Is coronavirus different in the UK and Italy?

BBC UK writes, Coronavirus: Three reasons why the UK might not look like Italy. They point to three observations about the epidemic so far:

  1. Different early transmission – the UK lags the epidemic in Italy
  2. Italy’s epidemic is more concentrated
  3. More of Italy’s confirmed cases are fatal

I think these speculations are misguided, and give a potentially-disastrous impression that the UK might somehow dodge a bullet without really trying. That’s only slightly mitigated by the warning at the end,

Don’t relax quite yet

Even though our epidemic may not follow Italy’s exactly, that doesn’t mean the UK will escape serious changes to its way of life.

Epidemiologist Adam Kucharski warns against simple comparisons of case numbers and that “without efforts to control the virus we could still see a situation evolve like that in Italy”, even if not necessarily in the next four weeks.

… which should be in red 72-point text right at the top.

Will the epidemic play out differently in the UK? Surely. But it really look qualitatively different? I doubt it, unless the reaction is different.

The fundamental problem is that the structure of a system determines its behavior. A slinky will bounce if you jiggle it, but more fundamentally it bounces because it’s a spring. You can jiggle a brick all you want, but you won’t get much bouncing.

The system of a virus spreading through a population is the same. The structure of the system says that, as long as the virus can infect people faster than they recover, it grows exponentially. It’s inevitable; it’s what a virus does. The only way to change that is to change the structure of the system by slowing the reproduction. That happens when there’s no one left to infect, or when we artificially reduce the infection rate though social distancing, sterilization and quarantine.

A change to the initial timing or distribution of the epidemic doesn’t change the structure at all. The slinky is still a slinky, and the epidemic will still unfold exponentially. Our job, therefore, is to make ourselves into bricks.

The third point, that fatality rates are lower, may also be a consequence of the UK starting from a different state today. In Italy, infections have grown high enough to overwhelm the health care system, which increases the fatality rate. The UK may not be there yet. However, a few doublings of the number of infected will quickly close the gap. This may also be an artifact of incomplete testing and lags in reporting.

Here’s a more detailed explanation:

More Interactive Coronavirus Models

Jeroen Struben has a nice interactive web simulation running online at Forio. It’s multiregion, with diffusion of infection across borders, and includes some of the interesting structures I excluded from my simple model, including explicit quarantine and vaccination, and testing and reporting lags.

The NYT has a very simple interactive simulation embedded in:

How Much Worse the
Coronavirus Could Get, in Charts

As always, I’m eager to know of more – please comment!

Dynamics of Hoarding

“I’m not hoarding, I’m just stocking up before the hoarders get here.”
Behavioral causes of phantom ordering in supply chains
John D. Sterman
Gokhan Dogan

When suppliers are unable to fill orders, delivery delays increase and customers receive less than they desire. Customers often respond by seeking larger safety stocks (hoarding) and by ordering more than they need to meet demand (phantom ordering). Such actions cause still longer delivery times, creating positive feedbacks that intensify scarcity and destabilize supply chains. Hoarding and phantom ordering can be rational when customers compete for limited supply in the presence of uncertainty or capacity constraints. But they may also be behavioral and emotional responses to scarcity. To address this question we extend Croson et al.’s (2014) experimental study with the Beer Distribution Game. Hoarding and phantom ordering are never rational in the experiment because there is no horizontal competition, randomness, or capacity constraint; further, customer demand is constant and participants have common knowledge of that fact. Nevertheless 22% of participants place orders more than 25 times greater than the known, constant demand. We generalize the ordering heuristic used in prior research to include the possibility of endogenous hoarding and phantom ordering. Estimation results strongly support the hypothesis, with hoarding and phantom ordering particularly strong for the outliers who placed extremely large orders. We discuss psychiatric and neuroanatomical evidence showing that environmental stressors can trigger the impulse to hoard, overwhelming rational decision‐making. We speculate that stressors such as large orders, backlogs or late deliveries trigger hoarding and phantom ordering for some participants even though these behaviors are irrational. We discuss implications for supply chain design and behavioral operations research.

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 7.zip

Update 3/12: community corona 8-mdl+vpmx.zip

There’s another copy at https://vensim.com/coronavirus/ along with links to the software.

Coronavirus – Really Simple Math

Why border control has limits, and mild cases don’t matter.

At the top, the US coronavirus response seems to be operating with (at least) two misperceptions. First, that border control works. Second, that a lower fatality rate means fewer deaths. Here’s how it really works.

Consider an extremely simplified SEIRD model. This is a generalization of the simple SIR framework to include asymptomatic, non-infective Exposed people and the Deceased:

The parameters are such that the disease takes about a week to incubate, and about a week to resolve. The transmission rate is such that cases double about once a week, if left uncontrolled.

