Materials and methods
Model
We used a “target-cell limited” model with an eclipse phase based on
an analysis published by Goncalves et.al., 2020 [14] that was used
to characterize the viral load dynamics of 13 hospitalized patients from
frequent nasopharyngeal swabs. Readers are directed to that publication
for details on the analysis, assumptions and data. The authors performed
a similar analysis presented here, focusing on specific drug effects and
intervention time.
Specific model parameters for this exercise were: V0=0.1 #/mL,
T0=1.33E5 #/mL, k=3 1/d, δ=0.60 1/d, β=2.21E-5
mL/#/day, ρ=22.7 1/d, c=10 1/d. For state variables representing cells
and virions, the meaning of “#” was “cells” and “copies”,
respectively. The parameter β was derived from the reported R0 of 8.6
with the equation β =R0*δ*c/[T0*(ρ-R0*δ)].
Intervention effects
Interventions were posited for the targets in the viral life cycle given
in Figure 1 . Intervention effects were modeled as inhibitory
functions for β, k, ρ (e.g. ß*[1-Imax(t)]) and stimulatory function
for δ, c (e.g. δ*[1+Smax(t)]). Smax(t) and Imax(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, +6 days. Intervention at viral peak -6 and -3 days represent cases
of pre- and post-exposure prophylaxis; intervention at 0 and +3 days
represent cases of symptomatic presentation; intervention at +6 days
represent cases of advanced infection.
Specific values of inhibition (Imax) and stimulation (Smax) were
selected with the intention to “blanket” the space of pharmaceutical
intervention from low to very high potency Supplemental Figure
1 reports the specific values, noting that the choices are
interconvertible and can be expressed in terms of drug effect, Imax or
Smax:
log10 Drug Effect = log10[Smax+1] = -log10[1-Imax]
With this particular formation, a fair assessment of e.g. 1 log10 change
in an inhibitory versus stimulatory effects can be made. Additionally,
the specific values of individual effect (0, 0.333, 0.667, 1, 1.33,
1.67, 2 log10 change) can be summed for easy comparison. For example, a
single effect with 1 log10 change (90% inhibition or 9-fold
stimulation) can be compared to an intervention with three effects each
with 0.333 log10 change (53.6% inhibition or 1.15-fold simulation,
each) fairly. If the three effects are strictly additive, then the total
effect is 100*(1-(1-0.536)3)=90% and would result in
the same effect as a monotherapy effect of 90%, if the effect is
additive and targets the same pathway. In these simulations, different
pathways are explicitly targeted and the model is nonlinear
(second-order) in the dynamics. Thus, difference in simulation outcome
for two interventions with the same summed log10 change effect describe
synergy and anergy of targeting different pathways.
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. A R script reproducing these results is
provided in Supplemental Script 1 .
Each of the five checkpoints (β, k, ρ, δ, c) were probed with seven drug
effect levels (0, 0.333, 0.667, 1, 1.33, 1.67, 2 log10 change) for a
total of 16,797 simulation conditions. Each condition was replicated
over five intervention times (viral peak at 9 -6, -3, 0, +3, +6 days)
for a total of 84,035 condition-times. However, simulations were reduced
to cases with summed intervention effect between 0.333 and 2 log10
change, reducing the total simulations to 2,310 intervention conditions.
Endpoints and Metrics
Viral load dynamics has been elevated to surrogate status in the
management of HIV by the FDA, and is aligned with clinical outcome for
respiratory viral infections including seasonal and emerging influenza
strains in various populations [15] and correlated with clinical
outcome in SARS-COV-2 infection [16]. 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 [17]. Such
endpoints have been critical importance in informing procurement and
deployment decisions for interventions within health care systems during
outbreak scenarios. Viral kinetic modelling has also been extensively
used to support drug development decisions in the respiratory virus
space [18].
Nevertheless it is unknown what specific features of SARS-CoV-2
infection captured in the existing model relate to individual patient
outcome and also transmission of infection.
As such, we generated three key metrics for each simulation case: