key: cord-1013823-42et03u8
authors: Goyal, Ashish; Duke, Elizabeth R.; Cardozo-Ojeda, E. Fabian; Schiffer, Joshua T.
title: Modeling explains prolonged SARS-CoV-2 nasal shedding relative to lung shedding in remdesivir treated rhesus macaques
date: 2022-05-25
journal: iScience
DOI: 10.1016/j.isci.2022.104448
sha: c461a18af634fa0d2f49b29c9eae36d9239710e2
doc_id: 1013823
cord_uid: 42et03u8

In clinical trials, remdesivir decreased recovery time in hospitalized patients with SARS- CoV-2 and prevented hospitalization when given early during infection, despite not reducing nasal viral loads. In rhesus macaques, early remdesivir prevented pneumonia and lowered lung viral loads, but viral loads increased in nasal passages after five days. We developed mathematical models to explain these results. Our model raises the hypotheses that: 1) in contrast to nasal passages viral load monotonically decreases in lungs during therapy because of infection-dependent generation of refractory cells, 2) slight reduction in lung viral loads with an imperfect agent may result in a substantial decrease in lung damage, and 3) increases in nasal viral load may occur due to a blunting of peak viral load which decreases the intensity of the innate immune response. We demonstrate that a higher potency drug could lower viral loads in nasal passages and lung.

But prolonged viral shedding in nasal passages A mathematical model to explain why remdesevir has a greater antiviral effect on SARS-CoV-2 in lung versus nasal passages in rhesus macaques 3. Data best supported two models shown in METHODOLOGY for two different regions and the presence of refractory cells in lung but not in nasal passages.

4. Antivitral efficacy in lung and nasal passages is similar but activity is slightly delayed in latter.

5. Fitting yields that viral loads continue to decrease in lung due to infection-dependent generation of refractory cells.

6. Increases in nasal viral load may occur due to a slight blunting of peak viral load which decreases the intensity of the innate immune responses.

7. Even slight reduction in lung viral load may result in a substantial decrease in lung damage.

There is a desperate need for treatments for SARS-CoV-2, the virus which causes COVID-19 17 disease . One unmet need of antiviral therapy development is identification of 18 virologic surrogates for clinically meaningful endpoints such as death or need for hospitalization. Viral 19 load surrogate endpoints allow for much smaller and efficient clinical trials (Block et al., 2017; Chen et 20 al., 2013; Duke et al., 2021; Murray et al., 1999; Natori et al., 2018) . In the case of SARS-CoV-2-21 infected people, viral load can be routinely measured in nasal samples or saliva (Wölfel et al., 2020) . 22

However, the primary site of disease is lung tissue. Therefore, bronchoalveolar lavage (BAL) of lungs 23 would be an ideal sample. However, BAL is usually not necessary for diagnosis, represents an infection 24 risk to medical personnel and is rarely performed in the care of COVID-19 patients. When BAL does 25 occur, it is often late during disease in critically ill patients rather than at early clinical presentation. 26

Additionally, BAL only samples select lobes of the lung and is not spatially comprehensive. Thus, the 27 natural kinetics of SARS-CoV-2 in lungs is likely to remain unknown in humans. 28

In humans, a double-blind, randomized, placebo-controlled trial showed that the nucleoside 29 analog remdesivir limited the duration of illness and approached statistical significance for reduction in 30 mortality when given later in disease (Beigel et al., 2020) . In a separate study with an overall later time of 31 treatment initiation, remdesivir had no effect on viral load or clinical outcome (Wang et al., 2020b) . A 32 more recent trial showed that remdesivir given early during infection in the outpatient setting dramatically 33 decreased the likelihood of hospitalization and/or death (https://www.gilead.com/news-and-press/press-34 room/press-releases/2021/9/veklury-remdesivir-significantly-reduced-risk-of-hospitalization-in-highrisk-35 patients-with-covid19). Surprisingly, nasal viral loads did not differ between the treatment and placebo 36 arms in this study raising the question of whether nasal viral loads could serve as a valid surrogate 37 endpoint for remdesivir or other antiviral agents of interest. In contrast, molnupiravir, an agent which 38 induces viral RNA copying errors, showed a reduction in viral loads in a similar study and has clinical 39 benefit (Fischer et al., 2021) , as did PF-07321332, a boosted protease inhibitor 40 higher (or lower) in nasal passages compared to lung because antiviral efficacy is inversely proportional 192 to the ratio of drug concentration and EC50. Our model also suggests that despite similar antiviral potency 193 in the two compartments, the antiviral effects are delayed by ~0.3 days from the time of first 194 administration in nasal passages whereas it is relatively quicker in lungs with a shorter delay of ~0. 1 day. 195 196 Lack of viral rebound in the lung may be explained by infection dependent generation of refractory 197 cells. We next performed counterfactual simulations assuming the six treated animals did not receive 198 treatment (ϵ U =0 and ϵ L =0). The viral load trajectories in these simulations (Fig. 7) appear similar to those 199 in untreated animals with BAL viral loads exceeding nasal viral loads at later time points (Fig 5a) . 200

