MSU Covid Evaluation

Well, my prediction of 10/9 covid cases at MSU, made on 10/6 using 10/2 data, was right on the money: I extrapolated 61 from cumulative cases, and the actual number was 60. (I must have made a typo or mental math error in reporting the expected cumulative cases, because 157+61 <> 207. The number I actually extrapolated was 157*e^.33 = 218 = 157 + 61.)

That’s pretty darn good, though I shouldn’t take too much credit, because my confidence bounds would have been wide, had I included them in the letter. Anyway, it was a fairly simpleminded exercise, far short of calibrating a real model.

Interestingly, the 10/16 release has 65 new cases, which is lower than the next simple extrapolation of 90 cases. However, Poisson noise in discrete events like this is large (the variance equals the mean, so this result is about two and a half standard deviations low), and we still don’t know how much testing is happening. I would still guess that case growth is positive, with R above 1, so it’s still an open question whether MSU will make it to finals with in-person classes.

Interestingly, the increased caseload in Gallatin County means that contact tracing and quarantine resources are now strained. This kicks off a positive feedback: increased caseload means that fewer contacts are traced and quarantined. That in turn means more transmission from infected people in the wild, further increasing caseload. MSU is relying on county resources for testing and tracing, so presumably the university is caught in this loop as well.



MSU Covid – what will tomorrow bring?

The following is a note I posted to a local listserv earlier in the week. It’s an example of back-of-the-envelope reasoning informed by experience with models, but without actually calibrating a model to verify the results. Often that turns out badly. I’m posting this to archive it for review and discussion later, after new data becomes available (as early as tomorrow, I expect).

I thought about responding to this thread two weeks ago, but at the time numbers were still very low, and data was scarce. However, as an MSU parent, I’ve been watching the reports closely. Now the picture is quite different.

If you haven’t discovered it, Gallatin County publishes MSU stats at the end of the weekly Surveillance Report, found here:

For the weeks ending 9/10, 9/17, 9/24, and 10/2, MSU had 3, 7, 66, and 43 new cases. Reported active cases are slightly lower, which indicates that the active case duration is less than a week. That’s inconsistent with the two-week quarantine period normally recommended. It’s hard to see how this could happen, unless quarantine compliance is low or delays cause much of the infectious period to be missed (not good either way).

The huge jump two weeks ago is a concern. That’s growth of 32% per day, faster than the typical uncontrolled increase in the early days of the epidemic. That could happen from a superspreader event, but more likely reflects insufficient testing to detect a latent outbreak.

Unfortunately they still don’t publish the number of tests done at MSU, so it’s hard to interpret any of the data. We know the upper bound, which is the 2000 or so tests per week reported for all of Gallatin county. Even if all of those were dedicated to MSU, it still wouldn’t be enough to put a serious dent in infection through testing, tracing and isolation. Contrast this with Colby College, which tests everyone twice a week, which is a test density about 100x greater than Gallatin County+MSU.

In spite of the uncertainty, I think it’s wrong to pin Gallatin County’s increase in cases on MSU. First, COVID prevalence among incoming students was unlikely to be much higher than in the general population. Second, Gallatin County is much larger than MSU, and students interact largely among themselves, so it would be hard for them to infect the broad population. Third, the county has its own reasons for an increase, like reopening schools. Depending on when you start the clock, MSU cases are 18 to 28% of the county total, which is at worst 50% above per capita parity. Recently, there is one feature of concern – the age structure of cases (bottom of page 3 of the surveillance report). This shows that the current acceleration is driven by the 10-19 and 20-29 age groups.

As a wild guess, reported cases might understate the truth by a factor of 10. That would mean 420 active cases at MSU when you account for undetected asymptomatics and presymptomatic untested contacts. That’s out of a student/faculty population of 20,000, so it’s roughly 2% prevalence. A class of 10 would have a 1/5 chance of a positive student, and for 20 it would be 1/3. But those #s could easily be off by a factor of 2 or more.

