Modeling of SARS-CoV-2 Treatment Effects for Informed Drug Repurposing

Introduction
Since the beginning of the ongoing global outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a variety of drug therapies have been proposed. Some are based on expert opinion, some on promising in vitro results, some on findings in case series from compassionate or off-label treatments. Unfortunately, whenever they are put through the rigorous process of randomized clinical trials, little evidence for palpable real-world benefits remains. Novel coronavirus disease 2019 (COVID-19) spreads rapidly not only from host to host but within each host as well. The infection progresses at a staggering speed in individual patients which may become infectious after 2–3 days and reach peak viral loads only a few days after the reverse-transcriptase polymerase chain reaction (RT-PCR) test becomes positive (To et al., 2020). The need for early initiation of drug therapy has been recognized as key for successful treatment of infectious diseases, and COVID-19 is unlikely to be an exception (Gonçalves et al., 2020). The repurposing of drugs with established supply chains and low manufacturing costs seems the straightest path towards a timely pharmacological intervention. Because our understanding of the pathophysiology of COVID-19 is still evolving, the selection of viable candidates is mostly dictated by extrapolations from in vitro and silico evidence. Identified drug targets include the viral structural spike (S) protein; the host type 2 transmembrane serine protease (TMPRSS2); 3-chymotrypsin-like (3CL) protease mediating proteolysis; RNA-dependent RNA polymerase; and interleukin-6 receptors (Arshad et al., 2020; Sanders et al., 2020).


Viral Kinetics Models
In the standard target cell limited model, virus particles V infect a pool of susceptible (target) cells, T, with the cellular infection rate β. Infected cells begin shedding virions at a production rate p (Canini and Perelson, 2014). The parameters c and δ determine the rate of clearance of virus and cell death of infected cells, respectively. The time-dependent number of susceptible cells (Eq. (1)), infected cells (Eq. (2)), and viral load (Eq. (3)) are described by a system of ordinary differential equations as follows:

Immune Response
Our understanding of SARS-CoV-2 immunity is still evolving. Immunity could involve cells entering into a refractory state or an antibody-mediated increase in viral clearance. Adding state would increase model complexity beyond what seems supported by the source data. We, therefore, chose to enter acquired immune response as a time-dependent covariate effect on viral clearance c. Temporal dynamics are based on Long et al. (2020) who evaluated seroconversion for IgM and IgG in 285 patients from three hospitals in Chongqing (neighboring Hubei Province). Data were extracted with digitizing software and fitted to a sigmoidal Emax model. As the effect size of the immune response in SARS-CoV-2 infection (Emax, immunity) is unknown, we estimated this value together with the models of viral kinetics.

Methods


Viral kinetic profiles of COVID-19 patients were taken from Young et al. (2020), a study that followed the first patients (n = 18) in four hospitals in Singapore (Chinese nationals: n = 16, Singapore residents: n = 2). We read out values using digitizing software. Most (n = 13) were not on specific therapy and were included in the analysis. Viral load was measured from nasopharyngeal swabs with RT-PCR and presented in cycle threshold (Ct) values (Young et al., 2020). As the correlation between Ct values and viral load varies by laboratory and analytical conditions, we chose to relate model output with observed Ct values with a published regression fit (Chu et al., 2020). Since the time of infection was not recorded, this value had to be estimated. Although the incubation period varies between patients, an average incubation period of 5 days fitted well for all patients (Lauer et al., 2020). We fixed the positivity threshold at 35 cycles, corresponding to 101.58 copies/ml (Wang et al., 2020b).

Pharmacokinetic Models
We simulated pharmacokinetics (PK) of HCQ, IVM, LPV/r, and ART from published population pharmacokinetic models. Profiles for HCQ were simulated from healthy volunteers reported by Lim et al. (2009). The IVM model was taken from Duthaler et al. and simulated using fed state dosing (Duthaler et al., 2019). The LPV/r model by Dickinson et al. (2011) was built from data of healthy volunteers receiving 400/100 mg, the dose that was under investigation in WHO Solidarity. For ART we directly implemented the model developed by Birgersson et al. in healthy male volunteers with a dosing regimen of 500 mg daily for 5 days (similar to historical dosing recommendations in malaria) (Birgersson et al., 2016). No published pharmacometric model is available for NTZ. The drug is rapidly and completely hydrolyzed to an active metabolite, nitazoxanide (TZ). We, therefore, extracted the mean TZ pharmacokinetic profile from a study in healthy Mexican volunteers with digitizing software, fitted a one-compartment oral absorption model with lag time, and used this for simulation (Balderas-Acata et al., 2011). As the protein-bound fraction of a drug is considered not interacting with its target, we only considered the unbound fractions of the drugs to be available (Supplementary Table S2), i.e. 50% for HCQ (Furst, 1996), 7% for IVM (Klotz et al., 1990), 1% for NTZ (FDA, 2005), and 1% for LPV (Boffito et al., 2004). No human in vivo data exists for lung concentrations in any of the drugs in this study. We used literature-based approximations to adjust for differences between plasma and lung concentration profiles. The issue of lung tissue concentrations is particularly contentious for HCQ, with some reports of the lung: plasma ratio ranging from 27 to 177 in macaques (Maisonnasse et al., 2020). Recent evidence suggests that in COVID-19 HCQ plasma concentrations are more representative (Fan et al., 2020). For IVM lung accumulation, we used cattle data published by Lifschitz et al., an approach also used in another publication discussing the potential role of IVM in COVID-19 (Lifschitz et al., 2000; Schmith et al., 2020). LPV concentrations in lung tissue were assumed to be 1.78 times higher than in plasma, and protein binding was set to 99% (Atzori et al., 2003; FDA, 2013). For NTZ we used estimates from a recently republished physiology-based pharmacokinetic (PBPK) model for lung partitioning (Rajoli et al., 2020).