Comparisons of the counterfactual viral load tracings to the treated animals suggests that a majority of 201 viral load decrease in lungs is achieved following the first dose and is then carried forward throughout the 202 duration of therapy with unchanged decay slopes. On the other hand, in nasal passages, viral load is 203 decreased initially during therapy but then stabilizes or even increases, leading to higher viral loads than 204 counterfactual projections (Fig 7) . 205

In the nasal cavity, somewhere between day 2 and 6 of therapy, the tracings cross and viral loads 206 of the treated animals are predicted to exceed the counterfactual simulations of the same animals off 207 therapy (Fig. 7) . The model projects that early treatment reduces viral load, thereby decreasing new early 208 infection and preventing depletion of susceptible cells in the nasal passages (Fig S3) . Even without 209 assuming susceptible cell proliferation, there is an adequate population of these cells to establish a steady 210 state of viral replication (Fig S3) . In the lung, even with remdesivir moderate potency, initially 211 susceptible cells rapidly become refractory to infection and treatment leads to a slower depletion of 212 susceptible cells. These cells are nevertheless depleted in a nonlinear fashion as they convert to a 213 refractory state (Fig S3) . Inclusion of a refractory cell compartment is therefore necessary in our model to 214 allow the elimination of virus from serial BAL samples. 215 216 J o u r n a l P r e -p r o o f Decreased cell death in the lungs of remdesivir treated animals. We longitudinally assessed cell death 217 over time in our counterfactual simulations as an approximation of total lung damage. In each case, 218 therapy decreased the degree of peak cell death by 15-67% (Fig. S4) and significantly decreased the 219 cumulative number of dead cells over 7 days (p=0.03, Wilcoxon rank-sum test). While lung damage is 220 multi-factorial during COVID-19 and may involve immune-mediated destruction, this finding is 221 qualitatively compatible with the observation that early remdesivir spared these 6 animals from severe 222 clinical disease and abnormal lung histopathology. 223 224 Projected nasal and lung viral load trajectories at higher drug potency. Next, we performed sensitivity 225 analyses in which we assumed a more potent antiviral effect, which could arise either from different 226 dosing of remdesivir or a drug with a lower EC50. In nasal passages ( Fig S5a) and in lungs (Fig S5b) , the 227 impact of the first dose is more profound with higher potency leading to a more abrupt decline in viral 228 load in both compartments. 229

We estimate that minimum drug efficacies of 99.0% and 99.9% would be required to drive the 230 viral load below the detection limit (i.e., 100 copies/mL) in the nasal passages and lungs within 5 days of 231 treatment initiation, when treatment is initiated 12 hours post-infection. The need for such high potency 232 reflects the lack of a concurrent immune response at this early stage of infection. dose several days later (Goyal et al., 2020) . Our simulations of the rhesus macaque data arrive at a similar 238 conclusion in the nasal passage, that, paradoxically, later treatment with a moderate potency drug results 239 in lower viral loads, whereas treatment started before peak results in increased late viral loads (Fig S6a) . 240

In contrast, in the lungs, later treatment at days 2 or 4 leads to a subsequent viral load trajectory similar to 241 that of the earlier treated animals during the later stages of infection (Fig S6b) . 242 J o u r n a l P r e -p r o o f

