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first virus and release of the first produced virus), and the proportion of produc-
tively infectious virions, is either uncorroborated, unknown, or known with poor
precision. This makes modeling influenza from data available in the literature
a near impossibility, and it points to the need for generating experimental data
aimed directly at the needs of both computational and mathematical models.
This paper describes the computer modeling side of a project that is integrat-
ing in vitro experiments with computer modeling to address this problem. We are
focusing on the early dynamics of influenza infection in a human airway epithe-
lial cell monolayer using both in vitro and computer models. The in vitro model
uses primary human differentiated lung epithelial cells grown in an air-liquid
interface (ALI) culture to document the kinetics of influenza spread in tissue.
The computer model consists of an agent-based model (ABM) implementation
of the in vitro system. Its architecture is modular so that more details can be
added whenever data from the in vitro system justifies it. Here, we will describe
the implementation of the computer model and report some initial simulation
results.
To our knowledge, only four mathematical models for influenza dynamics have
ever been proposed. The first and oldest one is from 1976 and consists of a very
basic compartmental model for influenza in experimentally infected mice [8]. Af-
ter a gap of 18 years, Bocharov et al. proposed an exhaustive ordinary differential
equation model based on the basic viral infection model but extended to include
12 different cell populations described by 60 parameters [9]. More recently, one of
us co-authored a paper presenting another ordinary differential equation model
with very slight modifications from the basic viral infection model [10] and a
second paper presenting a simple ABM for influenza [11]. All of these models
either perform poorly when compared to experimental data or are too simplistic
to capture the dynamics of interest in influenza.
2
Agent-Based Modeling
The spatial distribution of agents is an important and often neglected aspect of
influenza dynamics. We capture spatial dynamics through the use of an agent-
based model (also known as an individual-based) cellular automata style model.
Each epithelial cell in the monolayer is represented explicitly, and a computer
program encodes the cell's behavior and rules for interacting with other cells and
its environment. The cells live on a hexagonal lattice and interact locally with
other cells and virions in their neighborhood following a set of predefined rules.
Thus, the behavior of the low-level entities is pre-specified, and the simulation
is run to observe high-level behaviors (e.g. to determine an epidemic threshold).
This style of modeling emphasizes local interactions, and those interactions in
turn give rise to the large-scale complex dynamics of interest.
This modeling approach can be more detailed than other approaches. The
programs can directly incorporate biological knowledge or hypotheses about
low-level components. Data from multiple experiments can be combined into
a single simulation, to test for consistency across experiments or to identify gaps
