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Improved Continuous Approximation of PEPA Models through Epidemiological Examples

Authors
Journal
Electronic Notes in Theoretical Computer Science
1571-0661
Publisher
Elsevier
Publication Date
Volume
229
Issue
1
Identifiers
DOI: 10.1016/j.entcs.2009.02.005
Keywords
  • Pepa
  • Process Algebra
  • Changing Scale
  • Individual Based Model
  • Population Based Model
Disciplines
  • Mathematics
  • Medicine

Abstract

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).

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