Last week I wrote about the alarming math of a viral pandemic. We talked about how infectious diseases spread exponentially , not linearly–and how that can clear what seems, for weeks, like a little problem unexpectedly extremely, very big. That’s the challenge faced by managers: Sometimes the only way to avoid disaster is to take action before it seems warranted.
As an example, I worked some lists from the CDC on total cases of Covid-1 9 in the US. On Monday, March 16, the weigh was 4,000; by Wednesday it had grown to 8,000. If you carried that out in a straight line, you’d say: Hmm, it’s increasing by 4,000 every two days. Then you’d expect 12,000 lawsuits on Friday and 16,000 by Sunday, March 22. Oh, if only.
Instead, abusing an exponential growth simulation, “youre telling”, what’s the rate of growing? And you see that the digit double-faced from Monday to Wednesday. If it continued at that rate–increasing by 100 percentage every two days–you’d have prophesied 16,000 lawsuits on Friday and 32,000 by Sunday. Well? As I write this, on Sunday, March 22, the official tally is 32, 644.
That’s exponential rise. If it continued on the same path, we’d have a million occurrences really 10 epoches from now, and inside of a few months, each person in the US would be infected. Now for the good news: That’s not going to happen! Things will get bad, but not that bad, and today I’m going to show you why. That simple exponential modeling, it turns out, goes us only so far.
Recall why an outbreak spreads exponentially at first. Say you have a certain number N of polluted people, and each of them( following the pattern above) infects a new person every two days. So in two days, there’s twice as many people( 2N) carrying the virus. Then each of these foul a new person, for a total of 4N, and so on. The more infected people there are, the more new people get infected at each step. It’s a blowout freight train.
In general terms, we wrote this as an update formula, where the change in total cases( DeltaN) per time period( Deltat )– let’s define this as one day now–is proportional to the total( N ), and that proportionality point, a, is the percentage daily illnes rate.