Those fortuitous time constants make it really simple to model the spread in discrete time. First, abstract away the susceptible (who are abundant early in the epidemic) and the resolved cases (which are few and don’t participate further):

In this dirt-simple model,

  • This week’s infected will all resolve
  • This week’s exposed will advance to become next week’s infected
  • Next week’s exposed are the ones the current infected are infecting now.

If the disease is doubling weekly, then for every 1 infected person there must be 2 exposed people in the pipeline. And each of those infected people must expose 4 others. (Note that this is seemingly an R0 of 4, which is higher than what’s usually quoted, but the difference is partly due to discrete vs. continuous compounding. The R0 of 2.2 that’s currently common seems too low to fit the data though – more on that another time.)

What does this imply for control strategy? It means that, on the day you close the border, the infected arrivals you’ve captured and isolated understate the true problem. For every infected person, there are two exposed people on the loose, initiating domestic community spread. Because it’s doubling weekly, community infections very quickly replace the imports, even if a travel ban is 100% effective.

Mild Cases

Now consider the claim that the fatality rate is much lower than reported, because there are many unobserved mild cases:

In other words, the reported fatality rate is Deceased/(Recovered+Deceased), but the “real” fatality rate is Deceased/(Recovered+Deceased+Mild Recovered). That’s great, but where did all those mild cases come from? If they are sufficiently numerous to dilute the fatality rate by, say, a factor of 10, then there must also be 9 people with mild infections going undetected for every known infected case. That doesn’t help the prognosis for deaths a bit, because (one tenth the fatality rate) x (ten times the cases) yields the same outcome. Actually, this makes the border control and community containment problem much harder, because there are now 10x as many contacts to trace and isolate. Fortunately this appears to be pure speculation.

Dweilen met de kraan open

Modeling expressions of futility for fun.

I just learned a beautiful Dutch idiom, dweilen met de kraan open. It means “mopping [the floor] with the the faucet running.” I’m not sure there’s a common English equivalent that’s so poetic, but perhaps “treating the symptoms, not the cause” is closest.

This makes a nice little model:

If you’re a slow mopper, you can never catch up with the tap:

If you’re fast, you can catch up, but not reverse the process:

Either way, as long as you don’t turn off the tap, there will always be water on the floor:

The Vensim model: dweilen 1.mdl

Filling a leaky bucket

The structure of the system above is nearly the same as filling a leaky bucket, except that the user is concerned with the inflow rather than the outflow.

Failure to patch the leak is equally frustrating. (If you implement this, beware: leaky buckets are nonlinear!)

Beating a dead horse and fiddling while Rome burns

These control systems are definitely going nowhere:

Biting off more than you can chew

This one’s fun because it only becomes an exercise in futility when you cross a nonlinear threshold.

As long as you take small bites, the red loop of “normal” chewing clears the backlog of food in mouth in a reasonable time. But when you take a huge bite, you exceed the mouth’s capacity. This activates the blue positive loop, which slows chewing until the burden has been reduced somewhat.  When the blue loop kicks in, the behavior mode changes (green), greatly delaying the process:

The Vensim model: chewing 1.mdl

Emptying the ocean with a thimble

I think the futility of this endeavor is normally thought of as a question of scale. The volume of the ocean is about 1.35 trillion trillion cubic centimeters, and a thimble contains about 1 cc. But suppose you could cycle that thimble really fast? I think you still have feedback problems:

First, you have the mopping problem: as the ocean empties, the job gets harder, because you’ll be carrying water uphill … a lot (the average depth of the ocean is about 4000 meters). Second, you have the leaky bucket problem. Where are you going to put all that water? Evaporation and surface flow are inevitably going to take some back to the ocean.

 

Coronavirus Containment Reference Mode

I ran across this twitter thread this morning, describing how a focus on border security and containment of existing cases has failed to prevent the takeoff of coronavirus.

Here’s the data on US confirmed cases that goes with it:

US confirmed coronavirus cases, as of 3/2/2019. Source: Johns Hopkins CSSE dashboard, https://gisanddata.maps.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6

It’s easy to see how this behavior could lure managers into a self-confirming attributions trap. After a surge of imports, they close the borders. Cases flatten. Problem solved. Why go looking for trouble?

The problem is that containment alone doesn’t work, because the structure of the system defeats it. You can’t intercept every infected person, because some are exposed but not yet symptomatic, or have mild cases. As soon as a few of these people slip into the wild, the positive loops that drive infection operate as they always have. Once the virus is in the wild, it’s essential to change behavior enough to lower its reproduction below replacement.