  We present in this paper a very adapted finite volume numerical scheme for
transport type-equation. The scheme is an hybrid one combining an
anti-dissipative method with down-winding approach for the flux and an high
accurate method as the WENO5 one. The main goal is to construct a scheme able
to capture in exact way the numerical solution of transport type-equation
without artifact like numerical diffusion or without "stairs" like oscillations
and this for any regular or discontinuous initial distribution. This kind of
numerical hybrid scheme is very suitable when properties on the long term
asymptotic behavior of the solution are of central importance in the modeling
what is often the case in context of population dynamics where the final
distribution of the considered population and its mass preservation relation
are required for prediction.
