title: A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology.
abstract: 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 interactions.
authors.affiliation: Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK. cmc@cs.stir.ac.uk
authors.forename: Chris
authors.initials: C
authors.lastname: McCaig
authors.forename: Mike
authors.initials: M
authors.lastname: Begon
authors.forename: Rachel
authors.initials: R
authors.lastname: Norman
authors.forename: Carron
authors.initials: C
authors.lastname: Shankland
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D003198:Computer Simulation; D004196:Disease Outbreaks; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D013269:Stochastic Processes
references.citation: Science. 2002 Mar 1;295(5560):1662-4
references.pmid: 11872829
references.citation: Oecologia. 2009 Aug;161(2):227-39
references.pmid: 19484269
references.citation: J Theor Biol. 2001 Jun 21;210(4):435-47
references.pmid: 11403564
references.citation: Math Biosci. 2008 Nov;216(1):56-62
references.pmid: 18783724
references.citation: Epidemiol Infect. 2002 Aug;129(1):147-53
references.pmid: 12211582
references.citation: Proc Biol Sci. 2001 May 7;268(1470):925-32
references.pmid: 11370965
references.citation: J Theor Biol. 1991 Dec 7;153(3):301-21
references.pmid: 1798335
references.citation: J Theor Biol. 2007 Nov 7;249(1):140-52
references.pmid: 17719608
references.citation: Am Nat. 2002 Jun;159(6):706-13
references.pmid: 18707391
references.citation: Proc Biol Sci. 2004 Jun 22;271(1545):1243-50
references.pmid: 15306348
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):036114
references.pmid: 15524594
references.citation: Theor Popul Biol. 2007 Mar;71(2):251-66
references.pmid: 17084872
references.citation: Pac Symp Biocomput. 2001;:459-70
references.pmid: 11262964
references.citation: Proc Biol Sci. 2003 Jan 7;270(1510):105-12
references.pmid: 12590777