In this talk we present the Generalized Lotka–Volterra dynamics associated to the model of C-difficile infection of the intestine microbiote and aiming to transfer the system from an infected state to an healthy state. The control inputs are of two types : fecal injection or bactericides which act as Dirac pulses and prebiotics or antibiotics which act as continuous controls. An uniform frame can be introduced using the tools from geometric control to analyze the accessibility set as the orbit of a pseudo-semi group. Optimal control can be considered in the frame of permanent control or sampled-data control. The later being adapted to the practical constraints of a finite set of medical interventions. In both case the optimal control problems can be analyzed using direct and indirect schemes aiming to reach an healthy state. Such methods are tested on toys models in dimension 2 and 3 related to the construction of reduced dynamics. Even those simple situations lead to interesting questions of accessibility and integrability issues in relation with the study of dynamical systems.