Improved Continuous Approximation of PEPA Models through Epidemiological Examples

Citation

Benkirane S, Hillston J, McCaig C, Norman R & Shankland C (2009) Improved Continuous Approximation of PEPA Models through Epidemiological Examples. From Biology To Concurrency and back (FBTC 2008), A Satellite Workshop of ICALP 2008, 12.07.2008-12.07.2008. Electronic Notes in Theoretical Computer Science, 229 (1), pp. 59-74. https://doi.org/10.1016/j.entcs.2009.02.005

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).

Keywords
process algebra; systems biology; theoretical computer science; ODE generation; Parallel processing (Electronic computers); Electronic data processing Distributed processing; Disease Transmission; Epidemiology; Mathematical models

Journal
Electronic Notes in Theoretical Computer Science: Volume 229, Issue 1

People

Professor Rachel Norman

Chair in Food Security & Sustainability, Mathematics