Modeling the Spread of COVID-19: Part 1 - Why a lockdown is still needed

As the first wave of COVID-19 in the United States starts to recede, at least for those of us in the Northeast, there is talk about reopening and going back to school in the fall (or even before that), because, well, it's been long enough, dammit!   Current plans are that Pennsylvania will reopen on June 26th according to the governor's office.  Their guidelines for "going green" are that:

"A target goal for reopening was initially set at having fewer than 50 new confirmed cases per 100,000 population reported to DOH in the previous 14 days."

This sounds pretty reasonable, right? 

What does this mean?  There are 12.7 million people in the state of Pennsylvania.  So if you take the number of new cases, divide it by this population, and then multiply by 100,000, you will get the number of cases per 100,000 population.  As of June 21st according to Google, there were 464 new cases in PA.  So 464 cases out of 12.7 million (the population of PA) is 3.6 per 100,000 individuals.  This means we're safe, right? 

Not so fast! The guidelines don't call for fewer than 50 new confirmed cases per 100,000 per day, they are stricter than that.  They call for fewer than 50 new confirmed cases per 100,000 per two week period.  Using the data from the state's own website, we can quickly get this total for the last 14 days - and it is 6293 new cases in two weeks.  This divides down to 49.55 cases per 100,000 as of today (June 22).   Therefore we must surely be safe!

I want to point out that in the context of the epidemic thus far, this number (while impressive sounding) is ultimately pretty arbitrary.  While it is true that there are more options to treat and there is more contact tracing, the number of new cases yesterday, 464, is 23 times higher than the number of cases per day on March 16, one day after the lockdown in PA began.

On March 15 in Chester County, Pennsylvania, the schools closed, and a lockdown was initiated. On March 16, according  to the county data dashboard, there were 16 positive COVID-19 tests.  The reason the curve shown above is falling is due to mitigating measures.  Going "green" at a point where we have many more cases when things started removes many such measures and ensures that the curve will rebound.  This is especially true in light of the fact that PA does not currently have sufficient contact tracing.

Unfortunately, the virus doesn't particularly care about our preferences, politics, or anything at all, really.  It's an inanimate bit of genetic material in a protein and lipid capsule which is a little nano-machine.  It doesn't set out to give you pneumonia or to clot your blood, these are side effects of its replication program, and evolution has determined that by behaving in this way, it has the maximum chance of replicating.  (Note: it's not even trying to replicate, replication is just all it can do.)  Furthermore, depending on the R value (which is the number of individuals infected per person infected), the growth rate of this can well go exponential.  Starting with 464 new infections per day is much worse than 16 as in March so far as exponential growth is concerned.  So unless I miss my guess, we're going to be back to square one or worse in 2-3 weeks, and the Northeast, and PA in particular are going to have a second wave.