Abstract
We demonstrate the use of the process algebra PEPA for realistic models of epidemiology. The results of stochastic simulation of the model are shown, and ease of modelling is compared to that of Bio-PEPA. PEPA is shown to be capable of capturing the complex disease dynamics of the historic data for measles epidemics in the UK from 1944–1964, including persistent fluctuations due to seasonal effects.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, R.M., May, R.M.: The population-dynamics of micro-parasites and their invertebrate hosts. Philosophical Transactions of the Royal Society of London Series B 291, 451–524 (1981)
Benkirane, S.: Process algebra for epidemiology: evaluating and enhancing the ability of PEPA to describe biological systems. Ph.D. thesis, University of Stirling (2011), http://hdl.handle.net/1893/3603
Benkirane, S., Hillston, J., McCaig, C., Norman, R., Shankland, C.: Improved Continuous Approximation of PEPA Models through Epidemiological Examples. In: From Biology to Concurrency and Back, FBTC 2008. ENTCS, vol. 229, pp. 59–74. Elsevier (2008)
Bjørnstad, O.N., Finkenstädt, B.F., Grenfell, B.T.: Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model. Ecological Monographs 72(2), 169–184 (2002)
Bolker, B., Grenfell, B.: Space, persistence and dynamics of measles epidemics. Philosophical Transactions of the Royal Society of London - Series B: Biological Sciences 348(1325), 309–320 (1995)
Ciocchetta, F., Hillston, J.: Bio-PEPA: A framework for the modelling and analysis of biological systems. Theor. Comput. Sci. 410(33-34), 3065–3084 (2009)
Ciocchetta, F., Hillston, J.: Bio-PEPA for epidemiological models. Electronic Notes in Theoretical Computer Science 261, 43–69 (2010); Proceedings of Practical Application of Stochastic Modelling (PASM 2009)
Duguid, A., Gilmore, S., Guerriero, M.L., Hillston, J., Loewe, L.: Design and development of software tools for Bio-PEPA. In: Proc. of Winter Simulation Conference 2009, pp. 956–967 (2009)
Duke, T., Mgone, C.S.: Measles: not just another viral exanthem. The Lancet 361, 763–773 (2003)
Durrett, R.: Probability: Theory and Examples. Cambridge Series in Statistical and Probabilistic Mathematics (2010)
Fine, P.E., Clarkson, J.A.: Measles in England and Wales–I: An analysis of factors underlying seasonal patterns. Int. Journal of Epidemiology 11(1), 5–14 (1982)
Finkenstädt, B.F., Keeling, M., Grenfell, B.T.: Patterns of density dependence in measles dynamics. Proceedings of the Royal Society B 265, 753–762 (1998)
Gilmore, S., Tribastone, M., Duguid, A., Clark, A.: PEPA plug-in for eclipse (2008), homepages.inf.ed.ac.uk/mtribast/plugin/
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press (1996)
Hillston, J.: Tuning systems: From composition to performance. The Computer Journal 48(4), 385–400 (2005); The Needham Lecture Paper
Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics. Proceedings of the Royal Society of London A 115, 700–721 (1927)
McCaig, C., Begon, M., Norman, R., Shankland, C.: A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology. Theory in Biosciences 130, 19–29 (2011); special issue on emerging modelling methodologies
McCaig, C., Norman, R., Shankland, C.: From individuals to populations: A symbolic process algebra approach to epidemiology. Mathematics in Computer Science 2(3), 139–155 (2009)
McCaig, C.: From individuals to populations: changing scale in process algebra models of biological systems. Ph.D. thesis, University of Stirling (2008), http://hdl.handle.net/1893/398
Miller, D.L.: Frequency of complications of measles, 1963. British Medical Journal 2, 75–78 (1964)
Norman, R., Shankland, C.: Developing the Use of Process Algebra in the Derivation and Analysis of Mathematical Models of Infectious Disease. In: Moreno-Díaz Jr., R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 404–414. Springer, Heidelberg (2003)
Perry, R., Halsey, N.: The clinical significance of measles: A review. Journal of Infectious Diseases 189(1), S4–S16 (2004)
The Medical News: Measles history, http://www.news-medical.net/health/Measles-History.aspx
Tofts, C.: Processes with probabilities, priority and time. Formal Aspects of Computing 6, 536–564 (1994)
University of Cambridge: Pathogen population dynamics (2002), http://www.zoo.cam.ac.uk/zoostaff/grenfell/measles.htm
World Health Organization: The world health report 2004 (2004), http://www.who.int/whr/2004/annex/topic/en/annex_2_en.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benkirane, S., Norman, R., Scott, E., Shankland, C. (2012). Measles Epidemics and PEPA: An Exploration of Historic Disease Dynamics Using Process Algebra. In: Giannakopoulou, D., Méry, D. (eds) FM 2012: Formal Methods. FM 2012. Lecture Notes in Computer Science, vol 7436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32759-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-32759-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32758-2
Online ISBN: 978-3-642-32759-9
eBook Packages: Computer ScienceComputer Science (R0)