We estimate that minimum drug efficacies of 70% and 99% would be required to drive the viral 243 load below the detection limit (i.e., 100 copies/mL) in the nasal passages and lungs within 5 days of 244 treatment initiation, when treatment is initiated 4 days post-infection. This result is due to the higher 245 remaining viral load in the lungs of animals during the first untreated 4 days of infection. 246 J o u r n a l P r e -p r o o f Viral load is a valid surrogate endpoint for treatment efficacy of several viruses including HIV, 248 hepatitis B, hepatitis C and cytomegalovirus (Block et al., 2017; Chen et al., 2013; Duke et al., 2021; 249 Murray et al., 1999; Natori et al., 2018) . It is plausible that SARS-CoV-2 lung viral load is also predictive 250 of disease severity in humans. Viral loads from swabs of infected tissue provide an approximation of the 251 number of infected cells at a given point in time, and therefore the surface area of infected tissue (Schiffer 252 et al., 2010; Schiffer et al., 2013a) . Unfortunately, it is less certain whether viral load measurements can 253 be leveraged for SARS-CoV-2 treatment response in humans because BAL is required to measure lung 254 viral load but these are never performed longitudinally in infected people as part of routine clinical care. 255

Experience from other respiratory viruses suggests that viral load measures in the upper airway by nasal 256 swab or saliva may or may not be representative of those in the lung (Seo et al., 2014) . 257

Here we apply mathematical models to remdesivir treatment data in rhesus macaques in which 258 both lung and nasal viral load were measured. We believe that our model explains the observed data in its 259 entirety and allows several testable hypotheses not generated by existing models (Gonçalves et al., 2021; 260 Kim et al., 2021b; Rodriguez and Dobrovolny, 2021) . Specifically, our model provides a plausible 261 explanation for prolonged viral shedding in nasal passages in treated animals while also capturing lower 262 lung viral load kinetics and limited pulmonary pathology in treated animals. We identify that the 263 relationship between lung and nasal viral load in the context of antiviral treatment is complex and 264 dependent on the potency and timing of therapy. With an assumed potency of ~70 % for remdesivir 265 (consistent with estimates from (Kim et al., 2021b )), our model projects lower viral loads in the lung over 266 the 7 days following infection, but viral loads in the nasal mucosa are only transiently lowered. Several 267 days into treatment viral loads increased slightly and surpassed what might have occurred without 268

This result suggests that nasal viral load may not be an optimal surrogate for lung disease in the 270 context of a partially effective antiviral therapy such as remdesivir at the doses used in this study. On the 271 other hand, when we assume a more potent therapy with a lower in vivo EC50, then nasal viral loads are 272 J o u r n a l P r e -p r o o f predicted to decrease in an exponential manner, in lock step with lung viral loads, immediately after 273 starting treatment. Therefore, nasal viral loads in humans, measured either by duration of shedding or 274 viral decay slope, may be a viable surrogate endpoint for lung viral load and downstream lung damage, 275 but only in the context of a highly potent agent. This observation may explain the observed reduction in 276 viral loads in trials for two other oral agents as well as monoclonal antibodies which were given early 277 during therapy and shown to also lower hospitalization rates (https://www.pfizer.com/news/press-278 release/press-release-detail/pfizer-announces-additional-phase-23-study-results; Dougan et al., 2021; 279 Fischer et al., 2021; Weinreich et al., 2021) . 280

The experimental results highlight inherent strengths and limitations of the rhesus macaque 281 model. Nasal passage viral kinetics and histologic lung damage appear similar between humans and 282 rhesus macaques (Goyal et al., 2020; Zhang et al., 2020) . We are also encouraged by the fact that a nearly 283 equivalent mathematical model with a similar parameter set explains nasal viral loads in humans and 284 rhesus macaques during the first week of infection (Goyal et al., 2020) , (though the acquired immune 285 response is not modeled in the macaques because we do not observe complete viral elimination within the 286 experimental timeframe). Similarly, our modeling of human data led to the prediction that a semi-potent 287 treatment given extremely early during infection might allow higher late nasal viral loads (Goyal et al., 288 2020) , which was observed in the rhesus macaque experiments described herein. 289

