The Issues With the Minnesota Model, Part 3

By April 22, 2020 Commentary

Okay, so a brief recapitulation.  So far we have started the virus running through our population.  Everyone, over time, is going to move from Susceptible to Exposed to Infected.  Now what happens, what determines who goes where from Infected?  As discussed in Part 1, there are two intermediate buckets that some people (subject to that delta or detection rate term) go to:  Hospitalized or ICU.  And there are two final destinations, Recovered or Dead.  Some Infecteds go right to Recovered.   There are formulas that tell you what percent of Infected go to each of the intermediate buckets and what percent go right to Recovered.

Just as the average person spent 5 days in Exposed before moving to Infected, the average person spends 8 days in Infected before moving on.  Every day the model is running, some people are moving from Exposed to Infected, and every day some people are moving from Infected to Hospitalized, ICU or Recovered.  One regulator out of Infected is that 8 day period, which is based on data on how long it takes the average person to demonstrate the need to be Hospitalized or placed in ICU (again, this is from pretty untrustworthy China data, adjusted for global demographics).  The formula to determine how many go to the Hospitalized bucket is also based on hospitalization rates from, you guessed it, China.  The formula to determine how many people go to ICU is based on ICU admission rates, again from China.  So every day some number of people, based on these formulas, are moving out of Infected to Hospitalized or ICU.  The remainder of the Infecteds who would move on a given day, after those lucky souls who are sent to Hospitalized and ICU have been determined, go to Recovered.

But now our little delta, the detection rate comes into play.  We described in the first post that, to account for asymptomatic patients, every formula has the detection rate term which adjusts the number of people who would otherwise move to a bucket down by 25 percentage points, so that only 75% actually move.  As we said in that post, seems like a weird way to deal with this issue.  And as we noted before, while you would think that the 25% who are asymptomatic would go right to Recovered after their average 8 day sentence in Infected, they don’t, they disappear in essence, they have no destination. (Unless we are missing a formula, this appears to be what happens.  The other possibility, which would be worse, is that they end up staying in the Infected bucket, and therefore would be subject to resampling on future days. In that case they wouldn’t really be treated as asymptomatic.  It is just very strange.)

For those persons who did go to Hospitalized, the average stay is about 13 days, and as the paper says (although the formulas don’t) all these people end up going to Recovered.  For those persons who did go to ICU, the average stay is about 10 days.  The paper says this is until recovery, but some of the ICU group die, so it isn’t clear if the average length of stay includes those who die.  Disposition from the ICU is to either Recovered or Dead.  Mortality is based on China data, is age-specific and includes the comorbidity indicator in its calculation.   So now we have taken a group of people all the way through the model.  After being Exposed, the average person is going to spend between 13 and 26 days in various buckets before final disposition.

As the model runs day after day, it is taking the number of Susceptible people down.  We have all seen the images of the epidemic curves.  The number of Susceptibles is declining pretty rapidly at first, because people are having lots of contact with those nasty Infecteds and becoming Exposed, so the Exposed group is rising rapidly and the Infected group grows quickly.  But as time goes on, and the number of Susceptibles drops appreciably, there are simply far fewer opportunities for contacts between Infecteds and Susceptibles, and the movement into the Exposed bucket begins to slow and subsequently the movement into Infected.  In the absence of measures to slow the spread, a highly transmissible virus like this strain of coronavirus would burn through the population pretty quickly (the slide deck suggests this must be less than 20 weeks), and the epidemic would be over relatively soon, with only a residual low level of infections occurring.

If you make mitigation of spread attempts, the more strict and successful they are, the longer the epidemic is going to run.  And leaving aside the issue of health resources adequate to care for patients at any one time, you are going to end up with the same number of deaths.  So that is the hard choice, do you want this over quickly, with more acute pain, or do you want it to drag on indefinitely with a lower level but not pleasant level of pain.  And in terms of the harms from the mitigation measures, and they aren’t cost-free, the inverse pattern occurs.  You can have a brief period of low economic disruption, or you can have a long interval of high economic damage.  And there is some in-between, maybe we could figure that out like Sweden has.

A quick summary:

  1. the basic approach of the Minnesota model isn’t inappropriate, but the clinical flow isn’t optimal
  2. the data used for assumptions and parameters isn’t particularly trustworthy and should be updated
  3. current research would suggest that estimates of the number of undetected infections is far higher than the model assumes, which biases all results under the model upward.

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