Bayesian workflow for disease transmission modeling in Stan

TL;DR

This tutorial guides researchers in building, fitting, and diagnosing Bayesian disease transmission models in Stan, emphasizing transparency, uncertainty quantification, and advanced modeling techniques for infectious diseases like COVID-19.

Contribution

It demonstrates how to formulate, fit, and diagnose complex transmission models in Stan, including advanced techniques for scaling and model validation.

Findings

Successful implementation of SIR and COVID-19 transmission models in Stan

Use of diagnostics to verify inference reliability

Techniques for scaling models with differential equations

Abstract

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.