One of the things we should be doing when comparing priors is:
Prior predictive checks: what sort of trajectory I(t) [or R(t)] does a particular prior on R0 or beta and gamma induce;
and
Posterior predictive checks: sure, a prior might change the posterior slightly or even a lot, but what is the effect on the predicted quantities of the model, such as the time to peak incidence or the trajectory R(t)?
One of the things we should be doing when comparing priors is:
I(t)[orR(t)] does a particular prior onR0orbetaandgammainduce; andR(t)?