Projet M3NWe start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel . A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximat- ed via a mixed finite element technique. The solution algorithm is then described and finally we give some preliminary numerical results.Especially our method is well adapted to compute the concentration of bacteria