On the other hand, in rhesus macaques, peak viral load, extensive lung damage and clinic illness 290 is observed within two days of infection, which is not in keeping with severe illness in humans which 291 usually emerges at least a week after the initial phase of illness (Munster et al., 2020; Wang et al., 2020a; 292 Williamson et al., 2020b) . We hypothesize that direct intratracheal inoculation of macaques with a high 293 viral titer result in more immediate infection of lung and early peaking of viral load. In humans, 294 respiratory viruses may start replicating in the upper airway and then transmit to the lungs in a second 295 stage of infection (Chemaly et al., 2014 ). An alternative and not mutually exclusive explanation is that the 296 degree of viral replication in the lung can also be established extremely early in humans, but that the more 297 extensive immune-mediated damage which may be correlated with the extent of early viral replication, 298 J o u r n a l P r e -p r o o f occurs 1-2 weeks later. Had the rhesus macaques with the highest lung viral loads been followed for a 299 longer time, it is possible that a more severe pneumonia would have developed at later time points. The 300 observed differences in the pathology and viral kinetics between humans and rhesus macaques might also 301 be one of the reasons for why our best model that is designed to explain data in rhesus macaques is 302 structurally different to the model that describes human data (Ke et al., 2021a) . 303 A counterintuitive result predicted by our model is that the activity of remdesivir is slightly more 304 delayed in the nasal cavity than in the lung (assuming that drug levels are indeed equivalent in the two 305 compartments). This could perhaps be because that the distribution of the drug to one compartment takes 306 less time than the other among other reasons. For example, highly perfused organs (including lung) will 307 receive drug sooner than the slowly perfused organs in the body. Nevertheless, SARS-CoV-2 is not 308 cleared in nasal passages as effectively as in the lungs while on treatment, because the effectiveness of 309 antiviral therapies is never independent of the concurrent intensity of the immune response to infection 310 (Schiffer et al., 2013b; Schiffer et al., 2016) . We previously predicted that a more potent therapy is 311 needed after 2 days of SARS-CoV-2 infection relative to >5 days after infection because there is little 312 innate immune pressure against the virus during its early expansion phase (Goyal et al., 2020) . As a 313 result, despite a slight blunting of initial viral loads, virus will rebound or stabilize and end up at a higher 314 viral level in the nose than in the absence of treatment. 315

Here, we recapitulate this finding in the nasal passages, but also predict why this does not occur 316 in the lungs of macaques. In the lung as in the nasal cavity, we assume density dependent killing as a 317 proxy for an intensifying innate response to a higher burden of infection. However, our model also 318 suggests that ongoing infection drives a percentage of lung cells to become temporarily refractory to 319 infection. Inclusion of this assumption is required to recapitulate lung viral load data and to explain the 320 observation that lung damage is severely blunted in animals receiving treatment. This assumption is 321 supported by modeling of influenza infection (Pawelek et al., 2012) In conclusion, we demonstrate that in rhesus macaques, the non-linear forces governing SARS-326

CoV-2 viral load trajectories in the lung and nasal passages differ substantially in the presence of a 327 partially effective antiviral therapy. To the extent that the rhesus macaque model approximates human 328 infection, nasal viral load remains a promising surrogate endpoint marker, but perhaps only in the context 329 of a highly potent antiviral therapy. There are several limitations of our approach. First, our approximation of lung damage is 334 relatively coarse based on the complexity of this post-viral inflammatory process which may be mediated 335 by factors other than number of infected cells. This is therefore a qualitative target of our modeling. 336

Second, our fits to nasal viral load are imperfect which may be due to imprecision in viral load 337 measurements or to missed components within the model. In the case of RM2, there is substantial viral 338 rebound that may be due to incomplete innate responses to the first pulse of infection, or to de novo drug 339 resistance. Third, we only model early infection and therefore neglect the critical impact of the late 340 acquired immune response (Braun et al., 2020; Suthar et al., 2020; Weiskopf et al., 2020) . This may 341 represent a fundamental shortcoming of the non-human primate model in which virus is cleared extremely 342 rapidly. Fourth, while in vitro evidence supports the possibility of interferon mediated refractory target 343 cells (Blanco-Melo et al., 2020; Sa Ribero et al., 2020) , this model prediction is not yet experimentally 344 verified. We support experiments assessing for upregulation of interferon simulated genes in uninfected 345 cells during natural SARS-CoV-2 infection. Fifth, while we can confidently conclude that compartmental 346 drug potency is the same in nasal and lung sites, we cannot discriminate differences in active drug levels 347 or intracellular drug potency in the upper versus lower airway. We start with the unverified assumption 348 that nucleoside GS-441524 is at the same levels in nasal passages and lung, and then solve for EC50 which 349 J o u r n a l P r e -p r o o f also ends up nearly the same in both locations. However, only the combination of these values is truly 350 identifiable. Sixth, our PK model has parameters that are not fully identifiable. However, the goal of our 351 modeling exercise in this case was just to reproduce drug, and metabolite, levels rather than identify a 352 fully mechanistic PK model. Seventh, the viral inoculum in the animals is extremely high which may 353 explain the peak in viral load at day 1 or 2 after infection, which is earlier than in humans. However, the 354 upslope of viral expansion appears similar in humans and macaques. We surmise that lower inoculum in 355 humans may prolong time to viral detection. Finally, the number of studied animals is small. Our results 356

