  Recent works have derived and proven the large-population mean-field limit
for several classes of particle-based stochastic reaction-diffusion (PBSRD)
models. These limits correspond to systems of partial integral-differential
equations (PIDEs) that generalize standard mass-action reaction-diffusion PDE
models. In this work we derive and prove the next order fluctuation corrections
to such limits, which we show satisfy systems of stochastic PIDEs with Gaussian
noise. Numerical examples are presented to illustrate how including the
fluctuation corrections can enable the accurate estimation of higher order
statistics of the underlying PBSRD model.
