectious Diseases. 2024 Sep 23;230(3):662-9.

609
610

26. Magnus C. Virus Neutralisation: New Insights from Kinetic Neutralisation Curves. PLOS Computational Biology. 2013 Feb 28;9(2):e1002900.

611
612
613

27. Balelli I, Pasin C, Prague M, Crauste F, Effelterre TV, Bockstal V, et al. A model for establishment, maintenance and reactivation of the immune response after vaccination against Ebola virus. Journal of Theoretical Biology. 2020 Jun;495:110254.
614
615
616

28. Clairon Q, Prague M, Planas D, Bruel T, Hocqueloux L, Prazuck T, et al. Modeling the kinetics of the neutralizing antibody response against SARS-CoV-2 variants after several administrations of Bnt162b2. PLoS Comput Biol. 2023 Aug;19(8):e1011282.

617
618
619

29. Wagstaffe HR, Thwaites RS, Reynaldi A, Sidhu JK, McKendry R, Ascough S, et al. Mucosal and systemic immune correlates of viral control after SARS-CoV-2 infection challenge in seronegative adults. Science Immunology. 2024 Feb 9;9(92):eadj9285.

620
621
622

30. Iyaniwura SA, Ribeiro RM, Zitzmann C, Phan T, Ke R, Perelson AS. The kinetics of SARS-CoV-2 infection based on a human challenge study. Proceedings of the National Academy of Sciences. 2024 Nov 12;121(46):e2406303121.

623
624
625

31. Ito J, Suzuki R, Uriu K, Itakura Y, Zahradnik J, Kimura KT, et al. Convergent evolution of SARS-CoV-2 Omicron subvariants leading to the emergence of BQ.1.1 variant. Nat Commun. 2023 May 11;14(1):2671.

626
627
628

32. Dhama K, Dhawan, Manish, Tiwari, Ruchi, Emran, Talha Bin, Mitra, Saikat, Rabaan, Ali A., et al. COVID-19 intranasal vaccines: current progress, advantages, prospects, and challenges. Human Vaccines & Immunotherapeutics. 2022 Nov 30;18(5):2045853.

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630

33. Havervall S, Marking U, Svensson J, Greilert-Norin N, Bacchus P, Nilsson P, et al. Anti-Spike Mucosal IgA Protection against SARS-CoV-2 Omicron Infection. N Engl J Med. 2022 Oct 6;387(14):1333-6.

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632
633
634

34. Institut Pasteur. Protocol: Real-time RT-PCR assays for the detection of SARS-CoV-2 [Internet]. www.who.int; 2020 [cited 2025 Jul 18]. Available from: https://www.who.int/docs/default-source/coronaviruse/real-time-rt-pcr-assays-for-the-detection-of-sars-cov-2-institut-pasteur-paris.pdf?sfvrsn=3662fcb6_2

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636
637

35. Gonçalves A, Maisonnasse P, Donati F, Albert M, Behillil S, Contreras V, et al. SARS-CoV-2 viral dynamics in non-human primates. Regoes RR, editor. PLoS Comput Biol. 2021 Mar 17;17(3):e1008785.

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36. Inizan C, Courtot A, Sturmach C, Griffon AF, Biron A, Bruel T, et al. Levels and functionality of Pacific Islanders' hybrid humoral immune response to BNT162b2 vaccination and delta/omicron infection: A cohort study in New Caledonia. PLOS Medicine. 2024 Sep 26;21(9):e1004397.

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642
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37. Phan T, Zitzmann C, Chew KW, Smith DM, Daar ES, Wohl DA, et al. Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody. PLOS Pathogens. 2024 Apr 18;20(4):e1011680.

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38. Beaulieu M, Gaymard A, Massonnaud C, Peiffer-Smadja N, Bouscambert-Duchamp M, Carcelain G, et al. Antiviral effect of Evusheld in COVID-19 hospitalized patients infected with pre-Omicron or Omicron variants: a modelling analysis of the randomized DisCoVeRy trial. Journal of Antimicrobial Chemotherapy. 2024 Nov 1;79(11):2887-95.

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39. Bryan WR. INTERPRETATION OF HOST RESPONSE IN QUANTITATIVE STUDIES ON ANIMAL VIRUSES. Annals of the New York Academy of Sciences. 1957 Dec;69(4):698-728.

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40. Raftery AE. Bayesian Model Selection in Social Research. Sociological Methodology. 1995;25:111-63.

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41. Diekmann O, Heesterbeek JAP, Roberts MG. The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface. 2010 Jun 6;7(47):873-85.

