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in our knowledge. Through its functional specifications of cell behavior, our can
potentially bridge the current gap between intracellular descriptions and infec-
tion dynamics models. Similar approaches have been used to model a variety
of host-pathogen systems ranging from general immune system simulation plat-
forms [12,13,14,15,16] to models of specific diseases including tuberculosis [17,18],
Alzheimer's disease [19], cancer [20,21,22,23,24,25], and HIV [26,27].
The spatially explicit agent-based approach is an appropriate method for this
project. The ALI is a complex biological system in which many different defenses
(e.g. mucus, cytokines) interact and biologically relevant values cannot always
be measured directly. In addition, recent high-profile publications have demon-
strated that entry of avian and human-adapted influenza viruses into different
airway epithelial cells depends on the cell receptor which in turn is dependent on
cell type and location in the airway [28,29]. Our modeling approach will facilitate
the exploration of spatially heterogeneous populations of cells.
3
Influenza Model
Our current model is extremely simple. We plan to gradually add more detail,
ensuring at each step that the additions are justified by our experimental data.
Here, we describe the model as it is currently implemented.
We are modeling influenza dynamics on an epithelial cell monolayer in vitro.
The monolayer is represented as a two-dimensional hexagonal lattice where each
site represents one epithelial cell. The spread of the infection is modeled by
including virions. Rather than treat each virion explicitly, the model instead
considers the concentration of virions by associating a continuous real-valued
variable with each lattice site, which stores the local concentration of virions
at that site. These local concentrations are then allowed to change, following a
discretized version of the diffusion equation with a production term. The rules
governing epithelial cell and virion concentration dynamics are described below.
3.1
Epithelial Cell Dynamics
The epithelial cells can be found in any of the four states shown in Fig. 1, namely
healthy, containing, secreting, and dead. For simplicity, we assume that there is
no cell division or differentiation over the course of the infection. The parameters
responsible for the transition between these states are as follows.
Infection of Epithelial Cells by Virions (
k
):
Each site keeps track of the
number of virions local to the site,
V
m,n
. But while there are
V
m,n
virions at site
(
m, n
) at a given time step, depending on the length of a time step, not all of these
virions necessarily come in contact with the cell, and some may contact it more
than once. Alternatively, a particular strain of virions may not be as successful
at binding the cell's receptors and being absorbed by the cell. To reflect this real-
ity, we introduce the parameter
k
which gives the probability per hour per virion
