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k, V
m,n
Containing
τ
r
Healthy
Dead
τ
d
± σ
d
Secreting
Infected
Fig. 1.
The agent-based model's four states for epithelial cells, (Healthy, Containing,
Secreting, and Dead), and the parameters responsible for controlling the transitions
between these states
that a healthy cell will become infected (enter the containing stage). In other
words,
k
V
m,n
gives the probability that the healthy cell located at site (
m, n
)
will become infected over the course of an hour. In order to fit experimental
data, we set the rate of infection of cells per virions in our model to
k
=8per
virion at that site per hour.
×
Duration of the Viral Replication Cycle (
τ
r
):
This variable represents the
time that elapses between entry of the first successful virion and release of the
first virion produced by the infected cell. From the experiments, we found this
to be about 7 h, and hence we set
τ
r
=7hintheABM.
Lifespan of Infectious Cells (
τ
d
±
σ
d
):
Once infected (containing), a cell
typically lives 24 h-36 h (from experimental observations). Given that the repli-
cation cycle lasts
τ
r
= 7 h, this means that once it starts secreting virions, an
infectious cell typically lives 17 h-29 h or about 23
6 h. Thus, we set the lifes-
pan of each infected cell individually by picking it randomly from a Gaussian
distribution of mean
τ
d
= 23 h and standard deviation
σ
d
=6h.InourABM,
cell death is taken to mean the time at which cells cease to produce virions.
Note that in vitro, a cell undergoing apoptosis will eventually detach from the
monolayer and will be replaced by a differentiating basal cell. For the moment,
we neglect these processes and reduce their impact by fitting our ABM to ex-
perimental results over no more than the first 25 h after virion deposition.
±
3.2
Virion Dynamics
As mentioned earlier, virions are not represented explicitly. Instead, we track the
concentration of virions stored as a real-valued continuous variable at each site
of the lattice. The diffusion of virions is then modeled using a finite difference
approximation to the diffusion equation. The continuous diffusion equation of
the concentration of virions,
V
, is described by
∂V
∂t
2
V,
=
D
V
∇
(1)