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<table><thead><tr><th>Parameter</th><th>Description</th><th>Value (RSE)</th><th>95% confidence intervals</th><th>SD of the random effects (RSE)</th><th>Reference</th></tr></thead><tbody><tr><td colspan="6" style="text-align: center; font-weight: bold;">Viral load dynamics</td></tr><tr><td>β (mL·d<sup>-1</sup>)</td><td>Infection rate</td><td>3.0 x 10<sup>-3</sup> (24)</td><td>[2.0 x 10<sup>-3</sup> - 4.6 x 10<sup>-3</sup>]</td><td></td><td></td></tr><tr><td>κ (d<sup>-1</sup>)</td><td>Transfer rate between infected and productive infected cells</td><td>4</td><td></td><td></td><td>(18)</td></tr><tr><td>p (d<sup>-1</sup>)</td><td>Viral production rate</td><td>4.6 x 10<sup>4</sup> (18)</td><td>[3.3 x 10<sup>4</sup> - 6.4 x 10<sup>4</sup>]</td><td>1.3 (35)</td><td></td></tr><tr><td>δ<sub>1,0</sub> (d<sup>-1</sup>)</td><td>Baseline Loss rate of infected cells</td><td>0.99 (1.1)</td><td>[0.97 - 1.0]</td><td></td><td></td></tr><tr><td>β<sub>inf</sub>, δ<sub>1</sub></td><td>Covariate effect of infection on δ<sub>1</sub></td><td>2.8 (19)</td><td>[1.8 - 4.0]</td><td></td><td></td></tr><tr><td>β<sub>mono, δ<sub>1</sub></sub></td><td>Covariate effect of monovalent vaccination on δ<sub>1</sub></td><td>0.14 (29)</td><td>[0.07 - 0.22]</td><td></td><td></td></tr><tr><td>β<sub>bi, δ<sub>1</sub></sub></td><td>Covariate effect of bivalent vaccination on δ<sub>1</sub></td><td>0.69 (14)</td><td>[0.50 - 0.88]</td><td></td><td></td></tr><tr><td>f</td><td>Subgenomic scale factor</td><td>3.3 x 10<sup>-4</sup> (30)</td><td>[1.8 x 10<sup>-4</sup> - 5.6 x 10<sup>-4</sup>]</td><td></td><td></td></tr><tr><td>μ</td><td>Proportion of infectious virions produced</td><td>2.3 x 10<sup>-4</sup> (21)</td><td>[1.5 x 10<sup>-4</sup> - 3.2 x 10<sup>-4</sup>]</td><td></td><td></td></tr><tr><td>h</td><td>Proportion of inoculum reaching its target</td><td>0.05</td><td></td><td></td><td>*</td></tr><tr><td>c<sub>V</sub> (d<sup>-1</sup>)</td><td>Clearance rate of the free viral particles</td><td>12 (28)</td><td>[7.5 - 21]</td><td></td><td></td></tr><tr><td>T<sub>0</sub> (mL<sup>-1</sup>)</td><td>Initial concentration of target cells (epithelial cells expressing ACE2)</td><td>2.0 x 10<sup>4</sup></td><td></td><td></td><td>(15,35)</td></tr><tr><td>ν<sub>N</sub> (mL)</td><td>Nasopharyngeal volume</td><td>6.3</td><td></td><td></td><td>(35)</td></tr><tr><td>ν<sub>T</sub> (mL)</td><td>Tracheal volume</td><td>1.2</td><td></td><td></td><td>(35)</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">Antibody dynamics</td></tr><tr><td>Ab<sub>0</sub><br>log<sub>10</sub>(AU·mL<sup>-1</sup>)</td><td>Naïve animal binding level</td><td>1.5 (3.4)</td><td>[1.4 - 1.6]</td><td></td><td></td></tr><tr><td>θ (AU·mL<sup>-1</sup>·d<sup>-1</sup>)</td><td>Binding antibody production per B Cell</td><td>4.9 (32)</td><td>[2.8 - 9.2]</td><td>1.9 (10)</td><td></td></tr><tr><td>r<sub>0</sub> (d<sup>-1</sup>)</td><td>Baseline Proliferation rate of B Cells</td><td>76 (32)</td><td>[42 - 147]</td><td></td><td></td></tr><tr><td>β<sub>inf,r</sub></td><td>Covariate effect of infection on r</td><td>0.43 (36)</td><td>[0.15 - 0.72]</td><td></td><td></td></tr><tr><td>ρ</td><td>Proportion of B Cells differentiating into long-lived secreting cells (L)</td><td>2.4 x 10<sup>-3</sup> (33)</td><td>[2.0 x 10<sup>-3</sup> - 4.6 x 10<sup>-3</sup>]</td><td>0.3 (21)</td><td></td></tr><tr><td>τ<sub>vac</sub> (d)</td><td>Length of the vaccine induced B Cell recruitment</td><td>12 (10)</td><td>[10 - 15]</td><td></td><td></td></tr><tr><td>τ<sub>VL</sub><sup>1</sup> (d)</td><td>Delay before B Cell recruitment during an infection as first exposure</td><td>9.5 (2.4)</td><td>[9.1 - 10.0]</td><td></td><td></td></tr><tr><td>τ<sub>VL</sub><sup>2</sup> (d)</td><td>Delay before B Cell recruitment during an infection