System Dynamics from Individual Interactions: A process algebra approach to epidemiology
Lead Research Organisation:
University of Stirling
Department Name: Computing Science and Mathematics
Abstract
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.
Publications
Benkirane S
(2009)
Improved Continuous Approximation of PEPA Models through Epidemiological Examples
in Electronic Notes in Theoretical Computer Science
McCaig C
(2011)
From individuals to populations: A mean field semantics for process algebra
in Theoretical Computer Science
McCaig C
(2008)
Algebraic Biology
McCaig C
(2011)
A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology.
in Theory in biosciences = Theorie in den Biowissenschaften
McCaig C
(2013)
Using process algebra to develop predator-prey models of within-host parasite dynamics.
in Journal of theoretical biology
McCaig C
(2009)
From Individuals to Populations: A Symbolic Process Algebra Approach to Epidemiology
in Mathematics in Computer Science
McCaig C
(2011)
A symbolic investigation of superspreaders.
in Bulletin of mathematical biology
Description | Disease can be viewed as a threat (e.g. epidemics such as swine flu) or as a tool (e.g. crop control). 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 feasible, 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 have been used to model diseases. The unique benefits of this approach are threefold. Firstly, experimentalists obtain data about disease largely from individuals. Using process algebra 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, thus obtaining the overall system dynamics for the disease spread. Thirdly, the system can be formally investigated to establish features of the system dynamics, allowing us to answer the sort of questions posed above. 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. During this project we have: Established a sound theoretical basis for extracting system dynamics from process algebra. This allows us to easily move from individual-based stochastic models to population-based deterministic models. Established features of modelling languages required for disease spread and other biological interactions. Developed useful process algebra based models of disease spread. Most have been models exploring particular features of disease transmission in a population. For example: fluctuating populations (through births, deaths and migration), control (such as vaccination and quarantine), and contest between individuals for resources. 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. Classified the ways in which individuals interact and how this affects transmission. Customised models to fit particular diseases: HIV, bubonic plague in prairie dogs, and measles in the UK population. Translated our work in epidemiology to computer applications and to immunology. Disseminated our results widely, through publication, and also through a workshop run at Stirling in 2010. Our group is the foremost in the world in the application of process algebra to disease spread. The System Dynamics project has allowed us to put our work on a firm technical footing, producing an approach to modelling and analysing biological systems that is more flexible and well understood in terms of individual behaviour than current approaches. We are now in a position to consider more complex epidemiological phenomena in the setting of particular disease, and to use models to drive treatment and policy decisions. |
Exploitation Route | There are potential uses in public health policy making, where modelling a range of outcomes before making a decision is important. The work may be used to develop models of disease spread, which may be used to inform treatment of disease, and policy decisions. Note that the approach would have to be customised to the particular disease under investigation first: the models created during this project were mainly idealised benchmark studies. |
Sectors | Digital/Communication/Information Technologies (including Software),Healthcare |
URL | http://www.cs.stir.ac.uk/~ces/SystemDynamics/ |
Description | Carnegie Trust Research Grant |
Amount | £1,510 (GBP) |
Organisation | Carnegie Trust |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 04/2012 |
End | 06/2012 |
Description | Carnegie Trust Undergraduate Research Bursary |
Amount | £720 (GBP) |
Organisation | Carnegie Trust |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 07/2012 |
End | 08/2012 |
Description | Carnegie Trust Undergraduate Research Bursary |
Amount | £720 (GBP) |
Organisation | Carnegie Trust |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 07/2010 |
End | 08/2010 |
Description | The Wellcome Trust Undergraduate Research Bursary |
Amount | £1,440 (GBP) |
Organisation | Wellcome Trust |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 07/2009 |
End | 08/2009 |
Description | University of Stirling |
Amount | £19,414 (GBP) |
Funding ID | internal/no reference |
Organisation | University of Stirling |
Sector | Academic/University |
Country | United Kingdom |
Start | 07/2009 |
End | 12/2009 |
Description | Graham @ Princeton |
Organisation | Princeton University |
Country | United States |
Sector | Academic/University |
PI Contribution | Research visit in 2012 to work on cast study in immunology |
Collaborator Contribution | Hosting visit, work on resulting paper |
Impact | D. Marco, E. Scott, D. Cairns, A. Graham, J. Allen, S. Mahajan, and C. Shankland. Investigating Co-infection Dynamics through Evolution of Bio-PEPA Model Parameters: A Combined Process Algebra and Evolutionary Computing Approach. In proceedings of Computational Methods in Systems Biology (CMSB 2012), D. Gilbert and M. Heiner (Eds.), LNCS 7605, pp. 227-246, Springer 2012. Computing Science, Biology/Immunology |
Start Year | 2010 |