A simple model is developed for membrane fouling, taking into account two main fouling phenomena: cake formation, due to attached solids onto the membrane surface and pores clogging, due to retained compounds inside the pores. The model is coupled with a simple anaerobic digestion model for describing the dynamics of an Anaerobic Membrane BioReactor (AnMBR). In simulations, we investigate its qualitative behavior: it is shown that the model exhibits satisfying properties in terms of flux decrease due to membrane fouling. Comparing simulation and experimental data, the model is shown to predict quite well the dynamics of an AnMBR. The simulated flux best fits the experimental flux with a correlation coefficient r^2 = 0.968 for the calibration data set and r^2 = 0.938 for the validation data set. General discussions are given on possible control strategies to limit fouling and optimize the flux production. We show in simulations that these strategies allow one to increase the mean production flux to 33 L/(h.m^2), whereas without control it was 18 L/(h.m^2).