Improved continuous approximation of PEPA models through epidemiological examples

Benkirane, S. and Hilston, J. and McCaig, Chris and Norman, R. and Shankland, C. (2009) Improved continuous approximation of PEPA models through epidemiological examples. Electronic Notes in Theoretical Computer Science, 229 (1). 59–74. ISSN 1571-0661

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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).