  In this paper, we provide the $O(\epsilon)$ corrections to the hydrodynamic
model derived by Degond and Motsch from a kinetic version of the model by
Vicsek & coauthors describing flocking biological agents. The parameter
$\epsilon$ stands for the ratio of the microscopic to the macroscopic scales.
The $O(\epsilon)$ corrected model involves diffusion terms in both the mass and
velocity equations as well as terms which are quadratic functions of the first
order derivatives of the density and velocity. The derivation method is based
on the standard Chapman-Enskog theory, but is significantly more complex than
usual due to both the non-isotropy of the fluid and the lack of momentum
conservation.
