So, there are Governors in several states that are opening up their economies this week. They insist that they are going to do this in stages, following CDC guidelines and will monitor for spikes in the disease so that they know if they need to dial back those openings. Even without substantial testing available, they are convinced that they can manage these openings safely and allow their citizens to go back to work and earn a living.
We are all aware of the inherent problems with this strategy including:
What if you open your restaurant and no one comes? Who pays for the employee’s salary?
How do you prevent people from other states coming into yours and bringing virus with them, or taking it back home?
How do you enforce the rules and regulations?
Every state will need to deal with those questions. My interest here is not with those questions. I am more interested in the issue of “monitoring for spikes”. Here, the politics are in direct conflict with the arithmetic. Let’s see why.
For this simple example we need to make some basic assumptions, and I will try to use conservative numbers.
We will consider a “model state”.
We will assume that on the first day of opening the economy, 200 people state-wide who had not been previously infected, acquire the virus. (using 200 is just to make the calculations easy, you can scale it up or down based on your own estimates).
We will assume that the doubling rate of infection is 3.5 days. (this is a conservative number, but it allows us to use the numbers to make our calculations per week easier).
We will assume that of the infected population 80% remain asymptomatic.
We will assume that the overall death rate for infections is 0.5%. (this is a very low number compared to what we actually see in the field).
Now we can look at what happens in the state after opening the economy.
On DAY-1, as we said, we will assume that in the entire state, 200 people get newly infected because they encounter someone who is shedding virus, not taking appropriate precautions, or is unaware that they are contagious. We can call these 200 people the NEW-200.
For the Governor, there is no evidence of this happening anywhere in the state.
On DAY-7, at the end of the first week, the number of infected people, just from the NEW-200, will have doubled twice, first to 400 and then to 800. So now the number of new infections is 800.
At this point 80% will be asymptomatic, but 20% of the NEW-200 will begin to show symptoms. In other words, 40 people who were infected on DAY-1 will begin to show symptoms.
The Governor will be happy because there is no evidence of any spike in disease at the end of the first week. Any disease seen that week will be part of the previous wave of infections and may well be decreasing. All very good signs.
On DAY-14, at the end of the second week of the reopening, the number of infected people, just from the NEW-200 will have doubled twice again, first to 1,600 and then to 3,200.
At this point the very first patients from the NEW-200 will begin to show up at the hospital. Of the 40 that showed symptoms a week earlier, 20 will be admitted to the hospital.
The Governor will be even happier because so few new cases are being seen, and he may now begin to ease up on the reopening even more.
On DAY-28, two weeks after admission to the hospital, the first patient will die. At a lethality of 0.5%, from the NEW-200, ONE patient will die on DAY-28, but the inexorable force of arithmetic will now have doubled the infections FOUR times since DAY-14; first to 6,400, then 12,800, then 25,600 and finally 51,200.
Now a full month into the reopening, the governor, happy that there have been so few deaths will be claiming victory and justifying his/her early decision to open their economies.
HOWEVER…. There are now over 50,000 new infections in the state. And of those 50,000 new infections, and with a lethality of 0.5%, over the next few weeks an additional 2,500 people will die.
By the time the “spike” is actually identified, the state will be deep into the next wave.
Please, please, please; I don’t want to be told in July, that “no one ever expected this to happen; we had no idea that this could occur.”
This is why testing is so critical to the package. If you were doing statistically valid random testing of the community, you could actually see the increase in infections a month before you saw the healthcare impact. Without the testing, you are flying blind.