I found this piece a bit strange (theguardian.com/world/2020/may…) e.g. claiming "our predictions have been accurate to within a day or two, so there is a predictive validity to our models that the conventional ones lack" (arxiv.org/pdf/2004.04463…), when cited paper made this prediction: 
Implementing Bayesian state-space models with an observation process (which seems to be the basis of 'dynamic causal modelling') is a common approach in epidemiological modelling, so it also seems odd to claim that it's a new/different method...
And as noted by my colleague, the immunological 'dark matter' seems to be an extra parameter added to make the model fit the data, without a clear biological/epidemiological justification:
That being said, the underlying modelling approach (estimating latent states from available data in Bayesian framework) is a potentially useful one, so it will be interesting to see how the broader work progresses.
