  The simulation of stochastic reaction-diffusion systems using fine-grained
representations can become computationally prohibitive when particle numbers
become large. If particle numbers are sufficiently high then it may be possible
to ignore stochastic fluctuations and use a more efficient coarse-grained
simulation approach. Nevertheless, for multiscale systems which exhibit
significant spatial variation in concentration, a coarse-grained approach may
not be appropriate throughout the simulation domain. Such scenarios suggest a
hybrid paradigm in which a computationally cheap, coarse-grained model is
coupled to a more expensive, but more detailed fine-grained model enabling the
accurate simulation of the fine-scale dynamics at a reasonable computational
cost.
  In this paper, in order to couple two representations of reaction-diffusion
at distinct spatial scales, we allow them to overlap in a "blending region".
Both modelling paradigms provide a valid representation of the particle density
in this region. From one end of the blending region to the other, control of
the implementation of diffusion is passed from one modelling paradigm to
another through the use of complementary "blending functions" which scale up or
down the contribution of each model to the overall diffusion. We establish the
reliability of our novel hybrid paradigm by demonstrating its simulation on
four exemplar reaction-diffusion scenarios.
