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Duration of a Time Step (
Δt
):
The stability criterion for the finite difference
approximation to the diffusion equation presented in (4) requires that
(
Δx
)
2
4
D
V
Δt
≤
,
(5)
which is a more stringent requirement for larger values of
D
V
or smaller values
of
Δx
.Weuse
Δx
=11
µ
m which is the diameter of lung epithelial cells, and
10
−
15
m
2
s
−
1
D
V
=3
.
18
×
·
such that in order to satisfy the stability criterion,
we need
Δt
2
.
6 h. We found that setting
Δt
= 2 min satisfies the stability
criterion of the diffusion equation and accurately captures thebehaviourofthe
system.
≤
Virion Release Rate (
g
V
):
As seen above,
τ
r
= 7 h after becoming infected,
an epithelial cell will start secreting virions. In the model, secreting cells release
virions at a constant rate until the cell is considered “dead”, at which time
secretion is instantaneously stopped. This “shape” for the viral burst was chosen
arbitrarily as very little is known about the shape, duration, and magnitude of
the viral burst. We found that setting the release rate of virions by secreting
cells to
g
V
=0
.
05 virions per hour per secreting cell in our ABM yields a good
fit of the simulation to the experimental data.
3.3
Setting Up the Model
The infection of the epithelial cell monolayer with influenza virions in our in
vitro experiments proceeds as follows. An inoculum containing 50
,
000 competent
virions (or 50
,
000 plaque forming unit or pfu) is deposited evenly on the cell
monolayer. The solution is left there for one hour to permit the infection of the
cells and at time
t
= 0 h, the inoculum is harvested with a pipette. At that
time, not all the virions are removed: some are trapped in the mucus and get
left behind.
To avoid having to model the initial experimental manipulations and the
uncertainty in the viral removal, we start the ABM simulations at time
t
=2h
post-harvest. At that time, a fraction of cells have been infected by the inoculum
and a few virions have been left behind at harvest-time. To account for this fact,
we define two more parameters,
V
0
and
C
0
, which give the number of virions
per cell and the fraction of cells in the containing stage at time
t
=2hpost-
harvest, the initialization time of our simulations. In order to determine the
number of virions per cell, we also defined
N
cells
, the number of epithelial cells
in the experimental well. Parameters
N
cells
,
V
0
and
C
0
were set as follows.
Number of Epithelial Cells in the Experimental Well. (
N
cells
):
We
computed
N
cells
, the number of epithelial cells in the experimental well using the
measured diameter of the epithelial cells,
Δx
=11
m,andtheknownareaofthe
experimental well,
A
well
= 113 mm
2
. Assuming that the sum of the surface area
µ
