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A challenge for college/university re-opening plans.

Assume there are approximately the same # of circulating cases in August as there are now, a reasonable assumption given plateaus.

If so, how many expected positive #COVID19 cases will there be when classes begin?

A thread
First, although answers differ by state, let's start with a national metric... ~270K cases in the past 14 days reported via @COVID19Tracking, which given 10:1 under-reporting could mean 2.7M new cases in the past 2 weeks (or more).
Not all will be infectious at the same period, so we might get to ~1M active circulating case (conservatively, assuming 4-5 days of typical infectiousness).

Answers will vary based on geographic and socioeconomic profile of students.
Hence, in this simplest scenario, there may be a 0.3% chance that a random individual is infected if things stay about the same for the next 2 months (1M cases divided by 330M Americans).
With a 1/330 odds that someone is infected, how many individuals would arrive to campus infected in a school with 20,000+ students...

Answer: 60 (thereabouts)
But then what happens?

If universities test everyone (students, staff, and faculty); there will be delays in logistics, analyzing, reporting, and tracking. Given where we stand now, testing 25,000-30,000 people won't be easy (the 20,000 students + 5-10K of staff/faculty).
By the time one learns of the few dozen (or more) initial cases; even the best-laid plans will face a reality: students will have sat together in 'low-density' classrooms, passed close-by in dorms, parties, dining halls, gyms, etc.
Moreover, unlike 'ramp-up' periods now underway, staff and faculty will no longer be circulating in largely empty research and teaching buildings, but moving in and out of high density spaces.

And, this will bring with it new risks.
The age distribution of faculty shifts into the far more dangerous part of the age-stratified risk category for #COVID19, e.g., 37% of faculty are 55 or older (compared to 23% of the US population):

cupahr.org/wp-content/upl…
Moreover, how will universities take steps to protect 'essential' workers (facilities, food service, and more) so that re-opening does not further exacerbate the socioeconomic and racial disparities of #COVID19?
An initial group of 60 cases could lead to nearly 200 new cases within ~1 week; at which point the capacity for isolation, quarantining, etc. would become difficult given the high-density living situations on campus.
Partnership w/state health departments notwithstanding; everything we can do (collectively) to reduce circulating cases before the Fall will help make it possible to restart more safely.
And, before starting back: how will colleges/universities try to identify cases at the outset; and react accordingly?

One way: at-origin testing for all students before they travel to on-campus residences.
Steps that colleges take to reduce initial infectious case count will help efforts to minimize new transmission via mask-wearing policies and other on-campus initiatives.
In contrast, delays in identifying infected cases (and who potentially has been exposed) means that there's a greater chance for local spread that may rapidly exceed a college's ability to track, trace, and manage cases, and make a Fall term infeasible.

/end
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