The main goal of this work is the mathematical formulation, the analysis
and the numerical simulation of a prey-predator model by taking into account the
toxin produced by the phytoplankton species. The mathematical study of the model
leads us to have an idea on the existence of solution, the existence of equilibria and the
stability of the stationary equilibria. These results are obtained through the principle
of comparison. Finally, the numerical simulations in two-dimensional allowed us to
establish the formation of spatial patterns and a threshold of release of the toxin,
above which we talk about the phytoplankton blooms.