Everyone’s telling me about this paper (arXiv, Jon Zelner, the authors). In addition to the epidemiology content, it’s a very careful study of ODE models being fit with MCMC and with ADVI.
I’m in the same field, and have been fitting epidemic models with Stan for a few years. I was very excited to see this paper, and I think it is really great, with a few things missing:
A discussion about priors and prior predictive checks, which as I learned from several people on this forum (@bbbales2, @wds15, @charlesm93) are especially important here, as ODEs tend to blow up if given extreme parameter values – a problem that I experience on a daily basis.
Some discussion of the diagnostics of the MCMC, especially divergent transitions, which are also especially common with ODEs in my experience.
I vaguely know some of the authors and I will try to raise these points to them.