Compartmental models are widespread methods useful to understand and predict the dynamic of a phenomenon of interest, such as the spreading process of an infectious disease. Their formalization relies on systems of ordinary differential equations parameterized through some quantities of interest, such as the basic reproduction number and the duration of the infectious period. However, to account for the intrinsic uncertainty of an epidemic, we need a stochastic version of the equations based on a suitable statistical model. Unfortunately, the associated likelihood function is often intractable and requires specific methods for making inferences. In this work, we investigate three different strategies for addressing the intractability of the likelihood within a Bayesian framework. In particular, we consider Data-Augmentation and Pseudo-Marginal Markov Chain Monte Carlo algorithms, along with a likelihood-free approach based on Approximate Bayesian Computation. We describe and compare the methods at work on a simple SIR model to highlight their strengths and weaknesses.