The discrete Couzin-Vicsek algorithm (CVA) has been proposed to model the interactions of individuals among animal societies such as schools of fish. In this Note, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity. The result is based on the introduction of a non-conventional concept of a collisional invariant of the collision operator. To cite this article: P. Degond, S. Motsch, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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