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Editorial: Special issue on stochastic modelling of reaction-diffusion processes in biology. (English) Zbl 1296.00033

From the text: Reaction-diffusion equations are used to model many biological processes, ranging from intracellular signaling, metabolic processes and gene control at the cellular level, to birth-death processes and random movement at the organism and population levels. There are two fundamental approaches to the mathematical modelling of these processes: deterministic (mean-field) models which lead to partial differential equations for concentrations of biochemical species or for densities of individuals, and stochastic models in which individual events of reaction or diffusion are followed. In some cases – such as linear processes or pure reaction processes based on mass action kinetics – one can prove that the latter description converges to the former in an appropriate ‘large-number limit’, but this is still an open question in general, as some of the papers herein illustrate.

MSC:

00B15 Collections of articles of miscellaneous specific interest
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
60-06 Proceedings, conferences, collections, etc. pertaining to probability theory
92-06 Proceedings, conferences, collections, etc. pertaining to biology
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Software:

MCELL; MesoRD; URDME
PDFBibTeX XMLCite
Full Text: DOI

References:

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