suggest that partially efficacious therapies may have differential effects on viral load in the upper versus 357 the lungs. This result needs to be replicated in other animals to strengthen the veracity of our claims. Data and code availability. This paper analyzes existing, publicly available data. All data reported in this 424 paper will be shared by the lead contact upon request. All original code has been deposited at 425 https://github.com/ashish2goyal/Simulating-remdesevir-effect-in-RMs and is publicly available as of the 426 date of publication. Any additional information required to reanalyze the data reported in this paper is 427 available from the lead contact upon request. 428

Experimental data. We analyzed viral load observations from nasal passages and BAL from 12 SARS-432

CoV-2-infected rhesus macaques in which 6 were treated with remdesivir and 6 received a vehicle control 433 (Williamson et al., 2020b) . Remdesivir was infused 12 hours after infection at a dose 10mg/kg with 434 subsequent daily doses of 5 mg/kg until day 6, and remdesivir and its metabolites plasma concentrations 435

were measured. We also added viral loads from nasal passages and BAL from 8 additional untreated 436 animals (Munster et al., 2020) . In both studies, rhesus macaques were infected with 2.6x10 6 TCID50 of 437 SARS-CoV-2 strain. Details about the infection and treatment protocol can be found in these two articles. 438

We also analyzed more frequently sampled observations of remdesivir and its metabolites averaged 439 from three healthy animals after a single IV infusion of 10mg/kg of remdesivir. 440 441 J o u r n a l P r e -p r o o f Remdesivir pharmacokinetics model. We used a compartmental and metabolism pharmacokinetics (PK) 442 model for remdesivir. The goal of this model was to recapitulate the sparse data from remdesivir and its 443 metabolites after several doses to the SARS-CoV-2-infected animals (Williamson et al., 2020b) , along with 444 the very frequently sampled data after a single dose in healthy animals (Warren et al., 2016) . The PK model 445 (depicted in Fig 2) describes the metabolism of remdesivir Prodrug GS-5734 (A1), to the alanine metabolite 446 GS-704277 (A2) and subsequent parent Nucleoside GS-441524 (A3) in serum and their distribution to other 447 tissue (A1T, A2T, and A3T in the same order). Metabolism rates from GS-5734 to GS-704277 and to GS-448 441524 are described by parameters k12 and k23. Drug distribution to other tissues and back to plasma are 449 described by parameters k1T, k1e, k2T, k2e, k3T and k3e. We assumed that in other tissues the active triphosphate 450 metabolite (A4T) is metabolized from the parent nucleoside at rate k34 and ignored the drug distribution of 451 the active triphosphate metabolite between plasma and tissue compartments (Sun, 2020) . We finally 452 assumed all metabolites have clearance with rates kc1, kc2, kc3 in serum and kcT4 in tissue. These assumptions 453 are captured by the differential equations below: depends on the infected cell density (Holte et al., 2006; Smith et al., 2018) . This density dependent term 495 represents a combined death of infected cells due to cytopathic effects of the virus and the killing of infected 496 cells due to early immune responses. SARS-CoV-2 is produced at a rate π i and cleared with rate γ i (Pawelek 497 et al., 2012) . Free virus is allowed to be exchanged between the lungs and nasal passages and back at rates 498 and , respectively. 499

We also considered the possibility of the emergence of refractory cells. Due to antiviral actions of 500 cytokines such as interferon responses ( ), it has been experimentally demonstrated that uninfected lung 501 airway cells may become refractory ( ) at rate ′ (Pawelek et al., 2012) , and that infected cells may 502 convert directly to refractory cells ( ) at rate . Typically, the rate of change of interferon responses ( ) 503 in compartment 'i is given by = 1 − 2 (Ke et al., 2021a) , where 1 's are the production rates of 504 interferon in response to infection and 2 is the clearance of interferon responses. However, to limit the 505 number of unknown parameters (such as 1 's and 2 ) in the model in the absence of relevant information, 506 the interferon dynamics is assumed to be much faster than the dynamics of infected cells. This allows for . Refractory cells may lose their 508 refractory state and become susceptible at rate (Pawelek et al., 2012) . Since we are interested in the viral 509 dynamics in a short span of ~7 days (with or without treatment), we ignored the death rate of uninfected 510 and refractory cells in the lung, that are usually long-lived. 511

