Studying the effects of adding spatiality to a process algebra model

Citation

Maharaj S, McCaig C & Shankland C (2009) Studying the effects of adding spatiality to a process algebra model. In: Clark A & Guerriero M (eds.) 8th Workshop on Process Algebra and Stochastically Timed Activities: PASTA 2009. 8th Workshop on Process Algebra and Stochastically Timed Activities (PASTA 2009): Edinburgh, UK, Edinburgh, 26.08.2009-26.08.2009. Edinburgh, UK: University of Edinburgh, pp. 153-158. http://www.dcs.ed.ac.uk/pepa/group/pastaworkshop/PASTA09/proceedings.pdf

Abstract
We use NetLogo to create simulations of two models of disease transmission originally expressed in WSCCS. This allows us to introduce spatiality into the models and explore the consequences of having different contact structures among the agents. In previous work, mean field equations were derived from the WSCCS models, giving a description of the aggregate behaviour of the overall population of agents. These results turned out to differ from results obtained by another team using cellular automata models, which differ from process algebra by being inherently spatial. By using NetLogo we are able to explore whether spatiality, and resulting differences in the contact structures in the two kinds of models, are the reason for this different results. Our tentative conclusions, based at this point on informal observations of simulation results, are that space does indeed make a big difference. If space is ignored and individuals are allowed to mix randomly, then the simulations yield results that closely match the mean field equations, and consequently also match the associated global transmission terms (explained below). At the opposite extreme, if individuals can only contact their immediate neighbours, the simulation results are very different from the mean field equations (and also do not match the global transmission terms). These results are not surprising, and are consistent with other cellular automata-based approaches. We found that it was easy and convenient to implement and simulate the WSCCS models within NetLogo, and we recommend this approach to anyone wishing to explore the effects of introducing spatiality into a process algebra model.

Keywords
; Communicable diseases; Transmission Mathematical models