2,365 research outputs found

    A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology

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    Changing scale, for example the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interaction

    From Individuals to Populations: A Symbolic Process Algebra Approach to Epidemiology

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    Is it possible to symbolically express and analyse an individual-based model of disease spread, including realistic population dynamics? This problem is addressed through the use of process algebra and a novel method for transforming process algebra into Mean Field Equations. A number of stochastic models of population growth are presented, exploring different representations based on alternative views of individual behaviour. The overall population dynamics in terms of mean field equations are derived using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. The utility of our approach for epidemiology is confirmed by constructing a model combining population growth with disease spread and fitting it to data on HIV in the UK population

    Process Algebra Models of Population Dynamics

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    It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread

    Deriving Mean Field Equations from Large Process Algebra Models

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    In many domain areas the behaviour of a system can be described at two levels: the behaviour of individual components, and the behaviour of the system as a whole. Often deriving one from the other is impossible, or at least intractable, especially when realistically large systems are considered. Here we present a rigorous algorithm which, given an individual based model in the process algebra WSCCS describing the components of a system and the way they interact, can produce a system of mean field equations which describe the mean behaviour of the system as a whole. This transformation circumvents the state explosion problem, allowing us to handle systems of any size by providing an approximation of the system behaviour. From the mean field equations we can investigate the transient dynamics of the system. This approach was motivated by problems in biological systems, but is applicable to distributed systems in general

    From individuals to populations: changing scale in process algebra models of biological systems

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    The problem of changing scale in models of a system is relevant in many different fields. In this thesis we investigate the problem in models of biological systems, particularly infectious disease spread and population dynamics. We investigate this problem using the process algebra \emph{Weighted Synchronous Calculus of Communicating Systems} (WSCCS). In WSCCS we can describe the different types of individual in a population and study the population by placing many of these individuals in parallel. We present an algorithm that allows us to rigorously derive mean field equations (MFE) describing the average change in the population. The algorithm takes into account the Markov chain semantics of WSCCS such that as the system being considered becomes larger, the approximation offered by the MFE tends towards the mean of the Markov chain. The traditional approach to developing population level equations of a system involves making assumptions about the behaviour of the entire population. Our approach means that the population level dynamics explained by the MFE are a direct consequence of the behaviour of individuals, which is more readily observed and measured than the behaviour of the population. In this way we develop MFE models of several different systems and compare the equations obtained to the traditional mathematical models of the system

    Decision Support Based on Bio-PEPA Modeling and Decision Tree Induction: A New Approach, Applied to a Tuberculosis Case Study

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    The problem of selecting determinant features generating appropriate model structure is a challenge in epidemiological modelling. Disease spread is highly complex, and experts develop their understanding of its dynamic over years. There is an increasing variety and volume of epidemiological data which adds to the potential confusion. We propose here to make use of that data to better understand disease systems. Decision tree techniques have been extensively used to extract pertinent information and improve decision making. In this paper, we propose an innovative structured approach combining decision tree induction with Bio-PEPA computational modelling, and illustrate the approach through application to tuberculosis. By using decision tree induction, the enhanced Bio-PEPA model shows considerable improvement over the initial model with regard to the simulated results matching observed data. The key finding is that the developer expresses a realistic predictive model using relevant features, thus considering this approach as decision support, empowers the epidemiologist in his policy decision making

    Using process algebra to develop predator-prey models of within-host parasite dynamics

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    As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system
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