Pharmacodynamic Effects
The effectiveness of HCQ was shown in vitro in Vero E6 cells by Liu et al. (2020). The EC50 values at 48 h ranged between 4.06 and 12.96 µM, depending on the amount inoculated. We entered the mean of these values (8.51 µM) as an effect on the reduction of the cellular infection rate β. We simulated dosages of 200 mg q8h for 10 days as proposed by Gautret et al. and the scheme previously employed in the WHO Solidarity trial, 800 mg q12 h on the first day (loading dose) and 400 mg q12 h on days 2–10 (Gautret et al., 2020; WHO, 2020).

Results


We used the viral load profiles of untreated patients published by Young et al. (n = 13, Supplemental Material) (Young et al., 2020). We evaluated target cell limited and eclipse models, both with a time-varying effect on viral clearance c following a sigmoidal Emax model fitted to reported seroconversion data (Long et al., 2020). The averaged parameters estimates from individual profiles with the Nelder-Mead method were as follows (see also Supplementary Table S1 and Supplementary Figure S1):
• viral clearance c: 5.07,
• production rate p: 10.2,
• death rate of infected cells δ: 0.54, and
• maximal immune effect on clearance Emax, immunity: 57.0.
Nonlinear mixed-effects implementations of these models proved less robust to changes in initial estimates and suffered from numerical identifiability problems.
Profiles were best described by a standard target cell limited model. The addition of an eclipse phase did not improve fits and also introduced identifiability issues, as was already noted in another study (Hernandez-Vargas and Velasco-Hernandez, 2020). Left untreated, viral load exceeds the RT-PCR positivity threshold of 35 cycles at 5.4 dpi, peaks at 10.2 dpi with a Ct value of 28.4 cycles, and drops below the positivity limit at 18.9 dpi, similar to reports from clinical studies (Kim et al., 2020a; Lauer et al., 2020; To et al., 2020). Total viral exposure (measured as AUC) was 12’003 days*log(copies/ml).

Dosage and Effectiveness of Treatment
The temporal impact of treatment is shown as individual curves in Figure 1. Effect on viral exposure as the difference in the area under the curve (AUC), the relative change in duration, and change in peak cycle (Ct) is presented in Figure 2. Full results including changes in peak viral load and duration of disease are available in Supplementary Table S3 and Supplementary Figure S2. The PK curves of the treatments and the corresponding effect on SARS-CoV-2 viral kinetics are shown in Supplementary Figures S2–S5.















Discussion


Our modeling and simulation study described patient viral load well and captured the essential milestones of SARS-CoV-2 viral kinetics, e.g., duration of viral shedding and peak viral loads. It also shows that the window of opportunity to treat COVID-19 is narrow. As the infection spreads rapidly throughout the host, the pool of susceptible cells is quickly depleted. Drugs inhibiting viral entry (like HCQ) therefore only appear to have a role, if any, in the first days after inoculation (post-exposure prophylaxis) or as primary prophylactic agents handed out to at-risk individuals.
These findings may help to explain the disappointing results of clinical trials with HCQ: by the time patients are hospitalized or even transferred to critical care, few susceptible cells are left, so the little impact can be made at this point (Annie et al., 2020; Cavalcanti et al., 2020; Molina et al., 2020; Tang et al., 2020a). The WHO Solidarity trial’s dosing scheme was more effective than the one proposed by Gautret et al. (2020). However, even with the higher dosing scheme used in the WHO Solidarity trial, no appreciable effect of HCQ was observed and the treatment arm was prematurely terminated on June 18, 2020 (Pan et al., 2020). Of note, recent trials have also failed to find benefits for HCQ in pre-and post-exposure prophylactic indications (Boulware et al., 2020; Rajasingham et al., 2020). Since viral load is not the only determinant of disease state, one cannot directly deduce the clinical effect of any of the regimens from these simulations. Given the negative results of previous trials with HCQ, we suggest that HCQ results should be used as a lower threshold to rank other drugs against. We found the greatest effects for IVM. Again, the earlier and longer the exposure, the better, but compounds like IVM still convey some benefit if initiated at a later stage. When held to the HCQ benchmark, IVM 600 µg/kg daily for 3 days, particularly when given around the time of positivity, may have a meaningful impact whereas IVM 300 µg/kg daily for 3 days had efficacy comparable to HCQ regimens. This finding is in contrast to other analyses suggesting IVM is poorly druggable in COVID-19 (Schmith et al., 2020). It is important to stress that these IVM doses, while safe in healthy volunteers, are far higher than any dose approved for other indications (1 × 200 µg/kg to 1 × 400 µg/kg). At 3 × 600 µg/kg in a 70 kg patient, doses are similar to the maximum doses (120 mg single administration) described by Guzzo et al. (2002). Boosting exposure to IVM by co-administering inhibitors of its metabolism or elimination (such as the CYP3A4 and P-glycoprotein (P-GP) inhibitor ritonavir) is a theoretical option (Chaccour et al., 2017). However, there are concerns that inhibition of P-up as an integral part of the functional blood-brain barrier could lead to more central nervous adverse events (Chandler, 2018). Until this interaction has been studied systematically, it seems unwise to explore this strategy. For IVM, no results of clinical trials regarding its effectiveness in COVID-19 have been published yet.
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