Just extrapolating the growth rate (33%/week for cumulative cases), this Friday’s report would be for 61 new cases, 207 cumulative. If you keep going to finals, the cumulative would grow 10x – which basically means everyone gets it at some point, which won’t happen. I don’t know what quarantine capacity is, but suppose that MSU can handle a 300-case week (that’s where things fell apart at UNC). If so, the limit is reached in less than 5 weeks, just short of finals.

I’d say these numbers are discouraging. As a parent, I’m not yet concerned enough to pull my kids out, but they’re nonresidential so their exposure is low. Around classrooms on campus, compliance with masks, sanitizing and distancing is very good – certainly better than it is in town. My primary concern at present is that we don’t know what’s going on, because the published statistics are insufficient to make reliable judgments. Worse, I suspect that no one knows what’s going on, because there simply isn’t enough testing to tell. Tests are pretty cheap now, and the disruption from a surprise outbreak is enormous, so that seems penny wise and pound foolish. The next few weeks will reveal whether we are seeing random variation or the beginning of a large outbreak, but it would be far better to have enough surveillance and data transparency to know now.

A Community Coronavirus Model for Bozeman

This video explores a simple epidemic model for a community confronting coronavirus.

I built this to reflect my hometown, Bozeman MT and surrounding Gallatin County, with a population of 100,000 and no reported cases – yet. It shows the importance of an early, robust, multi-pronged approach to reducing infections. Because it’s simple, it can easily be adapted for other locations.

You can run the model using Vensim PLE or the Model Reader (or any higher version). Our getting started and running models videos provide a quick introduction to the software.

The model, in .mdl and .vpmx formats for any Vensim version:

community corona

Update 3/12: community corona

There’s another copy at along with links to the software.

Complexity should be the default assumption

Whether or not we can prove that a system experiences trophic cascades and other nonlinear side-effects, we should manage as if it does, because we know that these dynamics are common.

There’s been a long-running debate over whether wolf reintroduction led to a trophic cascade in Yellowstone. There’s a nice summary here:

Do Wolves Change Rivers?

Yesterday, June initiated an in depth discussion on the benefit of wolves in Yellowstone, in the form of trophic cascade with the video: How Wolves Change the River:

This was predicted by some, and has been studied by William Ripple, Robert Beschta Trophic Cascades in Yellowstone: The first fifteen years after wolf reintroduction

Shannon, Roger, and Mike, voiced caution that the verdict was still out.

I would like to caution that many of the reported “positive” impacts wolves have had on the environment after coming back to Yellowstone remain unproven or are at least controversial. This is still a hotly debated topic in science but in the popular media the idea that wolves can create a Utopian environment all too often appears to be readily accepted. If anyone is interested, I think Dave Mech wrote a very interesting article about this (attached). As he puts it “the wolf is neither a saint nor a sinner except to those who want to make it so”.

Mech: Is Science in Danger of Sanctifying Wolves

Roger added

I see 2 points of caution regarding reports of wolves having “positive” impacts in Yellowstone. One is that understanding cause and effect is always hard, nigh onto impossible, when faced with changes that occur in one place at one time. We know that conditions along rivers and streams have changed in Yellowstone but how much “cause” can be attributed to wolves is impossible to determine.

Perhaps even more important is that evaluations of whether changes are “positive” or “negative” are completely human value judgements and have no basis in science, in this case in the science of ecology.

-Ely Field Naturalists

Of course, in a forum discussion, this becomes:

Wolves changed rivers.

Not they didn’t.

Yes they did.

(iterate ad nauseam)

Prove it.

… with “prove it” roughly understood to mean establishing that river = a + b*wolves, rejecting the null hypothesis that b=0 at some level of statistical significance.

I would submit that this is a poor framing of the problem. Given what we know about nonlinear dynamics in  networks like an ecosystem, it’s almost inconceivable that there would not be trophic cascades. Moreover, it’s well known that simple correlation would not be able to detect such cascades in many cases anyway.

