Improved Continuous Approximation of PEPA Models through Epidemiological Examples

  • Authors:

  • Soufiene Benkirane;Jane Hillston;Chris McCaig;Rachel Norman;Carron Shankland

  • Affiliations:

  • Department of Computing Science and Mathematics, University of Stirling, UK;School of Informatics, University of Edinburgh, UK;Department of Computing Science and Mathematics, University of Stirling, UK;Department of Computing Science and Mathematics, University of Stirling, UK;Department of Computing Science and Mathematics, University of Stirling, UK

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

We present two individual based models of disease systems using PEPA (Performance Evaluation Process Algebra). The models explore contrasting mechanisms of disease transmission: direct transmission (e.g. measles) and indirect transmission (e.g. malaria, via mosquitos). We extract ordinary differential equations (ODEs) as a continuous approximation to the PEPA models using the Hillston method and compare these with the traditionally used ODE disease models and with the results of stochastic simulation. Improvements to the Hillston method of ODE extraction for this context are proposed, and the new results compare favourably with stochastic simulation results and to ODEs derived for equivalent models in WSCCS (Weighted Synchronous Calculus of Communicating Systems).