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.