Model‐informed drug repurposing: Viral kinetic modelling to prioritize rational drug combinations for COVID‐19

Aim We hypothesized that viral kinetic modelling could be helpful to prioritize rational drug combinations for COVID‐19. The aim of this research was to use a viral cell cycle model of SARS‐CoV‐2 to explore the potential impact drugs, or combinations of drugs, that act at different stages in the viral life cycle might have on various metrics of infection outcome relevant in the early stages of COVID‐19 disease. Methods Using a target‐cell limited model structure that has been used to characterize viral load dynamics from COVID‐19 patients, we performed simulations to inform on the combinations of therapeutics targeting specific rate constants. The endpoints and metrics included viral load area under the curve (AUC), duration of viral shedding and epithelial cells infected. Based on the known kinetics of the SARS‐CoV‐2 life cycle, we rank ordered potential targeted approaches involving repurposed, low‐potency agents. Results Our simulations suggest that targeting multiple points central to viral replication within infected host cells or release from those cells is a viable strategy for reducing both viral load and host cell infection. In addition, we observed that the time‐window opportunity for a therapeutic intervention to effect duration of viral shedding exceeds the effect on sparing epithelial cells from infection or impact on viral load AUC. Furthermore, the impact on reduction on duration of shedding may extend further in patients who exhibit a prolonged shedder phenotype. Conclusions Our work highlights the use of model‐informed drug repurposing approaches to better rationalize effective treatments for COVID‐19.

Patients progress to shock, vasoplegia, respiratory failure and cardiopulmonary collapse. Stage 3 is associated with a poor prognosis. 5 As of 11 June 2020, there were 1166 clinical interventional studies registered in clinicaltrials.gov with therapies targeting COVID-19.
The vast majority of these studies are not randomized placebocontrolled clinical trials and they often included patients with COVID-19 who were hospitalized and presented with the severe form, limiting the interpretation of results from a drug development perspective. [6][7][8][9] Significant inefficiencies in global clinical trials efforts for COVID-19 have also resulted in calls for action from the clinical and quantitative pharmacology community to support streamlining of efforts, including using model informed approaches. 10 Given the dearth of effective antiviral monotherapies for COVID-19, the need to evaluate therapeutic combinations is being re-emphasized, as was initially described in the World Health Organization's Novel Coronavirus Global Research and Innovation forum. 11 We hypothesize that there are two key considerations for candidate antiviral therapeutic interventions, one being the timing of interven-  12 and correlated with clinical outcome in SARS-CoV-2 infection. 13 Duration of viral shedding and impact of therapeutic interventions has been linked to transmission and health economic models, demonstrating indirect benefits of individual treatment to societal outcomes for pandemic influenza. 14 Such endpoints have been of critical importance in informing procurement and deployment decisions for interventions within healthcare systems during outbreak scenarios. Viral kinetic modelling has also been extensively used to support drug development decisions in the respiratory virus space. 15 The aim of this research was to leverage a model of SARS-CoV-2 infection to support prioritization of drug combinations based on how their mechanisms interacted in a simulation setting to improve various metrics of infection outcome.

| Model
We used a target-cell limited model with an eclipse phase based on an analysis published by Goncalves et al 16 that was used to characterize the viral load dynamics of 13 hospitalized COVID-19 patients from frequent nasopharyngeal swabs.
In simple terms, the target-cell limited model integrates four entities, uninfected susceptible epithelial target cells (T), latently infected cells (I1), productively infected cells (I2) and the virus load (V), and is described by a system of nonlinear ordinary differential equations. 17 Given the timescale of the infection, the model neglects target cell proliferation and natural death, and focuses on the process of epithelial cell depletion (T) by virus infection. When a virus (V) interacts with an uninfected target cell (T) at a defined infection rate, β, the target cells will become infected (I1) and remain so during an incubation period. These cells, in turn, convert to productively infected cells (I2) at a rate k. These cells then produce new virions (V) with a defined production rate ρ. Simultaneously, productively infected cells die at a certain rate δ. Circulating virions (V) are then cleared at a certain rate c from the body or go on to infect new cells as above. Based on the dynamics of the cell model and the associated mechanisms of actions of the currently experimented drugs for SARS-CoV-2 infection, we What is already known about this subject • Given the dearth of effective antiviral monotherapies for COVID-19, the need to evaluate combinations, as outlined by the World Health Organization in the initial coronavirus roadmap, is being re-emphasized. Significant inefficiencies in global clinical trials efforts for COVID -19 have also resulted in calls for action from the clinical and quantitative pharmacology community to support streamlining of efforts, including using model informed approaches.
• Viral cell cycle kinetics models as well as their limitations have been well described in the literature, but their potential to inform combination treatment strategies for SARS-CoV-2 has not been described.
• The fundamental principles of simple viral cell cycle models remain largely conserved across different viruses even though the specific kinetics within the viral cell cycle may differ, therefore lessons learned from prior applications can be leveraged to inform rationale drug treatments for COVID-19.

