  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. 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.
