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System Dynamics from Individual Interactions: A Process Algebra Approach
to Epidemiology
Disease can be viewed as a threat or as a tool. Modern society has
become vulnerable to wide spreading epidemics,
but we also use diseases to control pests in crops as a way of avoiding
the use of chemicals. Clearly it is important to
be able to understand the way the epidemic works: How much of the
population will be infected? Does the behaviour of
individuals change the spread of the disease? How long will it take
before the disease dies out? What is the most
effective way to control the disease?
Testing experimentally is not an option: there are ethical problems with
infecting people with diseases just to see what
happens, therefore we use mathematical models. These help us predict
the shape of epidemics and to evaluate
methods of control. In this project theoretical computer science
techniques known as process algebras will be used to
model diseases. The unique benefits of this approach are threefold.
Firstly, it is possible to describe the behaviour of
individuals directly. Secondly, those individuals can be rigorously
combined to give the behaviour of the system as a
whole. Thirdly, the system can be formally investigated to establish
features of the system dynamics, allowing us to
answer the sort of questions posed above. This approach, known as
individual-based, is particularly important because
in reality we can measure facts about individuals, but our questions
about epidemics all come from the population level.
The ability to move rigorously between different levels of abstraction
(individual to population) when describing disease
spread gives us completely new ways of thinking about epidemiology.
Our group is the foremost in the world in this work, but we are at the
start of a long term research programme. Having
built up domain expertise and techniques and tools for describing and
investigating simple disease systems in previous
work, we are now in a position to consider more complex epidemiological
phenomena, the particular modelling features
required for these, and further methods of investigation.
In this project we will build and investigate process algebra models of
specific biological features associated with
epidemiology. These are: fluctuating populations (Adding births and
deaths), interaction and transmission (If I sneeze
on you, will you get my flu? What about the others in the room?),
control (How many of the population need to be
vaccinated to protect the whole population from the disease?), and
contest between individuals (If I don't have enough
food will that make me more susceptible to disease?). These features
have been chosen as core to the representation
of population and epidemiological models and together give a more
realistic and rounded model of disease.
Exploration of more complex biological systems will require more complex
models. Process algebra is expressive
enough to describe these systems; however, such descriptions may be
clumsy and hard to understand. We will develop
new language constructs to allow population models to be more simply
expressed, yielding more easily constructed and
understood models. Once the model is constructed we have a range of
formal techniques to investigate its behaviour,
and to compare with other existing models in the literature. We will
develop those investigative techniques further,
based on the needs of epidemiological systems.
Finally, although we will concentrate on epidemiology, the features and
techniques developed will be applicable to other
areas of biology, and to computer science. For example, instead of
viewing an individual as a person or an animal, we
could view an individual as a single cell or a complex molecule. In the
computer science arena, we can use
epidemiological models to think about performance modelling, and also
malware (computer viruses, worms etc). This
general applicability makes our work particularly exciting.
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