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Improved continuous approximation of PEPA models through epidemiological examples. (English) Zbl 1283.92064
Cannata, Nicola (ed.) et al., Proceedings of the 2nd workshop – from biology to concurrency and back (FBTC 2008), Reykjavik, Iceland, July 12, 2008. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 229, No. 1, 59-74 (2009).
Summary: 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).
For the entire collection see [Zbl 1278.92003].

MSC:
92D30 Epidemiology
34C60 Qualitative investigation and simulation of ordinary differential equation models
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
Software:
PEPA; ipc
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