Contemporary statistical inference for infectious disease models using Stan.

This paper is concerned with the application of recently developed statistical methods for inference in infectious disease models. We use hierarchical models as well as deterministic and stochastic epidemic processes based upon systems of ordinary differential equations. We illustrate the application of Hamiltonian Monte Carlo and Variational Inference using the freely available software Stan. The methods are applied to real data from outbreaks as well as routinely collected observations. The results suggest that both inference methods are feasible in this context and show a trade-off between statistical efficiency versus computational speed. The latter appears particularly relevant for real-time applications.