We also included the possibility of regeneration of susceptible cells during infection. Innate 512 immune cells eliminate virus but can also induce pulmonary tissue damage or endothelium damage as part 513 of this process (Gorski et al., 2012; Newton et al., 2016) . The restoration of the respiratory epithelial barrier 514 after an injury happens within days after viral clearance (Fujino et al., 2019; Vaughan and Chapman, 2013; 515 Yoo et al., 2013) , depending on the severity of the infection and the extent of lung involvement. Indeed, 516 the proliferation of epithetical cells and progenitor stem cells (or distal airway stem cells or DASCs) is 517 critical for barrier repair following an inflammatory insult. Following lung injury, the tissue repair process 518 is promoted by immune cells including macrophages (Hung et al., 2019) . Epithelial restoration is initiated 519 locally by proliferating alveolar type II (AT2) cells (Olajuyin et al., 2019) . We modeled this restoration by 520 adding a logistic proliferation of susceptible and refractory but not infected epithelial cells with maximum 521 rate (Gibbs et al., 2009) . We included the possibility that proliferation might be a delayed process and 522 could happen after days post-infection (Yoo et al., 2013) . All the previous mechanisms are modeled by 523 the following differential equation system: Modeling remdesivir therapy. Here we assumed that RDV inhibits viral production (Cao et al., 2020; 553 Tchesnokov et al., 2019) . Thus, because of treatment, the viral production is reduced by a factor (1 − 554 3 3 + 50 ), where 50 is the in vivo EC50 of the nucleoside GS-441524 in the respective compartment . 555

To investigate whether the viral inhibition is independent of the drug concentration, we assumed a constant 556 J o u r n a l P r e -p r o o f efficacy of the treatment during 0.5-7 days ( ) or in other words, we simply assume that the viral production 557 is reduced by a factor . 558 559 Viral dynamics model fitting and selection. To fit different versions of the virus dynamics model to the 560 data we used a non-linear mixed effects approach (Chan et al., 2011; Karlsson et al., 2015) . Briefly, in this 561 approach observed viral load for animal at time is modeled as log 10 = ( , ) + being 562 the solution of model for the virus given the individual parameter vector and the measurement error. 563

Here, the individual-parameter vector is drawn from a population probability distribution. We estimated 573 cps/swab, (0) = 3.7 × 10 8 cells (based on 3.7×10 9 cells in humans from (Crapo et al., 1982) and 574 assumed ~10 fold lower number of cells in rhesus macaques based on differences in weight), (0) = 575 2.6 × 10 6 cells (Crapo et al., 1982; Zheng et al., 2000) . We used the concept of multiplicity of infection 576 (Table S3) . Our best estimate of = 10 −5 suggests that upon inoculation, there are ~26 infected 582 cells in the nasal and ~13,000 infected cells in the lung. This seems reasonable given that although animals 583 are inoculated with high TCID50, their baseline nasal viral loads are below the detection limit (Munster et 584 al., 2020) . It is to be further noted that ≥ 10 −4 achieves peak viral loads almost instantly due to large 585 number of initially infected cell population (Table S3 ) which seems biologically unreasonable for any 586

We also assumed a virus clearance rate to be the same in both compartments = = 15/day 588 along with = 3.7 × 10 8 cells and = 2.6 × 10 6 cells. We estimated the remaining parameters 589 depending on each model assumptions. The explored competing models on this stage are listed in Table  590 S3. 591

We next fit models to viral load and lung lesion observations from treated and untreated animals. 592

Here, we explored different competing models listed in Table S5 and described below. We explored models 593 that included cell proliferation and refractory cells in the lungs, fixing = 0 (Baccam et al., 2006) , = 594 0 and = 0. We explored the possibility that AT2 cells proliferate with maximum rate after some delay 595 (Yoo et al., 2013) , i.e. = 0 if < . Since we ignore the proliferation of cells in nasal passages, we also 596 assume = 0. During the estimation procedure, we also assumed that the maximum possible value of 597 to be 2/day, in between previous estimates 0.75/day (Quirouette et al., 2020) and 3.4/day for liver whose 598 regeneration capability is no less than extraordinary for an organ (Goyal et al., 2017) . 599

We also included models assuming that the antiviral activity of remdesivir in nasal passages and compartment. Here, we also assumed = 0 as the time of infection with same initial values and fixed 607 parameters , , and as before. We estimated the remaining parameters depending on each model 608 assumptions (Table S5) . 609

To determine the best and most parsimonious model among the instances above, we computed the 610 log-likelihood (log L) and the Akaike Information Criteria (AIC=-2log L+2m, where m is the number of 611 parameters estimated). We assumed a model has similar support from the data if the difference between its 612

AIC and the best model (lowest) AIC is less than two (Burnham and Anderson, 2002) . 

