A report by the Imperial College COVID Response Team has built a model for the "reproduction rate" Rt over time for Italy based on realized social distancing as measured by % reduction in movement in homes, transit, and and other mobility measured as an average of retail, recreation, grocery, pharmacy, workplace and parks. They noted a high correlation of intervention timing and reduction of these movement variables so use these movement variables as predictors.
They estimated a linear regression coefficient modeling the log-linear effect of these 3 mobility measures on Rt, and used this to make projections under three scenarios, assuming (1) no reduction in lockdowns, (2) 20% reduction from prelockdown mobility and (3) 40% reduction.
Their model is based on the infections disease dynamics of the classic epidemiological SIR model, with the time-varying reproduction rate depending on social mobility covariates, and then cases tied to deaths using a negative binomial model that also accounts for lag times from infection to death. The model is thorough and carefully done, and the Bayesian modeling approach yields uncertainty quantifications, but I have some key criticisms:
1. Covariate choices -- the only covariates used in the predictive model are the 3 social mobility variables. I would believe the model to be more accurate if other key covariates like population density and temperature were included. Also, I think the social mobility variables are useful in tracking the overall reduction of activity and social distancing from lockdowns, as we move forward I'm not sure this is the best measure to accurately distinguish between more and less risky behavior when lockdowns are lifted, so won't be useful in crafting more targeted strategies.
2. Ignoring uncounted cases -- herd immunity is not close, but given a 10:1 or 15:1 case to official case ratio that seems about right, places like Lombardy Italy or Queens New York could have case % as high as 20%, 30% or 40%, so this will attenuate any incidence in these places. At a national level, the highest case incidence would be more like 3%-5%, so not as much of a big deal, but if they are wanting to predict counties then they would need to account for this.
3. Death model: overall it is well done, but it assumes a homogeneous death rate, which is far from true -- given we know 25-50% of deaths are from nursing homes and other long-term care facilities in the USA, and we also know that older people with certain co-morbidities are much more likely to die of the disease. It would have been more interesting to model the deaths rate as modified by these covariates, using the demographics of the country in the model. This would also improve the model.
This is certainly a valuable modeling exercise as long as it is not over interpreted. The limitations I pointed out all make these predictions less accurate, typically in a conservative way, i.e. tending to push the incidence and death estimates higher. If they accounted for temperature, the incidence curve would go down significantly in many places, if it adjusted for uncounted cases, that would also attenuate the incidence especially in places already experiencing breakouts, and adjusting for density would have also produced more accurate numbers. The death numbers are also likely inflated, since they assume anyone infected has the same risk of death, while the risk of death is very highly concentrated in known groups. Plus simple preventative measures at long term care facilities can greatly reduce death rates, and they are likely to happen moving forward.
The biggest qualm I have with this paper is not the work but how it is likely to be portrayed: the take home message will be portrayed as "Even relaxing social distancing by 20% will lead to huge further outbreak and so we need to keep lockdowns in place indefinitely", and this will be used to try to persuade policymakers to keep these lockdowns in place longer term. This conclusion is a gross oversimplification and I don't believe the right message for several reasons:
1. Even if lockdowns are lifted, most people should practice a good deal of care and social distancing naturally, so the government mandates may not be required to achieve a good degree of viral spread mitigation
2. If targeted mitigation strategies like reducing large gatherings, encouraging or requiring mask wearing in public, and practicing basic social distancing is accompanied by a lifting of lockdowns and opening of many businesses, people's social mobility will increase to a degree but the viral spread may be very well mitigated. In that case, their model will in this case overestimate the incidence and spread.
3. If special protections are retained for the most vulnerable populations, the death rate can be attenuated significantly even in the event of an increase of incidence.
4. Modeling at the country level is interesting, but not useful for policy. Targeting projected incidence at more local levels would be more useful, and could account for important variables like density, use of mass transit, and demographics which play an important part in incidence and mortality.