From individuals to populations

a symbolic process algebra approach to epidemiology.

Chris McCaig, R. Norman, C. Shankland

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)535-556
Number of pages22
JournalMathematics in Computer Science
Volume2
Issue number3
DOIs
Publication statusPublished - 1 Mar 2009

Fingerprint

Epidemiology
Process Algebra
Algebra
Mean Field Equation
Population Growth
Population Dynamics
Population dynamics
Individual-based Model
Rewriting
System Dynamics
Stochastic Model
Ordinary differential equation
Express
Stochastic models
Ordinary differential equations
Model
Dynamical systems
Alternatives
Evaluation

Keywords

  • process algebra
  • population dynamics
  • epidemiology
  • mean field equations
  • symbolic computation

Cite this

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From individuals to populations : a symbolic process algebra approach to epidemiology. / McCaig, Chris; Norman, R.; Shankland, C.

In: Mathematics in Computer Science, Vol. 2, No. 3, 01.03.2009, p. 535-556.

Research output: Contribution to journalArticle

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AU - Norman, R.

AU - Shankland, C.

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KW - population dynamics

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