I study inference problems for irreversible stochastic epidemic models on network via Belief Propagation algorithm. Previous works derive equations which allow to compute posterior distributions of the time evolution of the state of each node given some observation. It has already been shown that this method outperforms previous ones in the particular case of finding "patient zero" of a SIR epidemic given an observation at a later unknown time. I study performances of this method on the inference of the time evolution of a SIR epidemic subsequent a given observation.