Before revision:  The deterministic rate equation (DRE) offers a macroscopic view of the system by means of a system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interactions such as in mass-action kinetics .
After revision:  The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interactions such as in mass-action kinetics .