key: cord-1031980-osolval7 authors: Gonçalves, Antonio; Bertrand, Julie; Ke, Ruian; Comets, Emmanuelle; de Lamballerie, Xavier; Malvy, Denis; Pizzorno, Andrés; Terrier, Olivier; Rosa Calatrava, Manuel; Mentré, France; Smith, Patrick; Perelson, Alan S; Guedj, Jérémie title: Timing of antiviral treatment initiation is critical to reduce SARS‐CoV‐2 viral load date: 2020-06-18 journal: CPT Pharmacometrics Syst Pharmacol DOI: 10.1002/psp4.12543 sha: dc81703966fcd2862380a6ab9f9dd82713fe8c5a doc_id: 1031980 cord_uid: osolval7 We modeled the viral dynamics of 13 untreated patients infected with SARS‐CoV‐2 to infer viral growth parameters and predict the effects of antiviral treatments. In order to reduce peak viral load by more than 2 logs, drug efficacy needs to be greater than 90% if treatment is administered after symptom onset; an efficacy of 60% could be sufficient if treatment is initiated before symptom onset. Given their pharmacokinetic/pharmacodynamic properties, current investigated drugs may be in a range of 6‐87% efficacy. They may help control virus if administered very early, but may not have a major effect in severe patients. The outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which originated in Wuhan, China, has become a global pandemic. By May 7 th , 2020, this virus had infected more than 3,700,000 people worldwide and caused more than 260,000 deaths. To readily propose a first line of defense and combat the virus in hospitalized patients, the World Health Organization relies on already existing drugs ("repurposed") that are immediately available in large quantities and have a good safety profile. In coordination with other European institutions, France is implementing a randomized clinical trial in hospitalized patients ("DisCoVery", NCT04315948) comparing the efficacy of lopinavir/ritonavir ± IFN-β-1a, remdesivir and hydroxychloroquine in hospitalized patients. However, the clinical efficacy of currently available therapies is unknown and could be limited 1 . This article is protected by copyright. All rights reserved Here we fit mathematical models of viral dynamics to in vivo data to estimate parameters driving viral replication. We then use these models to predict the needed efficacy of treatments 2 . By combining the expected drug concentrations and EC50 of drug candidates, we also use the model to predict the effects of various dosing regimens (doses, timing of treatment initiation) on viral load dynamics. We used published data from 13 untreated patients infected with SARS-CoV-2 that were followed in 4 Singapore hospitals 3 . Patients were hospitalized in median at day 3 after onset of symptoms (range: 1-10) and had a median symptomatic period of 12 days (range: [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] . Viral loads in nasopharyngeal swabs were measured by real time reverse transcriptase polymerase chain reaction (RT PCR, lower limit of quantification: 38 cycles, CT) at multiple time points with an observed peak of viral load at day 5 post onset of symptoms (range: 2-27 days). Data presented in CT were transformed to log10 copies/mL using a published relationship in Zou et al. 4 and the model was fit to the log10 viral load. Of note, the transformation from CT to log10 copies/mL does not affect the estimates of parameters of interest, in particular R0 and the death rate of productively infected cells. Time since infection was assumed to be 5 days before the onset of symptoms 5 . In a sensitivity analysis, we also examined values of 2 and 10 days. Viral dynamics was fitted using a target cell limited model with an eclipse phase. This article is protected by copyright. All rights reserved . To determine the target cell concentration, the following calculation was done. We assumed that the total number of epithelial cells in the upper respiratory tract was 4 × 10 8 cells, distributed in a volume of 30 mL 8 . Assuming that 1% of these cells express the ACE2 receptor and associated proteases needed for viral entry 9 , the target cell concentration, T0, was fixed to 1.33 × 10 5 cells/mL. Following what was found in other viral infections, including acute infection 6 , the clearance rate of virus, c, was assumed to be fast and equal to 10 d -1 but values of 5 and 20 d -1 were also evaluated. Because not all parameters can be identified when only viral load data are available, parameters V0 and k were fixed at 10 -1 copies/mL and 3 d -1 , respectively, which corresponds to an initiation of the viral production 8 hours after cell infection on average 10 This article is protected by copyright. All rights reserved analysis was also performed with different values of k={1, 3, 5}d -1 and V0={10 -3 , 10 -2 , 10 -1 } copies/mL to assess the robustness of the parameter estimates. The parameter R0 was estimated instead of the infection rate  by a change of variables in Eq. (1). Parameters were estimated in a non-linear mixed-effect modeling framework using the SAEM algorithm implemented in Monolix (www.lixoft.com). The model providing the best description of the data was used for the predictions and the individual data fitting, and model averaging was used to correct for the model uncertainty when calculating confidence intervals of estimated parameters 11 . We assumed that antivirals with a constant effectiveness ε could reduce R0 by a factor (1-ε), with ε taking values from 50% to 99% in Equation 2. We considered different times of treatment initiation, from the time of infection to 3 days after the symptom onset. For each treatment strategy, we calculated the reduction in viral load at the peak of infection in the absence of treatment, i.e., 5 days after symptom onset. We also examined the possibility that cell infection is limited by an innate immune response that renders cells refractory to infection, as was proposed for other acute viral infections 8, 12 . In this model, two additional