A “no effect” default in other situations seems equally naive. Is it really plausible that a disturbance to a project would not have any knock-on effects? That stressing a person’s endocrine system would not cause a path-dependent response? I don’t think so. Somehow we need ordinary conversations to employ more sophisticated notions about models and evidence in complex systems. I think at least two ideas are useful:

  • The idea that macro behavior emerges from micro structure. The appropriate level of description of an ecosystem, or a project, is not a few time series for key populations, but an operational, physical description of how species reproduce and interact with one another, or how tasks get done.
  • A Bayesian approach to model selection, in which our belief in a particular representation of a system is proportional to the degree to which it explains the evidence, relative to various alternative formulations, not just a naive null hypothesis.

In both cases, it’s important to recognize that the formal, numerical data is not the only data applicable to the system. It’s also crucial to respect conservation laws, units of measure, extreme conditions tests and other Reality Checks that essentially constitute free data points in parts of the parameter space that are otherwise unexplored.

The way we think and talk about these systems guides the way we act. Whether or not we can prove in specific instances that Yellowstone had a trophic cascade, or the Chunnel project had unintended consequences, we need to manage these systems as if they could. Complexity needs to be the default assumption.

Future Climate of the Bridgers

Ten years ago, I explored future climate analogs for my location in Montana:

When things really warm up, to +9 degrees F (not at all implausible in the long run), 16 of the top 20 analogs are in CO and UT, …

Looking at a lot of these future climate analogs on Google Earth, their common denominator appears to be rattlesnakes. I’m sure they’re all nice places in their own way, but I’m worried about my trees. I’ll continue to hope that my back-of-the-envelope analysis is wrong, but in the meantime I’m going to hedge by managing the forest to prepare for change.

I think there’s a lot more to worry about than trees. Fire, wildlife, orchids, snowpack, water availability, …

Recently I decided to take another look, partly inspired by the Bureau of Reclamation’s publication of downscaled data. This solves some of the bias correction issues I had in 2008. I grabbed the model output (36 runs from CMIP5) and observations for the 1/8 degree gridpoint containing Bridger Bowl:

Then I used Vensim to do a little data processing, converting the daily time series (which are extremely noisy weather) into 10-year moving averages (i.e., climate). Continue reading “Future Climate of the Bridgers”

Snow is Normal in Montana

In this case, I think it’s quite literally Normal a.k.a. Gaussian:

Normally distributed snow

Here’s what I think is happening. On windless days with powder, the snow dribbles off the edge of the roof (just above the center of the hump). Flakes drift down in a random walk. The railing terminates the walk after about four feet, by which time the distribution of flake positions has already reached the Normal you’d expect from the Central Limit Theorem.

Enough of the geek stuff; I think I’ll go ski the field.

Beggaring ourselves through coal mining

Old joke: How do you make a small fortune breeding horses? Start with a large fortune ….

It appears that the same logic applies to coal mining here in the Northern Rockies.

With US coal use in slight decline, exports are the growth market. Metallurgical and steam coal currently export for about $140 and $80 per short ton, respectively. But the public will see almost none of that, because unmanaged quantity and “competitive” auctions that are uncompetitive (just like Montana trust land oil & gas), plus low royalty, rent and bonus rates, result in a tiny slice of revenue accruing to the people (via federal and state governments) who actually own the resource.

For the Powder River Basin, here’s how it pencils out in rough terms:

Item $/ton
Minemouth price $10
Royalty, rents & bonus $2
Social Cost of Carbon (@ $21/tonCo2 medium value) -$55
US domestic SCC (at 15% of global, average of 7% damage share and 23% GDP share) -$8
Net US public benefit < -$6

In other words, the US public loses at least $3 for every $1 of coal revenue earned. The reality is probably worse, because the social cost of carbon estimate is extremely conservative, and other coal externalities are omitted. And of course the global harm is much greater than the US’ narrow interest.

Even if you think of coal mining as a jobs program, at Wyoming productivity, the climate subsidy alone is almost half a million dollars per worker.

This makes it hard to get enthusiastic about the planned expansion of exports.