Biology Reference
In-Depth Information
The chapter is organized as follows. The first section charts the uses of
mathematical models and types of model described in the literature to
date and key insights from these models. The second section outlines the
basic structure of a deterministic model and the properties that arise from
a simple hybrid structure in which the distribution of worm numbers per
person is treated as a probability distribution within deterministic
framework. This model is then extended to include age structure. The
third section outlines a set of key questions that arise in furthering our
understanding of the transmission dynamics of the parasite and its
control at a population level by various forms of community-based
treatment and how models can currently be used to address them. The
concluding section summarizes future needs in model development,
parameter estimation, comparison of prediction and observation, and
data capture in the modern age of web-based databases.
WHAT A
RE MATHEMATICAL MODELS U
SED FOR?
Mathematics provides a universal language which gives precision to
the description of pattern and process in the world around us. It also
provides a set of approaches or tools to help in analyzing pattern and
process. This applies equally in both the physical and biological worlds.
The use of mathematical methods has until recently been much more
common in the physical and chemical sciences and engineering. Biology
and medicine by contrast have remained disciplines where description
and observation dominate without the use of formal mathematical tools to
assess whether a hypothesis is indeed capable of generating the patterns
and processes observed. In part this is to be expected given the very
multivariate nature of many biological problems and the complex
nonlinear systems that dominate the organization and functioning of
living organisms. The arguments against using simplified mathematical
representations of complex biological processes hinge on the following
observation: how can a crude simplification capture the known
complexity of real biological systems? The counterarguments are many
and varied, but center on two key issues. First, it is often the case that
a few processes dominate outcome or observed pattern, even in very
complex systems. It is better to explore systematically how each indi-
vidual process, when added to the model step by step, affects outcome.
Second, in very complex systems, without some sort of formal represen-
tation and defined tools of analysis, rarely (if at all) will it be possible to
understand how each process, variable or parameter influences observed
pattern. The human immune system is a good example. With an ever-
expanding list of cell types and chemical entities for communication
between cells involved in even the simplest immune response, the range