compartments are added, one for a cytokine (eg., IFN) released in response to antigen, and one representing cells in an antiviral state that cannot be infected (Supplemental information). This article is protected by copyright. All rights reserved We relied on the literature to find PK population models and parameter values of lopinavir/ritonavir 13 , plasma hydroxychloroquine 14 , IFN-β-1a 15 and remdesivir as well as reported EC50 values in vitro (see Table 1 ). For lopinavir EC50, specific results were obtained as follows. Vero during the first week of treatment, and the mean value over the N profiles was given in Table 1 . For comparison purposes, we based the analysis on total plasma concentrations and did not adjust for plasma protein binding when computing efficacy. Since the pharmacokinetic parameters of remdesivir have not been reported yet in humans, the same method could not be applied. We used the summary statistics reported in the This article is protected by copyright. All rights reserved summary for compassionate use of remdesivir filed by Gilead to the EMEA 16 to derive the mean concentration of the active metabolite in PBMC, Cmean, using the AUC after a loading dose of 200 mg and after repeated doses of 100 mg QD and we assumed that the EC50 for the metabolite was equal to the EC50 of the parent 17 . We used a "target-cell limited" model with an eclipse phase 8 given by Eq. (1) (Table 2) . However, as shown previously, p cannot be uniquely identified unless the initial target cell density T0 is known 19, 20 . Therefore, the only quantity that can be reliably estimated is the product p×T0, equal to 3.0 × 10 6 copies d -1 (CI95% = [0-7.9×10 6 ]). Parameter estimates and confidence intervals were also consistent across models assuming a viral clearance c of 5 or 20 d -1 (see Table S1 ). This article is protected by copyright. All rights reserved Our model along with the parameter estimates given above also inform us both on the time to initiate antiviral treatment, and the level of efficacy that needs to be achieved to reduce viral load 6 . As limited information is available on the mechanisms leading to viral clearance, and how they may be modulated by treatment, we used our model to predict the effects of treatment at day 5 post symptoms, which corresponds to the time the viral load tends to peak in the absence of treatment in these data 3 . We considered a simple case where the drug effectiveness is assumed to be constant after therapy initiation (see methods) and we calculated the minimal efficacy that would be needed to generate more than 2 logs of viral decline at peak viral load in the 13 studied patients (Fig. 2) . As predicted by viral kinetic modeling theory 2 , we found that the impact of treatment on peak viral load is inversely correlated with the time of treatment initiation. For a putative treatment blocking the viral production p and initiated at the time of infection, symptom onset, or 3 days post symptom onset, a median efficacy of at least 60, 90 and 99% in reducing viral replication would be needed, respectively, to generate more than 2 log of decline in the peak viral load (Fig. 2) . The results obtained assuming 2 or 10 days of incubation are presented in Fig. S2 and S3. We also considered the case of a drug like hydroxychloroquine blocking viral infection (parameter β in Eq. 1). Results were similar to those obtained before as along as the treatment was initiated before or at symptom onset. However, initiating a treatment 3 days post-symptoms onset could not reduce peak viral load, regardless of the drug effectiveness (see Fig. S4 ). The model including an innate immune response did not improve the data fitting and therefore was not selected for inclusion in the main text. However, the same analysis on viral dynamics and treatment was conducted and the conclusions remained unchanged (see Fig. S5 , S6 and Table S2 ). This article is protected by copyright. All rights reserved How do these levels of effectiveness compare with the antiviral drugs that are currently being investigated? To study this question, we assumed that the treatment antiviral effectiveness at time t after treatment initiation, ( ), was related to the plasma total drug concentration, C(t): . Given their pharmacokinetic and pharmacodynamic properties (Table 1) , we calculated a mean antiviral effectiveness of up to 66% for lopinavir/ritonavir, 6% for hydroxychloroquine, 18% for IFN-β-1a and 87% for remdesivir. Given these estimates, these compounds are unlikely to have a dramatic effect on peak viral load if administered after the onset of symptoms. In fact, the effective concentrations will presumably be lower in patients, as drug availability may be further limited by protein binding (in particular for lopinavir, which has a protein binding rate > 98%) or capability to penetrate respiratory compartments. Importantly, levels of antiviral efficacy of ~50% could nonetheless be relevant in a prophylactic setting, before symptom onset, to reduce viral replication in the upper respiratory tract and reduce the risk of large infiltration to the lung before an effective immune response is mounted to clear virus 2 Note, above we calculated the effectiveness of drugs administered in monotherapy for their usual dosing regimen. We did not consider drugs that could directly target infected cells and lead to their elimination, such as some monoclonal antibodies. Overall our results emphasize that the PK/PD properties of lopinavir/ritonavir, hydroxychloroquine, IFN-β-1a and remdesivir make them unlikely to have a dramatic impact on nasopharyngeal viral load kinetics if they are administered after symptom onset. However, these drugs may be relevant to reduce viral replication if administered early, i.e., as a pre-or This article is protected by copyright. All rights reserved post-exposure prophylaxis. This conclusion however depends on