## Experimental procedure

Our study includes 31 cynomolgus macaques (16 male, 15 female) infected with 106 pfu of a primary isolate of SARS-CoV-2. Each animal received 5 mL of the total inoculum: 4.5 mL were injected by the intra-tracheal route and 0.5 mL by the intra-nasal route. Nasopharyngeal and tracheal swabs were collected longitudinally at days 1, 2, 3, 4, 5, 7, 9, 11, 13, 16 and 20 post-infection (pi). In parallel, broncho-alveolar lavages were collected at day 6, 13 and 20. Viral RNA levels were assessed in each sample using a real-time PCR, with 8540 and 180 copies/mL as quantification and detection limits, respectively.

The original study included 6 groups treated either by a high dosing regimen (Hi) of HCQ (90 mg/kg loading dose and 45 mg/kg maintenance dose) ± AZM (36 mg/kg of at 1 dpi, followed by a daily maintenance dose of 18 mg/kg), a low dosing regimen (Lo) of HCQ (30 mg/kg loading dose and 15 mg/kg maintenance dose) or a vehicle (water) as a placebo. Among the 23 treated animals, 14 were treated at 1 dpi with a Lo (n = 4), Hi (n = 5) dose of HCQ or HCQ + AZTH (n = 5). A late treatment initiation was also investigated in 4 animals receiving a Lo dosing regimen. Finally, 5 animals received HCQ at the Hi dose starting at day 7 prior to infection as a pre-exposure prophylaxis (PrEP). Given that HCQ was not associated to an antiviral effect 14, we pooled the data from either treated and untreated groups. Thus, we consider all animals as controls in our primary analysis but we investigated a potential effect of HCQ in reducing the viral production *p* (see supplementary information file 1).

## Viral dynamic model of SARS-CoV-2

*Model describing nasopharyngeal and tracheal swabs*

We developed a viral kinetic model that simultaneously characterizes nasopharyngeal and tracheal SARS-CoV-2 infection kinetics (**Fig. 2**). In this model, both nasopharynx and trachea were considered as distinct compartments, each one described by a target cell limited models 15,16. In the following, only a generic description of the model is presented and subscripts were omitted. Target cells (T) are infected by infectious viruses () at an infectivity rate *β*. After infection, infected cells enter an eclipse phase (I1) where they do not produce virions and enter into productively infected cells (I2) at a rate *k*. I2 cells produce *p* virions daily and are lost at a *per capita *rate *δ*. A proportion µ of the virions are infectious () and the remaining (1-*µ*) are noninfectious viruses (). Finally, both and are cleared at a rate *c*.

*Fixed parameters*

Because not all parameters could be properly estimated based on total RNA data only, some parameters had to be fixed based on the experimental setting or the current literature. First, the term *pT*0 is the only identifiable quantity in our model, were *T*0is the initial amount of susceptible cells at the beginning of the infection. Given the estimated surface of the trachea (*S*T= 9 cm2) and nasal cavities (*S*N=50 cm2) in cynomolgus macaques (data not shown) and the apical surface of one epithelial cell *s*=4 10-7 cm2/cell 21, one can calculate the number of target cells exposed to the virus in the nasopharynx and the trachea and , respectively. However, only a small fraction of these cells may express the ACE2 receptors needed for SARS-CoV-2 to enter a cell. Hence, assuming a proportion of 0.1% of cells expressing the ACE2 receptor, we set and cells in nasopharynx and trachea respectively. Second, we supposed the proportion of infectious viruses *µ* remained constant over time and equal to 0.001. Indeed, infectious titers measured by cell culture on tracheal swabs taken at 3 dpi (see details in supplementary information file 3) ranged from 1.2 to 3.2 log10 TCID50/mL i.e. 1,000 to 100,000 times lower than total RNA (**Fig. 7**).Third, we supposed that the eclipse phase duration was equal in the nasopharynx and in the trachea, and we set *k*=3 d-1 as the viral loads have been shown to increase 8h after infection 29. Fourth, the viral clearance *c* was assumed equal whatever the infectious nature of the virus and its location. Thus, we fixed *c* to 10 d-1 as the clearance is assumed to be fast in other respiratory infections 16. A sensitivity analyses was conducted with diffentent values of *c* and *k* (see supplementary information file 4). Lastly we derived secondary parameters summarizing the infection, namely the basic reproduction number and the burst-size .

*Statistical model*

The structural model used to describe the observed log10 viral loads of the ith animal at the jthtime point in the kth compartment (nasopharyngeal or tracheal)is

where θi is the vector of parameters of subject i and is the additive residual error. Individual parameters θi are supposed to follow a log-normal distribution:

(7)

where γ indicates the fixed effects and the random effects, which are supposed to follow a normal distribution of mean zero and standard deviation ω. The residual error eijk is assumed to follow a normal distribution of mean zero and constant standard deviation.

Standard errors were calculated by drawing parameters in the asymptotic distribution of the parameter estimators. For each parameter, we calculated the 2.5 and 97.5% percentile to derive the 95% confidence interval.

*Modelling strategy*

In order to reduce the number of parameters, we tested whether the transition rate between nasopharynx and trachea *g* could be set to 0. Then, we tested the possibility for parameters *β*, *δ*, *p* and *V*0 to be equal in both nasopharynx and trachea and tested if their variances could be set to 0. To do this, we used a backward selection procedure and stopped once the BIC did not decrease anymore. Lastly, based on the Empirical Bayes Estimates (EBE), we screened the random effects for correlations. Only correlations with a Pearson’s coefficient >0.8 were implemented in the model.

*Plasma cytokine analysis *

In all 31 macaques, the concentration of 30 cytokines were measured at 0, 2, 5, 7 and 9 dpi. Among them, CCL11, CCL2, IFN-⍺, Il-15, Il-1Ra and Il-2 were of particular interest as their kinetic changed during the infection (**Fig. 4**). To identify the cytokines to be incorporated in the model, we correlated the are under the cytokine curve (AUC, calculated by the linear trapezoidal method) with the AUC of log10 viral loads predicted by the model and calculated Spearman correlations (**Fig. 5**). Eventually, Spearman correlations with p-value<0.1 were further investigated and implemented in the viral dynamic model. In addition, we tested models involving IFN-⍺, a central element of the immune response against SARS-CoV-2 in humans 27.

*Parameter estimation*

Parameters were estimated with the SAEM algorithm implemented in MONOLIX® software version 2018R2 allowing to handle the left censored data 30. Likelihood was estimated using the importance sampling method and the Fisher Information Matrix (FIM) was calculated by stochastic approximation. Graphical and statistical analyses were performed using R version 3.4.3.

*Simulation of the infection time course in humans*

Assuming that the number of viruses entering a host is low in humans, the infection would start after a virus had infected its first cell. Thus, we scaled the compartments to human size considering a total URT cell count of 4x108 and 30 mL of volume 16,22 and assumed that the infection started after infection of one productive infected cell in the nasopharynx and in the trachea (i.e. 1 cell). We then computed the median and associated CI95% of peak viral load and viral shedding, as well as the generation time *T*gcorresponding to mean duration between a primary case and its associated secondary infections assuming that the infectiousness is proportional to the infectious viral load levels .