What this study adds
• This study postulates that a simple viral cell cycle model based on SARS-CoV-2 may serve as a framework to understand the impact of modulating specific rate constants as site of action for treatment interventions and proposes that effectiveness is directly related to these sites of action. and "copies", respectively. The parameter β was derived from the reported R 0 of 8.6 with the equation

| Intervention effects
Interventions were posited for the targets in the viral life cycle given in Figure 1. Intervention effects were modelled as inhibitory functions for β, k and ρ (eg, β × [1 -I max (t)]) and stimulatory functions for δ and c (eg, δ × [1 + S max (t)]). S max (t) and I max (t) were treated as step (Heaviside) functions with onset at times relative to the approximate viral peak, estimated as 9 days post infection: −6, −3, 0, +3 and +6 days. Intervention at viral peak −6 and −3 days represents cases of pre-and post-exposure prophylaxis, intervention at 0 and +3 days represents cases of symptomatic presentation and intervention at +6 days represents cases of advanced infection.
Specific values of inhibition (I max ) and stimulation (S max ) were selected with the intention to "blanket" the space of pharmaceutical intervention from low to very high potency. Supporting Information Figure S1 reports the specific values, noting that the choices are interconvertible and can be expressed in terms of drug effect, I max or S max :

| Simulations
Simulations were conducted in R (3.6.1) using the RxODE (0.9.2) package for numerical integration and the tidyverse (1.2.1) family of packages. An R script reproducing these results is provided in Supporting Information Data S1.

| Endpoints and metrics
We generated three key metrics for each simulation case.

| Duration of viral shedding
The duration of time (days) for which the virus concentration, V, exceeds 100 copies/mL is often the lower limit of detection for qPCR assays for SARS-CoV-2. 18 This duration of viral shedding metric summarizes the amount of time virus is detectable, which is considered a correlate with the time a patient is infectious.
Reducing the duration of detectable virus thereby impacts transmission dynamics and risk to others within a population, but also may impact on the duration of isolation, containment or hospitalization of a patient, even if it does not correlate directly with an individual patient's signs and symptoms.

| Epithelial cells infected
T represents the number of epithelial target cells that are infected (cells/mL) by virus. This metric summarizes the damage to host lung epithelial host cells during the course of infection and is considered a proxy for the degree of pulmonary inflammatory response and lung tissue damage, and hence pulmonary clinical signs and symptoms within an individual patient. There is increasing evidence that other tissues and organs may be infected by SARS-CoV-2, but this is beyond the scope of this model.
These endpoints were compared to the reference case of the natural history, and expressed as the metric: log10 treatment metric=no−treatment metric ð Þ Therefore, a difference of 1 unit of a metric between two treatments indicates an order of magnitude change (ie, a decibel scale).

| RESULTS
An overview of treatment effects by intervention time and disease metric is summarized in Figure 2.   Table 3.We assumed modest effect (0.333 log10 effect, 53.6% inhibition, 1.15 fold increase) for each target. Single-target interventions were selected as β, δ, ρ and c, two-target intervention was selected as δρ, three-target interventions were selected as δρc and βδρ, and a four-target intervention was selected as βδρc. Figure 4 shows the output of these simulations at selected intervention times. Supporting Information Figure S3 and Figure 4 report the predicted impact viral and infected epithelial cell kinetics assuming intervention 6 days before and 6 days after peak viral load, respectively. Figure   The predicted impact on viral and infected epithelial cell kinetics assuming intervention at peak viral load is shown in Figure 4B. As above, the single interventions have modest effect on viral load, with δ identified as ideal for reducing duration of viral shedding and c identified as ideal for reducing viral load AUC (Table 1). A 3 log10 reduction in uninfected epithelial cells is expected. The three-and four-target interventions somewhat improve duration of viral shedding, but the biggest gain is observed in a 1 log10 improvement in epithelial cells infected, with β identified as ideal (Table 1). Figure 4C shows the predicted impact on viral and infected epithelial cell kinetics assuming intervention 3 days before peak viral load. Some modest gains are possible for duration of viral shedding, with δ identified as ideal. Treatments targeting c are identified as ideal for reducing viral load AUC (Table 1). Very little improvement in epithelial cells infected is predicted, reinforcing the primary finding of this work and others that early intervention is critical. Here, we explicitly report the effect on host cell damage, which has been underappreciated in prior efforts.