a number of hypotheses that we discuss below. First we focused on the capability of drugs to reduce the peak viral load making the implicit hypothesis that reducing peak viral load would likely reduce symptoms and disease severity. However the relationship between viral kinetics and disease severity is still debated, with several studies suggesting that viral load did not differ between patients with severe and nonsevere disease 21, 22 . Related to this question, our study had some limitations. Our calculations relied on blood or plasma drug concentrations. Except for hydroxychloroquine, for which the ratio of lung to plasma concentration is known to be high 23, 24 , the lung exposure of the other drugs that we considered is unknown, and their effect on viral load in the lower respiratory tract, as measured from broncho-alveolar aspirates for instance, may differ. In addition, the drug EC50 that we used were determined on Vero E6 cells, an in vitro system that may not reflect the in vivo EC50. For instance, we found in another study that hydroxychloroquine had no antiviral activity in a more physiological model of reconstituted human airway epithelium, and this may explain the absence of antiviral of activity of HCQ in vivo against SARS-CoV-2 24,25 . Finally we focused solely on the antiviral effects of these drugs, and did not consider other potential effects of these drugs, such as their immunomodulatory effects. Such effects have been suggested for drugs that are not purely antivirals, such as hydroxychloroquine and IFN-β-1a 26, 27 . Another implicit implication of our work is the benefit of drugs used for prophylaxis, i.e., before exposure to the virus. In that case the objective of the treatment may be to "flatten the peak viral load" (by analogy with the now popular terminology of epidemiological models) but also to prevent infection. Our deterministic, ODE-based model, cannot reproduce virus extinction, but this can be captured using stochastic version of the same model 28 . This article is protected by copyright. All rights reserved Our modeling provides estimates of viral kinetic parameters, in particular R0 and the loss rate of infected cells, δ, and the limit of extrapolation of these parameters also need to be well understood. The advantage of studying this series of patients was the fact that viral load was sampled extremely frequently and early in the infection. However the number of patients we studied was quite small (only 13), and the patients were rather young (37 years, range 31-56 years) and may not be representative of patients that are typically evolve to have severe forms of the disease 21 . Therefore, more data will be needed, from various populations, to estimate precisely the parameter distribution in the population of patients that are most in need of antiviral therapy. Finally, our estimate of the loss rate of free virus and infected cells are constant over time, which neglects the effects of the adaptive immune response. For instance antibodies, that emerge in the second week after symptom onset 29,30 , may contribute to accelerate viral clearance or reduce viral infectivity. However, to include these effects would require more complex models and quantitative data on these antibodies and their in vivo effects, which are currently lacking. Further, our analysis of the antiviral effects of repurposed drugs focused on their ability to reduce the peak viral load, which typically occurs well before the antibody response emerges and hence the analysis we presented here should not be affected in any major way by our neglect of antibody responses. Future models of drug efficacy may need to account for viral resistance, as it is possible that continued viral replication in the presence of drug will select for drug resistant mutations 31 , although coronaviruses are unusual in that they appear to have low mutation rates due to RNA proofreading capability 32 . Drug combination therapy and more aggressive dosing, including consideration of loading doses to rapidly achieve therapeutic exposures, may be beneficial to maximize efficacy of these repurposed antiviral agents 33 . For all these reasons, the outcome of randomized clinical trials remains urgently needed, and the analysis of their impacts This article is protected by copyright. All rights reserved not only on viral clearance but also on disease severity will be critical to design more potent drugs.  What is the current knowledge on the topic? Repurposed drugs are being evaluated in clinical trials but little is known about their efficacy on SARS-CoV-2 viral kinetics.  What question did this study address? Our study aims to combine PK/PD and viral kinetics modelling to anticipate the effects of lopinavir/ritonavir, hydroxychloroquine, IFN-β-1a and remdesivir,  What does this study add to our knowledge? Given the predicted efficacy of lopinavir/ritonavir, hydroxychloroquine, IFN-β-1a and remdesivir, it is unlikely that these drugs will have a major effect on viral kinetics if they are administered as monotherapy after symptom onset.  How might this change drug discovery, development, and/or therapeutics? Our results suggest that these drugs should be evaluated in persons exposed to the virus but prior to appearance of the first symptoms. This article is protected by copyright. All rights reserved This article is protected by copyright. All rights reserved Table 1 : PK/PD properties of candidate antiviral drugs. We assume that the total concentrations were the driver of efficacy, and we did not consider intracellular metabolites or free drug concentrations Table 2 : Median and confidence intervals of R0 ,δ and p across models and following model averaging procedure A Trial of Lopinavir-Ritonavir in Adults Hospitalized with Severe Covid-19 Acute bacterial or viral infection-What's the difference? 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