V L π L γ SARS-COV-2 in BAL killing Early Response LUNG NASAL RDV (EC 50U ) Proliferation ρ L r L δ L I L k L δ U I U k L R L

RDV (EC 50L ) β L r L ζ L ζ U RDV (EC 50L ) RDV (EC 50U ) S U I U β U

ρ L r L θ LU θ UL φ L φ U δ L I L k L δ U I U k U R L R U

Refractory cells in Nasal Mucosa r L r U A)

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Please use the empty table that follows to organize the information in the sections defined by the subheading, skipping sections not relevant to your study. Please do not add subheadings. To add a row, place the cursor at the end of the row above where you would like to add the row, just outside the right border of the Figure 5 and Table S5 . A) Fits to 6 treated animals who received 10 mg/kg at day 0.5 and 5 mg/kg at days 1, 2, 3, 4, 5 and 6 (solid lines). Dashed lines represent fits to vehicle group. Pink and blue dots are nasal swabs and BAL data points, respectively. Dots overlying the dotted line are below the limit of detection. Time is in days from infection. B) Simulated percentage of dead lung target cells as a proxy for lung damage. Fits to 5 treated animals who received 10 mg/kg at day 0.5 and 5 mg/kg at days 1, 2, 3, 4, 5 and 6. We excluded RM2 from the fitting procedure as our model cannot reproduce viral rebound on treatment, as seen in RM2. Pink dots are nasal swabs datapoints and lines are model projections. Dots overlying the dotted line are below the limit of detection. J o u r n a l P r e -p r o o f Figure S3 : Mechanisms of lung protection in remdesivir treated animals, Related to Figure 5 . The number of susceptible cells is projected for simulations fit to treatment data (solid lines) and counterfactual simulations without therapy (dashed lines). In nasal passages, therapy limits initial depletion of susceptible cells which allows for persistent viral replication rather than elimination. In the lung (BAL specimens), depletion of susceptible cells occurs in part due to the cells entering a refractory state: treatment efficacy lowers the number of susceptible cells that become refractory to infection. The depletion of susceptible cells prevents persistent shedding. Simulations are based on data from RM 1-6. Time is in days from infection. J o u r n a l P r e -p r o o f We also estimated only the fixed effects of four parameters: +,* = +,) = 2.2 nM/gm, ) = 0 days and ) =2.0/day while fixing =1.9×10 -7 virions -1 .day -1 . In absence of the data on active metabolite concentration, the concentration of nucleoside GS-441524 in tissue (Nuc) was employed as a proxy to calculate EC50 [2] . Parameter units are: 's, day -1 cells -k ; 's, unitless; 's, day -1 ; ) ; day -1 cells -1 . 

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Management of respiratory viral infections in hematopoietic cell transplant recipients and patients with hematologic malignancies

Earlier sustained virologic response end points for regulatory approval and dose selection of hepatitis C therapies

Cell number and cell characteristics of the normal human lung

Quantifying the effect of remdesivir in rhesus macaques infected with SARS-CoV-2

Bamlanivimab plus Etesevimab in Mild or Moderate Covid-19

CMV viral load kinetics as surrogate endpoints after allogeneic transplantation

Molnupiravir, an Oral Antiviral Treatment for COVID-19

Sensing of apoptotic cells through Axl causes lung basal cell proliferation in inflammatory diseases

Cell cycle arrest by transforming growth factor beta1 enhances replication of respiratory syncytial virus in lung epithelial cells

SARS-CoV-2 viral dynamics in non-human primates

Recent insights into pulmonary repair following virus-induced inflammation of the respiratory tract

Potency and timing of antiviral therapy as determinants of duration of SARS-CoV-2 shedding and intensity of inflammatory response

The Role of Infected Cell Proliferation in the Clearance of Acute HBV Infection in Humans

Density-dependent decay in HIV-1 dynamics

Macrophages promote epithelial proliferation following infectious and non-infectious lung injury through a Trefoil factor 2-dependent mechanism

