Agent-Based Models and Optimal Control in Biology: A Discrete Approach - Mathematical Concepts and Methods in Modern Biology - page 147

In developing the best drug to administer to treat a particular disease, researchers in
the past have relied on trial-and-error methods via repeated experimentation on live
subjects. With an accurate model of the subject, however, such experiments can often
be faithfully reproduced in silico ; that is, they can be run on a computer and analyzed
with far less preparation and expense. This highlights another benefit to mathematical
modeling: given an accurate model of the system in question, a year's worth of real
time can be simulated in several minutes.
Experimentation remains part of the process - a model will always have a limited
ability to predict and must be correlated against empirical data in order to ensure that
the models are indeed faithful simulations of the actual physical system. Thus, models
are best used to inform in vivo experimentation, which in turn produces results that
can be used to calibrate the model further.
Agent-based models are a class of computer models in which entities (referred to
as agents) interact with each other and or their local environment. Formally:
Definition 5.1 (Agent-basedmodel). Acomputermodel that consists of a collection
of agents/variables that can take on a typically finite collection of states. The state
of an agent at a given point in time is determined through a collection of rules that
describe the agent's interaction with other agents. These rules may be deterministic
or stochastic. The agent's state depends on the agent's previous state and the state of
a collection of other agents with whom it interacts. [ 7 ]
Systems (such as the human immune system) are increasingly being implemented
in the form of agent-based models (with individual cells as the agents, of which there
may be many types) as more and more research involves the use of in silico simulation
to study the properties of this and other similarly complex systems.
Agent-based models have the advantage of being well suited for modeling many
different types of systems. They have been used to study social interactions among
individuals, the spread of disease through populations, scheduling and efficiency of
factory processes, how cells react to drug treatments, and many other systems. It is
perhaps worth noting that many of the current issues in the scientific community
are interdisciplinary. Finding a cure for cancer will involve geneticists, biologists,
mathematicians, chemists, and perhaps many other specialists. Agent-based models
have an intuitive formulation and can often be examined via a graphical interface. Thus
they are a natural tool for promoting interdisciplinary research, as the mathematics
underlying the models is hidden in the programming; in other words, it is possible for
biologists, chemists, and other researchers to make use of agent-based models without
a full background in the mathematics that are involved in creation and analysis of the
model. At the same time, the mathematical structure remains and can be explored
concurrently by mathematicians.
Even within the scope of mathematical modeling, there are several noteworthy
advantages to agent-based modeling. One such advantage is that they are effective
for modeling systems wherein many agents follow the same set of rules (e.g., rabbit
populations or blood cell types). In particular, models containing spatial heterogeneity
can be effectively represented via agent-based models while perhaps not so easily