Important updates to this webpage (April 19): (i) revision of my comments, with a link to an opinion piece criticizing IHME methodology; (ii) a comment on herd immunity; (iii) additional comments, which are more technical, may be found at the end. Also, I am adding links as I become aware of them, but I am trying to keep the whole as brief as I can. As of April 19, NIH's curated publication database had about 1500 papers (link below).>
National Academy of Medicine >Nature Medicine Click on ``Covid-19 Research in Brief" Note: other specific journals are also good, e.g., JAMA, Science, Lancet, and don't forget the CDC webpage! Also, NIH has a curated, searchable database of Covid papers.
fivethirtyeight.com shines in this context. They are reporting on a survey of expert opinion (a survey of knowledgeable epidemiologists conducted by someone at U Mass), which is helpful due to the very large uncertainties. The April 2 article is here.
See also Nate Silver's April 4 article.
Vox is also doing a nice job. See the pair of April 10 articles on difficulties of prediction and on plans for reopening. Related to reopening: on April 17, an expert committee at Johns Hopkins released a guide for governors. Also on April 17 Science magazine published a short overview news article on next steps.
A nice April 7 article in the NY Times features a professional friend, David Spiegelhalter, who is especially good about public communication, and also Neil Ferguson, head of the Imperial College group. More may be found in David's April 12 overview article from The Guardian, written with Sylvia Richardson.
An April 13 overview on immunity, in the NY Times, by a leading epidemiology modeler (whom I don't know, but who is a colleague and collaborator of an old friend) is here.
Very nice ongoing data summaries.
The IHME model, which is popular and is used by the White House Task Force, but involves very simple curve fitting, is described and here. In contrast, a sophisticated SEIR modeling approach is taken by the Imperial College group.
I provide links to some modeling resources, including tutorials, below (additional comments).
Carnegie Mellon's excellent flu forecasting group (led by two of my close colleagues) has come online with COVID now-casting, with forecasting coming.
Here is a discussion of available R code related to Covid.
As always, a lot of interesting statistical discussion at Andrew Gelman's blog.
Just a few, done by excellent researchers. An early (influential) one here.
Another by the same group, April 8.
And one by the Imperial College group, March 30.
An interesting simulation study that's relevant to policiesfor living with Covid (or "re-opening") is reported and discussed in this article in Science, published April 14.
More on projections. In the the original version of IHME they (i) fit a curve to summarize the trend in accumulated deaths, across time, in Wuhan, and then, (ii) focusing on the time from social distancing until the curve's rate of increase (the death rate) starts to decrease, assumed the analogous curve for any particular U.S. state would be similar (after adjusting for the age distribution in the local population), and fit such curves to all of the states that had sufficient data (which was most of them, but not all). They used what we statisticians call a hierarchical model, which allowed them to compute measures of uncertainty.
An interesting statistical aspect of the Imperial College work of March 30 is that, rather than estimating all parameters (unobserved variables) from current data, they fix some of them by a combination of judgment and past data. Personally, given the situation, I rather like that idea, as long as it can be justified reasonably well, and as long as it is clear how sensitive results are to the choices.
For those who might care, while the IHME and Imperial College methods are very different, they are both Bayesian.
More on SEIR modeling. For an overview of SEIR modeling, I like this 2018 summary and also a pair of older papers by Hethcote, who himself contributed to the field, one from 1989 and one from 2000. Another nice paper is this 2017 historical overview. There are two related aspects of the work I would call to your attention. First, the models are implicitly probabilistic but too often (for my statistician's taste) not explicitly so. The first appendix in the 2018 summary at least starts down this path. Full-fledged versions are often labeled "stochastic" as in this 2017 primer. Second, when we move from analytical and simulation models to data-based estimation, we need statistical models, in which the data are assumed to follow probability distributions, and this allows investigators to generate assessments of uncertainty. The January 31 paper and the March 30 paper mentioned above are examples. The journal Statistical Science in 2018 had a special issue devoted to inference for infectious disease dynamics (v. 33, no. 1). See the Introduction to that issue.
More on herd immunity. Concerning herd immunity, I would recommend the Hethcote papers from 1989 and from 2000. The starting point is the notion that herd immunity generates a steady state, or endemic, disease where it can be present at background levels but does not become an epidemic. The derivation of the key expression for contact number, which leads to the percentage needed for herd immunity, is based on finding a stable solution to the differential equations; it appeared in a 1975 paper by Dietz, see Equation (18). Here is a key table from the Hethcote 1989 review, based on data that had appeared in papers by Anderson and May a few years earlier.