Timing of antiviral treatment initiation is critical to reduce SARS-Cov-2 viral load

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 80% if treatment is administered after symptom onset; an efficacy of 50% could be sufficient if treatment is initiated before symptom onset. Given their pharmacokinetic/pharmacodynamic properties, current investigated drugs may be in a range of 20-70% efficacy. They may help control virus if administered very early, but may not have a major effect in severe patients.

We modeled the viral dynamics of 13 untreated patients infected with SARS-CoV-2 to infer 39 viral growth parameters and predict the effects of antiviral treatments. In order to reduce peak 40 viral load by more than 2 logs, drug efficacy needs to be greater than 80% if treatment is 41 administered after symptom onset; an efficacy of 50% could be sufficient if treatment is 42 initiated before symptom onset. Given their pharmacokinetic/pharmacodynamic properties, 43 current investigated drugs may be in a range of 20-70% efficacy. They may help control virus 44 if administered very early, but may not have a major effect in severe patients. 45 46 All rights reserved. No reuse allowed without permission. author/funder, who has granted medRxiv a license to display the preprint in perpetuity. author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which 54 originated in Wuhan, China, has become a global pandemic. By March 29, 2020, this virus 55 had infected more than 700,000 people worldwide and caused more than 30,000 deaths. 56 Despite the unprecedented mobilization of the clinical and scientific community, the 57 development and large scale implementation of new antiviral drugs or vaccines will take 58 months or more. To readily propose a first line of defense and combat the virus in hospitalized 59 patients, the World Health Organization relies on already existing drugs ("repurposed") that 60 are immediately available in large quantities and have a good safety profile. In coordination 61 with other European institutions, France is implementing a randomized clinical trial in 62 hospitalized patients ("DisCoVery", NCT04315948) comparing the efficacy of 63 lopinavir/ritonavir ± IFN-β-1a, remdesivir and hydroxychloroquine. Given the very limited 64 knowledge of the host/pathogen interaction the clinical efficacy of treatment strategies using 65 these drugs is largely unknown and could be limited [1]. 66 Fitting mathematical models of viral dynamics to in vivo data can provide estimates of 67 parameters driving viral replication. Such models can then be used to predict the needed 68 efficacy of treatments and to optimize their use [2]. By combining these predictions with the 69 expected drug concentrations and EC 50 of drug candidates, one can anticipate the effects of 70 various dosing regimens (doses, timing of treatment initiation) on viral load dynamics. 71

Methods 72
Data used for fitting 73 We used published data from 13 untreated patients infected with SARS-CoV-2 that were 74 followed in 4 Singapore hospitals [3]. Patients were hospitalized in median at day 3 after 75 onset of symptoms (range: 1-10) and had a median symptomatic period of 12 days (range: 5-76 All rights reserved. No reuse allowed without permission. author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.04.20047886 doi: medRxiv preprint 24). Viral loads in nasopharyngeal swabs were measured by real time reverse transcriptase 77 polymerase chain reaction (RT PCR, lower limit of quantification: 38 cycles, CT) at multiple 78 time points with an observed peak of viral load at day 5 post onset of symptoms (range: 2-27 79 days). Data presented in CT were transformed to log10 copies/mL using a published 80 relationship in Zou et al. [4] and the model was fit to the log10 viral load. Of note, the 81 transformation from CT to log 10 copies/mL does not affect the estimates of parameters of 82 interest, in particular R 0 and the death rate of productively infected cells. Time since infection 83 was assumed to be 5 days before the onset of symptoms [5]. In a sensitivity analysis, we also 84 examined values of 2 and 10 days. 85 Model 86 Viral dynamics was fitted using a target cell limited model with an eclipse phase 87 The model considers three populations of cells: target cells, T, infected cells in the 88 eclipse phase, I 1 , and productively infected cells, I 2. Given the timescale of the infection, we 89 neglect target cell proliferation and natural death, and we focused on the process of cell 90 depletion by virus infection. We assumed target cells become infected with rate constant β. 91 After an average time of 1/k, these cells start producing virus and are cleared with per capita 92 rate δ. Virions are released from productively infected cells I 2 at rate p per cell and are cleared 93 from the circulation at per capita rate c. Based on this model, the basic reproduction number, 94 All rights reserved. No reuse allowed without permission.
author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

