Bayesian workflow for disease transmission modeling in Stan

Abstract

Thistutorialshowshowtobuild,fit,andcriticizediseasetransmissionmodelsinStan, and should beusefulto researchersinterestedinmodelingthesevereacuterespiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic and other infec-tiousdiseasesinaBayesianframework.Bayesianmodelingprovidesaprincipledway to quantify uncertainty and incorporate both data and prior knowledge intothe model estimates. Stan is an expressive probabilistic programming languagethat abstracts the inference and allows users to focus on the modeling. As aresult, Stan code is readable and easily extensible, which makes the modeler’swork more transparent. Furthermore, Stan’s main inference engine, Hamilto-nian Monte Carlo sampling, is amiable to diagnostics, which means the usercan verify whether the obtained inference is reliable. In this tutorial, we demon-strate how to formulate, fit, and diagnose a compartmental transmission modelin Stan, first with a simple susceptible-infected-recovered model, then with amore elaborate transmission model used during the SARS-CoV-2 pandemic.We also cover advanced topics which can further help practitioners fit sophis-ticated models; notably, how to use simulations to probe the model and priors,and computational techniques to scale-up models based on ordinary differentialequations.