Tracking and Predicting the CoVID-19 Pandemic

On tracking and predicting the CoVID-19 thing. Disease grow exponentially. Exponential growth works like compound interest. You get paid based on how much you have, and then that gets added to what you have and you get paid on that. if you get 10% interest compounded annually, and you keep $10 in the account for five years, you get:

$10 times 1.1 times 1.1 times 1.1 times 1.1 times 1.1 = $10 times 1.61 = $16.10

By the same token, each sick person infects on average some number of other people, and when they get sick, they each infect that same number, and so on. The number of cases on one day is equal to the number of cases on the previous day times the growth rate. The average growth rate I'm seeing from the CDC.gov data since the beginning of March is 22%. Every day, 22% more people are getting sick. If you have some "historical" data, you can predict the growth rate. If you don't have historical data (numbers with dates) you can't predict anything.

The trouble here is that the number of cases (and deaths, by the way) starts to grow so fast that it gets really confusing, and it all starts to sneak up on you. The numbers are sort of trundling along when all of a sudden BOOM! it goes from "bad" to OMFG! That's bad enough, but it's also hard to tell if our prevention measures are doing any good, if it's getting worse, or maybe starting to get better. You can't tell -- it's a bunch of whacky numbers going up and up.
Note also that we can't see a connection between the total cases and deaths. Are people dying at the same rate? Spoiler alert, the death toll is going to take off and shoot up just like the total cases, but I'd sure like to know when and how many. Can't really see that here. 

One way to get a grip on this is to look at our numbers in terms of how fast they're growing, instead of their scary, galloping day to day values. This can be done with the logarithm (which is the "inverse function" of the exponential -- it flattens it out). We take the logarithm of the total cases against the logarithm of new cases each day, and that should (we hope) give us some idea of how it's growing.
The numbers on the sides are now powers of ten (2 = 100, 4 = 1,100, 5 = 100,000). The flat line means both new cases and deaths are growing exponentially at the same rate, not slowing down. What we want to see is both lines turn and drop straight down (China and South Korea did this). They aren't doing that, so we are not on top of this yet, so it's going to keep getting worse. Notice how we can start to compare the death rate and the infection rate, by the way, unlike with the first chart.

Okay, we have a clear idea of what's happening, so now it's prediction time.

Back to compound interest. We have an infection (and maybe death) rate of 22%, so that's 1.22 compound interest multiplier.

Idaho Governor Brad Little "locked down" the State of Idaho on March 25 -- stay at home, only essential businesses, etc. Other Governors had already taken that action or did so around the same time. Let's assume that's going to make a difference. Let's also assume that for fourteen days after that, we'll still see new cases from people already infected and so forth, so we don't expect to see the impact until two weeks later, or April 8.

The latest CDC numbers I have are 103,321 cases on March 27, which is twelve days before April 8. So I assume that the epidemic will continue as it has done, and then hopefully start to drop off during the week leading up to Easter. So the growth we'd expect to see based on these assumptions would be:

103,321 times 1.22 (times itself 12 times = 10.9) = 1,120,000 total cases by April 8

Assuming 22% growth rate for deaths, the total could be 14,000 to 18,000

So our health care system will be overwhelmed (no more beds) by then. Another bad thing is that if unslowed, it will be over two million by Good Friday, and deaths could be over thirty thousand by then. Of course, if the disease kills ten percent, then we'll eventually have a hundred thousand more deaths from the infections up to that time.

Anybody can track whether this prediction is correct by just following the CDC numbers as they come out each day. Hopefully we'll see it slow down before Easter, and this is how to tell. This is not difficult math for someone with a BS in engineering or mathematics (or even accounting), and everybody should understand it.

Anyway, that's my two cents


PS: Please post comments, including if you find anything that looks like an error.

No comments:

Post a Comment