  We derive in this note a high-order corrector estimate for the homogenization
of a microscopic semi-linear elliptic system posed in perforated domains. The
major challenges are the presence of nonlinear volume and surface reaction
rates. This type of correctors justifies mathematically the convergence rate of
formal asymptotic expansions for the two-scale homogenization settings. As main
tool, we follow the standard approach by the energy-like method to investigate
the error estimate between the micro and macro concentrations and micro and
macro concentration gradients. This work aims at generalizing the results
reported in [2, 7].
