Agent-Based Models and Optimal Control in Biology: A Discrete Approach - Mathematical Concepts and Methods in Modern Biology - page 148

using, for example, ordinary or partial differential equations (ODEs). Altering the
spatial dynamics of an agent-based model consists of changing several lines of code or
less, while such changes can be difficult (and perhaps even impossible) to implement
in an ODE model.
While agent-based models provide a convenient and natural setting for studying
complex systems, there are several issues within the research community that are
currently unresolved. A 2006 paper [ 8 ] written by a large group of researchers iden-
tified two main obstacles: the first is the lack of standardization of the description of
agent-based models, and the second is a lack of rigorous mathematical formulation of
the system itself. Descriptions of agent-based models can vary in different settings,
and as of this writing there is no standard definition that is universally agreed upon.
Some models are developed to simulate physical processes, and others are developed
in the framework of graph theory. In some cases models are developed in order to
study only a certain aspect of the given system; thus the model may have more vari-
ables pertaining to certain processes than others. A research article may begin with
the statement of an objective, or it may begin with a description of the model itself. In
some cases, the rules that govern the updating of the agents' state variables are deter-
ministic, and in other cases they are stochastic. All of these issues would be resolved
if there was a standard protocol for describing agent-based models (indeed, one such
protocol is proposed in [ 8 ]). The need for an agreed-upon structure to be followed
is perhaps most clearly felt in the model's presentation. In particular, the layout of
the model presentation ought to be standardized so that a reader immediately knows
where to look in the description in order to learn what the model describes and what
its rules are. In the current literature models are presented in myriad forms, and the
descriptions of the agents, environments, and rules come in no particular order. Thus
a reader is required to scour the paper for pertinent details that might otherwise be
presented in some standard way.
The second major issue concerns the lack of rigor in the formulation of the model.
In many cases, the description of a model is given in several paragraphs, describing
in some imprecise manner what the agents are and how they interact with each other.
In fact, in order for agent-based models to be implemented on computer software,
there are intricate rules embedded in the programming of the models. These rules
and equations are often glossed over if not entirely omitted; if they are given, it is
typically through a verbal description rather than a strict mathematical formulation.
Looking back on the example in Section 5.2 , the precise way in which the rabbits
move is not described. For example, it is unclear from a simple description whether
the rabbits can move diagonally, or whether the distance they move at each time step is
variable or constant. In fact, even running the model does not immediately answer this
question—it is only made explicitly clear by thorough examination of the computer
code. In order to describe such a model rigorously, it is necessary that this information
(and other similarly imprecise descriptions) be presented clearly and unambiguously.
In addition to these issues, an author may spend several paragraphs explaining
how the model was formulated that could just have easily been given in one or two
equations. Short and precise definitions can save time for the reader and also make the