Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian (Boston University. Department of Mechanical Engineering)
Guerrero, Pilar (University College London. Department of Mathematics)
Alarcón Cor, Tomás (Centre de Recerca Matemàtica)
Maini, Philip K. (University of Oxford. Wolfson Centre for Mathematical Biology)
Byrne, Helen (University of Oxford. Wolfson Centre for Mathematical Biology)

Data:	2015
Resum:	Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i. e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Ajuts:	Ministerio de Ciencia e Innovación MTM2011-29342 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-345
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Reaction-diffusion system ; Stochastic model ; Hybrid model ; Fisher-Kolmogorov equation ; Lotka-Volterra equation
Publicat a:	Journal of computational physics, Vol. 299 (Oct. 2015) , p. 429-445, ISSN 0021-9991

DOI: 10.1016/j.jcp.2015.07.002
PMID: 26478601

17 p, 1.1 MB

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