Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/398
 Appears in Collections: Computing Science and Mathematics eTheses Title: From individuals to populations: changing scale in process algebra models of biological systems Authors: McCaig, Chris Supervisor(s): Shankland, CarronNorman, Rachel A. Keywords: Process algebraChanging scaleEpidemicModels Issue Date: Oct-2007 Publisher: University of Stirling Abstract: 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. Type: Thesis or Dissertation URI: http://hdl.handle.net/1893/398 Affiliation: School of Natural SciencesComputing Science and Mathematics

Files in This Item:
File Description SizeFormat