Equation 2 97
We assumed that the target cell concentration is 1.33 × 10 7 cells/mL. author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.04.20047886 doi: medRxiv preprint absence of treatment, i.e., 5 days after symptom onset. The model providing the best 118 description of the data was used for the simulations, and sensitivity analyses were conducted 119 to evaluate the results obtained with different assumptions regarding the delay between time 120 of infection and time of symptom onset either 2 or 10 days (Supplemental information, Fig S1  121 and S2). 122

144
Here we used a "target-cell limited" model with an eclipse phase  Fig S4 and Table S1). In influenza A, another respiratory 154 infectious disease, estimates of the within host R 0 varied greatly, but the half-life of infected 155 cells was shorter than 10 hours (see more details in [15]), suggesting a faster clearance of 156 influenza infected cells than SARS-CoV-2.
These numbers also inform us both on the time to initiate antiviral treatment, and the 158 level of efficacy that needs to be achieved to reduce viral load [6]. As limited information is 159 available on the mechanisms leading to viral clearance, and how they may be modulated by 160 treatment, we used our model to predict the effects of treatment at day 5 post symptoms, 161 which corresponds to the time the viral load tends to peak in the absence of treatment [3]. We 162 considered a simple case where the drug effectiveness is assumed to be constant after therapy 163 initiation (see methods) and we calculated the minimal efficacy that would be needed to 164 generate more than 2 logs of viral decline at peak viral load in the 13 studied patients (Fig. 1). 165 As predicted by viral kinetic modeling theory [2], we found that the impact of treatment on 166 peak viral load is inversely correlated with the time of treatment initiation. For a putative 167 treatment initiated at the time of infection, symptom onset, or 3 days post symptom onset, a 168 median efficacy of at least 60, 90 and 99% in reducing viral replication would be needed, 169 respectively, to generate more than 2 log of decline in the peak viral load (Fig. 1). 170 author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
and the mean antiviral effectiveness during the first 7 178 days of treatment is given by . Given their pharmacokinetic and 179 pharmacodynamic properties (Table 1), we calculated a mean antiviral efficacy of up to 66% 180 for lopinavir/ritonavir, 18% for IFN-β-1a, and 33% for hydroxychloroquine. Given these 181 estimates, these compounds are unlikely to have a dramatic effect on peak viral load if 182 administered after the onset of symptoms. In fact, the effective concentrations will 183 presumably be lower in patients, as relevant drug may be further limited by protein binding 184 (in particular for lopinavir, which has a protein binding rate > 98%) or capability to penetrate 185 respiratory compartments, which is not well characterized. Importantly, levels of antiviral 186 efficacy of ~50% could nonetheless be relevant in a prophylactic setting, before symptom 187 onset, to reduce viral replication in the upper respiratory tract and reduce the risk of large 188 infiltration to the lung before an effective immune response is mounted to clear virus [2] 189 Note, above we calculated the effectiveness of drugs administered in monotherapy for their 190 usual dosing regimen. We also did not consider drugs that could directly target infected cells 191 and lead to their elimination, such as some monoclonal antibodies. 192

Discussion 193
Overall our results emphasize that the PK/PD properties of lopinavir/ritonavir, IFN-β-1a 194 and hydroxychloroquine make them unlikely to have a dramatic impact on viral load kinetics 195 in the nasopharynx if they are administered after symptom onset. Given this, it is possible that 196 continued viral replication in the presence of drug will select for drug resistant mutations as 197 has been seen with other RNA viruses [7], although coronaviruses are unusual in that they 198 All rights reserved. No reuse allowed without permission. author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.04.20047886 doi: medRxiv preprint appear to have low mutation rates due to RNA proofreading capability. Drug combination 199 therapy and more aggressive dosing, including consideration of loading doses to rapidly 200 achieve therapeutic exposures, may be beneficial to maximize efficacy of these repurposed 201 antiviral agents. However, they may be relevant in pre-or post-exposure prophylaxis 202 administration to reduce viral replication and hence the risk of disease progression. 203