| DISCUSSION
We have argued that the selectivity of antiviral therapy can be significantly enhanced by exploiting matching of the drug based on its purported mechanism of action with viral cell cycle dynamics. Table 2 summarizes the association of the mechanism of action of currently  According to our simulations, beginning treatment beyond 3 days after peak viral load is unlikely to have any meaningful impact on epithelial cells infected, which may correlate with patient symptoms, but benefit for later intervention may persist beyond 3 days for duration of viral shedding, which may correlated with clinical and public health endpoints. As prolonged viral shedding phenotypes are described for influenza 47 and COVID-19, 48 we performed sensitivity analyses with c and δ. We observed in prolonged viral shedder phenotypes that cessation of viral shedding benefit persists for therapeutics that promote virion kill (c) and infected cell death (δ) and inhibit virion release (ρ). Such interventions would be preferred to address so-called SARS-CoV-2 super spreaders. 49,50 The primary outcome of this simulation study is captured in Mechanisms that promote infected cell death (δ) and/or reduce copies of virions per infection (ρ) achieve these goals. Simulations results suggest interchangeability of these effects, with the noted exception of reducing duration of viral shedding where δ is superior to ρ.
Interchangeability suggests additive effects, from a simplistic anergy/additivity/synergy perspective, but also offers an opportunity to combine two low-potency agents, each targeting one mechanism, to boost the overall potency of the combination. Within the host cells, simply delaying the viral replication machinery (k) is not a good strategy.
Outside or on the border of host cells, Table 1  were the most effective, meaning that interventions like convalescent plasma or investigational antibodies would be anticipated to be most likely to impact total viral load meaningfully.
Of the therapies being investigated, remdesivir was recently shown in hospitalized adults with moderate disease to provide a 31% faster time to recovery than those who received placebo (P < 0.001), 8 but no virologic information was reported. However, in the study by Wang et al,7 remdesivir had no meaningful effect on viral load.
Remdesivir is thought to play a role in the incorporation into new viral RNA, leading to the inability of the viral polymerase to add new RNA.
In the absence of key mechanistic information, we assumed that remdesivir reduces the production of new virions by halting replication of its genome, and thus its effect is proximally associated with ρ.
It is possible that remdesivir may show meaningful efficacy if studied in an earlier infection phase. Future data on remdesivir in early onset mild patients with COVID-19, combined with suitable therapeutics, will likely inform on the benefits of early intervention for this molecule.
Duration of viral shedding is less time sensitive to perturbation than viral load AUC and epithelial cells infected, and is also

| FUTURE DIRECTIONS
Our model-informed analysis underscores the need to include the key features of the viral cell cycle from the perspective of dynamic models to leverage the significance of cell-cycle checkpoints (vis à vis specific rate constants) for emerging therapeutics. Our model builds upon previously described models by extending their utility into assessment of the value of combinations. Such an approach will be invaluable for clinicians and trialists to develop informed hypotheses based on cell-cycle selectivity and specificity. The fundamental premise for this approach assumes that cell kinetics and durability of response are intricately regulated and can only be disrupted by a drug that has the specificity for that particular phase.
The model leveraged here is parsimonious and offers a quick, reliable method to triage therapeutics entering clinical assessment for the ongoing pandemic. Efforts are ongoing to further integrate wet-lab inputs on the virus characterization model, including replication dynamics, tropism and cell culture susceptibility, but also integrating with drug characterization (including absorption, distribution, metabolism and elimination (ADME) profiles) and emerging clinical data from ongoing studies. We hope that further refinements as well as extension to broader incorporation of the downstream host inflammatory response and associated interventions such as immunomodulators, including IL-6 inhibitors, will provide a comprehensive disease model backbone that could be fungible for inputing emerging virus pathogens. We believe that a comprehensive quantitative and systems pharmacology approach linking to wet-lab data for emerging viruses can provide a structured scientific backbone that could revolutionize and rationalize our approach to selecting therapeutic interventions for future pandemics.