From individuals to populations: A mean field semantics for process algebra

McCaig, Chris; Norman, Rachel; Shankland, Carron

doi:10.1016/j.tcs.2010.09.024

Cited by 14 publications

(24 citation statements)

References 27 publications

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“…Algebraic rules are applied to the WSCCS syntax of the model to obtain a set of first-order difference equations expressing the average behaviour of the model. This is an approximation to the original transition-based semantics, but has been shown to be a close match with average results obtained from repeated simulations of the transition-based semantics [26]. There are four benefits to this approach.…”

Section: Deriving Mean Field Equationssupporting

confidence: 59%

“…In recent years, the analysis of process algebra models by fluid flow approximation [15,20,26,28] has become popular, i.e. rigorous derivation of population-level system dynamics, in the form of mean field equations or ordinary differential equations, from the individual-based process algebra model.…”

Section: Process Algebramentioning

confidence: 99%

“…McCaig et al [26] described a method to automatically derive mean field equations (MFEs) from WSCCS models. The translation is based on analysis of the potential actions of each agent in the context of the whole population, producing a term in the MFEs capturing change in the number of that agent.…”

Section: Process Algebramentioning

confidence: 99%

“…For WSCCS McCaig et al [26] presented an alternative and equivalent semantics is given for WSCCS in terms of Mean Field Equations. Algebraic rules are applied to the WSCCS syntax of the model to obtain a set of first-order difference equations expressing the average behaviour of the model.…”

Section: Deriving Mean Field Equationsmentioning

confidence: 99%

“…In particular the process algebra Weighted Synchronous Calculus of Communicating Systems (WSCCS) [37] has proven useful in studying a wide range of biological systems [19,28,27,29,35,36]. Our group has established a rigorous method for deriving equations to describe the mean behaviour of an infectious disease system as a whole [28,26]. This approach allows us to combine the benefits of ODEs and stochastic simulations.…”

Section: Introductionmentioning

confidence: 99%

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

McCaig

Fenton

Graham

et al. 2013

Journal of Theoretical Biology

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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 immunemediated 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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Section: Deriving Mean Field Equationssupporting

confidence: 59%

Section: Process Algebramentioning

confidence: 99%

Section: Process Algebramentioning

confidence: 99%

Section: Deriving Mean Field Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

McCaig

Fenton

Graham

et al. 2013

Journal of Theoretical Biology

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Process Ordering in a Process Calculus for Spatially-Explicit Ecological Models

Philippou

Toro

2014

Software Engineering and Formal Methods

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