This paper is concerned with the application of recent statistical advances to inference of infectious disease dynamics. We describe the fitting of a class of epidemic models using Hamiltonian Monte Carlo and variational inference as implemented in the freely available Stan software. We apply the two methods to real data from outbreaks as well as routinely collected observations. Our results suggest that both inference methods are computationally feasible in this context, and show a trade-off between statistical efficiency versus computational speed. The latter appears particularly relevant for real-time applications.