Juliette Unwin et al. write:
We model the epidemics in the US at the state-level, using publicly available death data within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the time-varying reproduction number (the average number of secondary infections caused by an infected person), the number of individuals that have been infected and the number of individuals that are currently infectious. We use changes in mobility as a proxy for the impact that NPIs and other behaviour changes have on the rate of transmission of SARS-CoV-2. We project the impact of future increases in mobility, assuming that the relationship between mobility and disease transmission remains constant. We do not address the potential effect of additional behavioural changes or interventions, such as increased mask-wearing or testing and tracing strategies.
Nationally, our estimates show that the percentage of individuals that have been infected is 4.1% [3.7%-4.5%], with wide variation between states. For all states, even for the worst affected states, we estimate that less than a quarter of the population has been infected; in New York, for example, we estimate that 16.6% [12.8%-21.6%] of individuals have been infected to date. Our attack rates for New York are in line with those from recent serological studies  broadly supporting our modelling choices.
There is variation in the initial reproduction number, which is likely due to a range of factors; we find a strong association between the initial reproduction number with both population density (measured at the state level) and the chronological date when 10 cumulative deaths occurred (a crude estimate of the date of locally sustained transmission).
Our estimates suggest that the epidemic is not under control in much of the US: as of 17 May 2020, the reproduction number is above the critical threshold (1.0) in 24 [95% CI: 20-30] states. Higher reproduction numbers are geographically clustered in the South and Midwest, where epidemics are still developing, while we estimate lower reproduction numbers in states that have already suffered high COVID-19 mortality (such as the Northeast). These estimates suggest that caution must be taken in loosening current restrictions if effective additional measures are not put in place.
We predict that increased mobility following relaxation of social distancing will lead to resurgence of transmission, keeping all else constant. We predict that deaths over the next two-month period could exceed current cumulative deaths by greater than two-fold, if the relationship between mobility and transmission remains unchanged. Our results suggest that factors modulating transmission such as rapid testing, contact tracing and behavioural precautions are crucial to offset the rise of transmission associated with loosening of social distancing.
Overall, we show that while all US states have substantially reduced their reproduction numbers, we find no evidence that any state is approaching herd immunity or that its epidemic is close to over.
One question I have is about the assumptions underlying “increased mobility following relaxation of social distancing.” Even if formal social distancing rules are relaxed, if the death rate continues, won’t enough people be scared enough that they’ll limit their exposure, thus reducing the rate of transmission? This is not to suggest that the epidemic will go away, just that maybe people’s behavior will keep the infections spreading at something like the current rate? Or maybe I’m missing something here.
The report and other information is at their website.
Below is our usual three panel plot showing our results for the five states we uses as a case study in the report – we chose them because we felt they showed different responses across the US. New in this report, we estimate the number of people who are currently infectious over time – the difference in this and those getting newly infected each day is quite stark.
We have also put the report on open review, which is an online platform enabling open reviews of scientific papers. It’s usually used for computer science conferences but Seth Flaxman has been in touch to partner with them to try it for a pre-print. If you’d like, click on the link and you can leave us a comment or recommend a reviewer.
Lots and lots of graphs (they even followed some of my suggestions, but I’m still concerned about the way that the upper ends of the uncertainty bounds are so visually prominent), and they fit a multilevel model in Stan, which I really think is the right way to go, as it allows a flexible workflow for model building, checking, and improvement.
You can make of the conclusions what you will: the model is transparent, so you should be able to map back from inferences to assumptions.