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1 results

  • 7 - SSAs for Reaction–Diffusion–Advection Processes

  • Radek Erban, University of Oxford, S. Jonathan Chapman, University of Oxford
  • Book:
    Stochastic Modelling of Reaction–Diffusion Processes
    Published online:
    04 November 2019
    Print publication:
    30 January 2020, pp 192-225

  • Summary

    This chapter shows how active transport (for example, by an electrical field, molecular and cellular motors, running, swimming or flying, all in response to external cues) can be incorporated into the stochastic diffusion and reaction–diffusion algorithms we have introduced in Chapters 4 and 6. The resulting stochastic diffusion–advection and reaction–diffusion–advection models are analysed. Applications include systems consisting of many interacting “particles”, where individual particles can range in size from small ions and molecules to individual cells and animals. Three examples illustrate this: mathematical modelling of ions and ion channels, modelling bacterial chemotaxis, and studying collective behaviour of social insects. The chapter concludes with the discussion of the Metropolis–Hastings algorithm, which can be used to compute stationary (equilibrium) properties of complicated diffusion–advection problems.