So Omicron gets discovered and it was only a matter of when the case counts in my fine state started to go up. It seems that 12/8 is when it began here. Similar to Greg Abbott in Texas, our governor, Ron DeSantis, says either nothing or something stupid. Any mitigation in this state will be voluntary by people, and thus be lagging in effectiveness.
I came to choose 12/8 as a starting point not only by eye, but by also examining the rate of change in that 7 day moving average curve. 12/8 is a day when the direction of the change changed…
Like any good exponential function — or in this case NEAR exponential (it’s actually the Logistic function), we see rapid growth after a modestly slow increase.
The logistic function, is the solution to Verhulst’s Equation, which is often used to model population growth that slows down as a “saturation point” is approached. To be really geeky, the daily new cases curve is the first derivative of the Logistic function — really called the Logistic Distribution...
Now, I’ve been lost in estimating these logistic curves in a Finite Difference world — that is in a spreadsheet. So the “rate” parameter I use and put in the following figure is influenced by 2 choices I make in my model — I use 300 “days”, and I model the time value in the actual calculations from -5 to +5. From playing with this spreadsheet for a year and a half I’ve figured out that the interplay of these 2 variables can lead to the exact same curve...it’s hampered me in try to play COVID forecaster in the past…
So I don’t really know how to put k=8.25 into pure math terms...but
- That is a value I have NEVER had to approach previously in my math games
- It is about 5 times as high as the K factor I was deriving in the July-August surge, early in the surge
So I think we can conclude this is spreading fast. How fast?
Well, let’s look at a the Delta surge from 7/7 through 7/22 of this year compared to the “Omicron” Surge from 12/15*:
By my calculation this surge is 160% faster, so far. A few days before I calculated 77% faster...oh boy.
Now, polishing off a turd — err, my forecasting tools, I started to try and fit the data from 12/8 to 12/23 on Christmas Eve. The following model was the closest to the data that came in for Friday — but had a modest number of expected infections for the state — about 600K (recalling these models are for 7 day moving averages, real #’s might be 25% or so higher). That seems low compared to the figures I’ve seen quoted from IHME and our local university (USF). They are saying 40k or more a day here in FL mid to late January I think. I’m getting a peak on 12/30 in this model:
Note — Tc (=300) is the number of “days” in my model, Ts1 is the first time step of that 300 that is used in the curve fitting.
One thing I noticed over the year and half of using these mathematical methods to model case surges is that in reality the K factor (roughly speaking the growth rate) and A (the expected number of infected people in the surge) don’t stay constant. K tends to drift down, A tends to grow larger, leading to surges that last longer than one would expect doing the simple math.
So that led me to think of another way to look at the estimate of A. In the APR discussion something triggered me to think of basing A off of the rate of testing done in the state. For Florida it works out to roughly 1 test per person in the state per year, so a 6 week period (kind of an arbitrary, wild ass guess). Would give about 2 ½ million tests. I suspect we 1) might see more, and 2) are going to see a ridiculous positivity rate in these test in January...so I decided to use ~2/3 of that number (1,750,000) for A in the next model, using a K factor cut in half:
This one peaks a bit higher than the estimates I’ve seen/heard...but the timing is closer to those estimates. This one peaks 1/12/2022 at about 58K new cases a day (again, 7 day moving averages are being modeled here)…
Now — another frightening estimate I’ve heard (I think from Peter Hotez, not some jamoke) is 1 million cases a day for the country. If Florida contributes it’s population percentage to that that is 60-70K a day in this state. I decided to do another arbitrary, wild assed bit of math to mash the two models together...with the slower, larger model not contributing anything until Christmas Eve, where I add 5 % of that model in, and each day increase it another 5%. So in 20 days (1/12/2022) this model is adding the 2 separate models together, but by the time we get to 100% of model 2, the first model is fairly small and getting smaller faster and faster…
This gives me a 2 week plateau from 1/1 — 1/15 2022, between 60 and 70K a day...which is close to the million a day scaled up the USA population. It still seems to plateau too rapidly…
Now, considering that the at the start of the Delta surge I was calculating K factors of a bit under 2, maybe the 2nd model should slow down even more (take K lower than 4), perhaps adding a few more unlucky MAGA’s/anti-vaxxers to the stats (bump A up to 2 million)?
Without actually plugging the numbers in and looking at the results, I’d suspect that might make a shorter plateau further out in January, at perhaps a little lower peak. So this will be the signal I’m suspicious about in the data, but going to take a week before the Christmas Crash subsides, and then we’ll have a New Year’s crash. So we might not be able to really get a good read on where this is going for another week and a half. If I recall, Hotez made a comment recently about what a joke data reporting in this country. A very fast moving virus exploits this failing…
So, please be safe and be well.
* orginally 12/8, but this figure shows when the growth took off quickly