with previous exposure</td><td>6.0 (1.6)</td><td>[5.8 - 6.2]</td><td></td><td></td></tr><tr><td>δ<sub>S</sub> (d<sup>-1</sup>)</td><td>S loss rate</td><td>1.4 (32)</td><td>[0.8 - 2.7]</td><td></td><td></td></tr><tr><td>δ<sub>L</sub> (d<sup>-1</sup>)</td><td>L loss rate</td><td>1 x 10<sup>-3</sup></td><td></td><td></td><td>*</td></tr><tr><td>δ<sub>Ab</sub> (d<sup>-1</sup>)</td><td>Antibodies elimination rate</td><td>5.5 x 10<sup>-2</sup></td><td></td><td></td><td>(13)</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">Interactions Viral load/Immune response</td></tr><tr><td>φ</td><td>Minimum total viral load to trigger B cell recruitment</td><td>3 x 10<sup>3</sup></td><td></td><td></td><td>*</td></tr><tr><td>k<sub>on</sub><br>(mL·AU<sup>-1</sup>·d<sup>-1</sup>)</td><td>Immune complex formation rate</td><td>4.3 x 10<sup>-4</sup> (42)</td><td>[1.8 x 10<sup>-4</sup> - 9.5 x 10<sup>-4</sup>]</td><td></td><td></td></tr><tr><td>c<sub>c</sub> (d<sup>-1</sup>)</td><td>Clearance rate of the immune complex</td><td>3 * c<sub>V</sub></td><td>[23 - 63]</td><td></td><td>(16)</td></tr><tr><td>γ<sub>0</sub></td><td>Baseline Complex neutralisation efficacy</td><td>0.75 (14)</td><td>[0.54 - 0.90]</td><td>1.1 (21)</td><td></td></tr><tr><td>β<sub>mono,γ</sub></td><td>Covariate effect of monovalent vaccination on γ</td><td>-1.5 (21)</td><td>[-2.1 - -0.8]</td><td></td><td></td></tr><tr><td>ID50<sub>max</sub></td><td>Maximum ID50 with the assay used</td><td>1 x 10<sup>3</sup></td><td></td><td></td><td>*</td></tr><tr><td>K<sub>N</sub> (d<sup>-1</sup>)</td><td>Neutralisation rate to reach ID50 = ID50<sub>max</sub>/2 (assay specific)</td><td>42 (43)</td><td>[18 - 96]</td><td></td><td></td></tr></tbody></table>
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**Figure 1:** Design and summary statistics of the NHP study. **A.** Study design, Red dotted lines represent viral challenges and the black ones represent vaccine doses. **B.** Peak viral load in the nasopharynx. **C.** Peak viral titers in the nasopharynx. **D.** Binding levels at time of viral challenge. **E.** Neutralisation levels at time of challenge.

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<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

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<figure><img src="image_4.png" /><figcaption>**Figure 2: Mechanistic model of immune and viral dynamics.** Schematic representation of the model described by equations (3). Dotted lines represent mechanisms happening only during antigenic stimulation.

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667 Created with BioRender.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 3:** Model-based predicted dynamics of antibodies and viral load. **A.** Individual dynamics of antibody binding (plain line, dots) and neutralisation (dashed, triangles) levels in blood. **B.** Individual dynamics of SARS-CoV-2 genomic RNA (plain line, dots) and viral titers (dashed, triangles) in the nasopharynx. Empty symbols: observations below the limit of quantification. Colours represent the experimental groups (Fig1).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 4: Binding and Neutralisation levels as Correlates of Protection against infection and transmission. A. (resp B.) Peak viral load (respectively peak viral titers) as a function of the binding level and exposure history. For each group, the median is represented with its 95% confidence interval. C. (respectively D.) Peak viral load (respectively titers) as a function of the binding and neutralization levels, after two doses of monovalent vaccine. E. (respectively F.) Peak viral load (respectively titers) as a function of the binding and neutralization levels, after exposure to one dose of monovalent and one dose of bivalent vaccine.</figcaption></figure>