We 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 [13].
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 approximated 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.