Nonlinear mixed-effects modelling for single cell estimation: when, why, and how to use it

Daily sampling of early SARS-CoV-2 infection reveals substantial heterogeneity in infectiousness. medRxiv, 2021

In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2

Incomplete antiviral treatment may induce longer durations of viral shedding during SARS-CoV-2 infection. Life science alliance 4

Respiratory disease in rhesus macaques inoculated with SARS-CoV-2

The use of plasma HIV RNA as a study endpoint in efficacy trials of antiretroviral drugs

Dynamically Linking Influenza Virus Infection with Lung Injury to Predict Disease Severity. bioRxiv

Use of Viral Load as a Surrogate Marker in Clinical Studies of Cytomegalovirus in Solid Organ Transplantation: A Systematic Review and Meta-analysis

The host immune response in respiratory virus infection: balancing virus clearance and immunopathology

Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort

Alveolar type 2 progenitor cells for lung injury repair

Modeling within-host dynamics of influenza virus infection including immune responses

A mathematical model describing the localization and spread of influenza A virus infection within the human respiratory tract

Estimation of viral kinetics model parameters in young and aged SARS-CoV-2 infected macaques

Interplay between SARS-CoV-2 and the type I interferon response

Mucosal host immune response predicts the severity and duration of herpes simplex virus-2 genital tract shedding episodes

An early test and treat strategy for SARS-CoV

Rapid localized spread and immunologic containment define Herpes simplex virus-2 reactivation in the human genital tract

Rapid viral expansion and short drug half-life explain the incomplete effectiveness of current herpes simplex virus 2-directed antiviral agents

Mathematical modeling of herpes simplex virus-2 suppression with pritelivir predicts trial outcomes

Parainfluenza virus lower respiratory tract disease after hematopoietic cell transplant: viral detection in the lung predicts outcome

Broad-spectrum antiviral GS-5734 inhibits both epidemic and zoonotic coronaviruses

Influenza Virus Infection Model With Density Dependence Supports Biphasic Viral Decay

Remdesivir for Treatment of COVID-19: Combination of Pulmonary and IV Administration May Offer Aditional Benefit

Rapid generation of neutralizing antibody responses in COVID-19 patients

Mechanism of Inhibition of Ebola Virus RNA-Dependent RNA Polymerase by Remdesivir

Modeling Within-Host Dynamics of SARS-CoV-2 Infection: A Case Study in Ferrets

Regenerative activity of the lung after epithelial injury

Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan

Remdesivir in adults with severe COVID-19: a randomised, double-blind, placebo-controlled, multicentre trial

Therapeutic efficacy of the small molecule GS-5734 against Ebola virus in rhesus monkeys

REGN-COV2, a Neutralizing Antibody Cocktail, in Outpatients with Covid-19

Phenotype and kinetics of SARS-CoV-2-specific T cells in COVID-19 patients with acute respiratory distress syndrome

WHO R&D Blueprint -Ad-hoc Expert Consultation on clinical trials for Ebola Therapeutics

Clinical benefit of remdesivir in rhesus macaques infected with SARS

Clinical benefit of remdesivir in rhesus macaques infected with SARS-CoV-2

Virological assessment of hospitalized patients with COVID-2019

Viral infection of the lung: host response and sequelae

Daily sampling of early SARS-CoV-2 infection reveals substantial heterogeneity in infectiousness. medRxiv

Clinical benefit of remdesivir in rhesus macaques infected with SARS-CoV-2

 ) . Models with the inclusion of refractory cells (in the form of ( ( and ( ( unless otherwise mentioned with *) and the delayed proliferation of susceptible cells in lung but not in the nasal passage are better equipped to explain the reduced lung damage in treated animals. All version of models assume )* = 0 and *) = 0 as their counterpart models with )* ≠ 0 and *) ≠ 0 have higher AIC. Moreover, 1 denote parameters for which both fixed and random effects are estimated, 2 denote parameters for which only fixed effects are estimated and 3 denote parameters for which fixed effects with fixed random effects (=0.1) are estimated, 4 denote parameters for which fixed effects with fixed random effects (=0.5) are estimated and 5 denote parameters for which fixed effects with fixed random effects (=1.0) are estimated. Here, 6 represents the situation where we assume the same distribution for +,) and +,* . Here, to avoid non-identifiability issues, population parameters such as ( , ( , ( and ( were kept fixed from [1] .