  This tutorial shows how to build, fit, and criticize disease transmission
models in Stan, and should be useful to researchers interested in modeling the
SARS-CoV-2 pandemic and other infectious diseases in a Bayesian framework.
Bayesian modeling provides a principled way to quantify uncertainty and
incorporate both data and prior knowledge into the model estimates. Stan is an
expressive probabilistic programming language that abstracts the inference and
allows users to focus on the modeling. As a result, Stan code is readable and
easily extensible, which makes the modeler's work more transparent.
Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is
amiable to diagnostics, which means the user can verify whether the obtained
inference is reliable. In this tutorial, we demonstrate how to formulate, fit,
and diagnose a compartmental transmission model in Stan, first with a simple
Susceptible-Infected-Recovered (SIR) model, then with a more elaborate
transmission model used during the SARS-CoV-2 pandemic. We also cover advanced
topics which can further help practitioners fit sophisticated models; notably,
how to use simulations to probe the model and priors, and computational
techniques to scale-up models based on ordinary differential equations.
