  In this note, we apply the theory of stochastic homogenization to find the
asymptotic behavior of the solution of a set of Smoluchowski's
coagulation-diffusion equations with non-homogeneous Neumann boundary
conditions. This system is meant to model the aggregation and diffusion of
$\beta$-amyloid peptide (A$\beta$) in the cerebral tissue, a process associated
with the development of Alzheimer's disease. In contrast to the approach used
in our previous works, in the present paper we account for the non-periodicity
of the cellular structure of the brain by assuming a stochastic model for the
spatial distribution of neurons. Further, we consider non-periodic random
diffusion coefficients for the amyloid aggregates and a random production of
A$\beta$ in the monomeric form at the level of neuronal membranes.
