**Warning: **Read this before you apply for the job.

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Contact tracing & testing is front and center as a fundamental component of the Coronavirus Task Force’s plan to go forward.

Dr. Fauci has said (over & over again) that the process worked fine 30 years ago when he was fighting AIDs … and the media says that the test & trace model has been South Korea’s secret sauce fighting the coronavirus.

The essence of the process: Do diagnostic surveillance testing to ID people currently infected with the coronavirus, then trace back to ID the people with whom they’ve been in contact … then notify those people and test them … if they test positive, repeat the process … then again and again.

Sounds easy enough, doesn’t it?

But, it might not be as easy as it sounds.

**Let’s run some numbers… **

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To start, we need to set a couple of parameters:

(1) What’s **R0 — the coronavirus reproduction rate (**aka “transmission rate”) ?

(2) How many **infectiously close contacts** does an average person have that need to be traced?

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In a prior post, we dove deep on the __virus reproduction rate__ — referred to as R0 — a number that indicates how many new cases (“infectees”) an infected person generates.

For details, see:So, how far & fast does a virus spread?

For today’s purpose, all we need to know is that the R0 for the coronavirus is estimated to be **between R0=2 and R0=3**.

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**The relevant number of contacts (#C) is more complex.**

When an infected person is identified, which of their contacts merit tracing and testing?

Even Dr. Fauci admits that for HIV, the answer was simple: Just ask the patient to disclose all sex partners and anybody who shared intravenous needles. That’s usually a relatively short list.

The Koreans reportedly confiscated patient’s cell phones, downloaded the contacts, mass ordered the contacts to self-quarantine and policed them to make sure that they were following orders.

For details, seeWas South Korea’s COVID success really attributable to testing?

My hunch: The Korean model won’t fly in the U.S.

The HIV model is operative, but the number of infectees and contacts is much larger for the coronavirus.

How much bigger?

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A recent Gallup survey found that, on average, even during the lockdown, people make infectiously close contact with about **10 people** each day.

For details, see:How many social contacts are people having during stay-at-home?

:Technical discussion

Let’s think about that Gallup number for a second.

The definition “infectiously close contact” makes sense.

But, what about theone-day time frame?

What we’d really like to know is the number of infectiously close contacts that an infected person makes when they are contagious. That’s more like a week or two.

That bumps the number of contacts up as high as 140.

Of course, the list can be pared down to contacts that arefrequentduring the infectious period, that are oflong duration(versus a simple “hi, how are you?”, andunmitigated(e.g. no masks or other spread inhibiting devices)

In real life, patients can be questioned to identify the most susceptible contacts based on those criteria.

We can’t do that so…

For the sake of illustration, **we’ll just run with #C = 10** … that’s probably a low-side estimate of infectiously high contacts, but high enough to make our point.

Note: In real life, an arbitrary limit can be set on the number of traced contacts to be notified and tested … 10 strikes me as a reasonable number.

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OK, let’s run** a scenario using: R0 = 3 and #C = 10 / day.**

Assume that a diagnostic surveillance test is done to ID people currently infected.

We’ll start with just 1 of those ID’ed infected people.

Since we’re assuming that #C=10, they have 10 contacts that need to traced and tested.

We’re assuming that those 10 are the “right” population of contacts for our initial infectee, so with R0 =3, 3 of the 10 are likely to test positive … and 7 are likely to test negative.

Note: If the 3 people that our infectee infects come from a contacts’ population greater than 10, the numbers that we’ll be running would get worse since even more contacts would need to be tested. Trust me on that, for now.

So again, at the first level of trace & test, 10 traced contacts get tested.

The likely outcome: 3 positive results, 7 negative results.

But now, we’ve identified 3 more infected people.

We need to trace & test their 30 contacts (3 x 10). With R0=3, 9 of the 30 are likely to test positive.

So, at the 2^{nd} level, we’re up to **40** total tests run … and **12** infected people identified.

Let’s run the process for one more level.

The 9 positives from level 2 have 90 more contacts that need to be traced & tested. With R0=3, 27 of the 90 are likely to test positive.

So, at the 3rd level, we’re at **130** total trace & tests … and **39** identified infected people.

For completeness, let’s run the numbers out to consider the old 6 degrees of separation…

That runs our totals up to **2,430** trace & tests … and **729** identified infected people.

**Keep in mind, that’s for just one infected person identified in the surveillance survey.**

Based on NY tests, if 1,000 people were randomly sampled, we’d expect at least 30 people (30%) to test positive.

For details, seeSqueezing the NY antibody test results

The scale-up numbers are simply multiplicative, so that would get us up to **72,900** contacts to be traced & tested … based on an original 1,000 person surveillance test panel … and some relatively conservative assumptions.

Whoa, Nellie … **72,900 !**

That’s a lot of tracing & testing.

Scale up to, say, 5,000 people in the initial random sample surveillance testing … and, you’ve essentially tested an entire small city.

That’s not surprising … it just validates the old 6 degrees of separation concept.

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If you’re not interested in statistical minutiae, it’s ok to skip this technical section…

Technical question:Hey, isn’t there double counting going on?

The implication: If yes, then the trace & test process is more manageable than it appears in the above scenario.

The argument: Social networks overlap. If Joe and Bob are infected and Jim is friends with both Joe and Bob, then Jim is traced twice … he’s being double-counted. And, if Jim tests positive, then his contact tracing is likely to flag both Joe and Bob. That’s circular tracing that double counts both Joe and Bob.

There’s some merit to that argument, but the unique nature of the coronavirus largely neutralizes the apparent statistical issue.

First, once a person tests positive, they should be removed from the population and not retested since they have likely developed some level of immunity. Retesting them would be double counting.

But, a contact who tests negative, most probably needs to be retested if they are traced from more than one identified infected people.

Key point #1: Testing negative today does not necessarily mean that you’ll test negative tomorrow.

Implication: The “statistical unit of observation” isn’t just a person. It’s person-day combination. For example, Jim on Tuesday is a different observation than Jim on Monday (that is, unless he tested positive on Monday).

Key point #2: People who test positive in a surveillance test are likely to be at different stages of their infection and its contagiousness. For example, Joe may be near the end of his infection and Bob may be at the early stages.

Implication: Jim would only be a double count if Joe and Bob are equally contagious on the same day that they have contagiously close contact with Jim. Otherwise, Jim is two statistical observations, not one (e.g. Jim-Monday and Jim-Tuesday).

My take: That “same day” scenario is possible, but not statistically significant. So, it isn’t worth fretting about.

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__Takeaway__: We’re dealing with a broadly infectious virus that has a head of team already. The trace & numbers grow exponentially.

**Said differently, the trace & test program makes sense conceptually … but, in real life, quickly gets unmanageable. **

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**If you’re more of a visual person than a quant jock**, here’s a way to visualize the trace & test mathematics.

In this classic 2-minute scene, just imagine that Lucy & Ethel are contact tracers and each of the chocolates is a contact to be traced. You’ll get the idea,

May 1, 2020 at 5:18 pm |

There’s double counting in the analysis. Chances are people are part of the same “community” so you end up in closed loops for a non-trivial number of cases.

The problem isn’t if it’s feasible because it is (at the end of the day we “only” need to track 350 million ppl). The real problem is that people – particularly in deep red America won’t cooperate and “name names.” The alternative of “smart” contact tracing via phones would also not fly in the US

May 3, 2020 at 9:00 am |

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