Hybrid approaches for multiple-species stochastic reaction-diffusion models

Research output: Contribution to journalArticle

Authors

  • Fabian Spill
  • Pilar Guerrero
  • Tomas Alarcon
  • Philip K. Maini
  • Helen Byrne

Colleges, School and Institutes

External organisations

  • MASSACHUSETTS INSTITUTE OF TECHNOLOGY
  • UCL
  • Centre de Recerca Matematica
  • OXFORD UNIVERSITY

Abstract

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.

Details

Original languageEnglish
Pages (from-to)429-445
Number of pages17
JournalJournal of Computational Physics
Volume299
Publication statusPublished - 5 Oct 2015

Keywords

  • Fisher-Kolmogorov equation, Hybrid model, Lotka-Volterra equation, Reaction-diffusion system, Stochastic model, Monte Carlo (MC) simulation, Optimization