Same here. I had two years of español in HS and probably couldn't say anything more than "good morning" or conjugate a verb or two. Then I went to work on a concrete crew. By payday I had a really good grasp of la jerga.
As usual, @bill93 has it right. The Algebra 2/Pre-calculus problem that we usually lead off with is the heroic worker who is to be rewarded whatever number of grains of wheat he wants for whatever heroic deed he performed. His choice is to fill a chess board with wheat, starting with 1 grain on square 1 and doubling for each successive square. Square 2 has 2 grains, square 3 has 4,square 4 has 8 and so on. The 64th square will have 2^63 grains, ~9.223 * 10^18, but the worker also has the contents of the other squares. His total wheat is the geometric sum of 64 terms beginning with 1 and having a common ratio of 2.
If the daily reported new cases is the measure,then the situation is analogous to the wheat problem. If cumulative cases are tracked, then it's a straight exponential growth problem.
Problem is, that growth rate is not constant and it's not constrained to behave well. For NC, I track what I have, and that's the cumulative number of positive coronavirus tests. On March 16, that number was 38. Today, it is 1,307.
But here's the rub. From 3/16 to 3/19 the daily exponential growth rate was 0.312. From 3/27 to 3/30, it is 0.179. So the growth rate in that number has slowed dramatically. Our UNC epidemiologist who predicted 4,000 cases by 4/2 also predicted 1,000 cases by 3/29. Yesterday's number was 1,040, she did her numbers on 3/16, so I think that is a numbers victory.
If we carry the 0.179 exponent forward to 4/2, we get 2,239 cases vs the 4,000 predicted earlier. Nothing is certain, but it looks like we're slowing and our shutdown and social distancing are starting to work very well.
Given the declining exponential rate, we can also now fit a logistic curve to the data. This curve is often used in predator-prey models because it models the limit on the size of a population. Used in covid-19 context, it gives a very, very rough idea of the maximum positive tests we will see. That number for NC is 1,953.
Note that the max from the logistic curve is less than the 4/2 number for 0.179 exponential growth. That's because the logistic model is using a decreasing rate and the other one is using a constant rate.
These are naive models because they identify no causalities and no linkages to population or anything else other than time. Real professional epidemiologists know what they're doing and should be listened to. People like me should be regarded as mere curiosities.
But real epidemiologists don't share a lot of detail with us. Maybe they need a board like this one.
Call it Realepistoday.com.
The Institute for Health Metrics and Evaluation has modeled sickness, hospital beds needed, intensive care beds needed and ventilators needed for each state.
Go here:?ÿ https://covid19.healthdata.org/projections
and find your state in the pull-down list in the green bar.
Then coronavirus will kill millions...because the additional stresses are huge. We might say our responses kill millions, but that is pure 20-20 hindsight, if that happens.
@flga
Ours already has! In fact, he designated pot stores as essential...so our trade is looking better and better?
Lets all remember that any projection of this sort requires subjective inputs.
Absolutely! For example, the model projection for NC for today is 591 hospitalized. The actual this morning at 11:00 was 137. That can change quickly, but it really looks as though our state-wide actions have had an effect.
Dr. Fauci spoke your point yesterday. He said, and I paraphrase, that tracking is as important as predicting.
I always liked naive models when I did forecasts for corporate planning. For the short term, like a few days in this case, they work very well. I really don't think that anybody can predict either the peak date or the numbers for that date right now. But we can look for interruptions to trends and try to interpret them. And in the end, any forecast is judgement regardless if it's based on assumptions or adjusted ad hoc from prior experiences.
My bosses always had a great attitude toward me. Their philosophy was to throw away the forecast but keep the forecaster. Future numbers are often worthless, but forecasters often develop valuable insights.
Let's hope the end to this thing comes before we expect it.
I am reminded of Harry Truman saying that he wanted a one armed economist - one that couldn't say "on the other hand". There is just so much we don't know. We don't know how many people have the virus, mildly, and haven't sought medical help. We don't know how many people are in hospitals but haven't been tested yet. We don't know how many positive tests haven't been reported and recorded (see Caucus, Iowa, 2020). We don't know - for sure - how long this thing incubates, nor how long it takes to recover, nor how it takes for a victim to become clear. We don't even know if a person who has had it can be re-infected. And so on. I've got to think that any projections we see today are, at best, highly conjectural.?ÿ?ÿ
The model posted last week predicts 431,000 total deaths in Texas with Social Distancing.
The model Math Teacher just posted predicts 4,150 total deaths in Texas. That is a very big difference.
I know which one I am rooting for!
James
Right again. I really don't think that anyone can predict either the timing of the peak or the number of sick people at the peak, for the reasons that you listed. Same for hospitalizations, ventilators and all the other numbers. Governors need estimates of future numbers, though, and the epidemiologists are the only ones who can give us those with any degree of confidence.
A week-old forecast is worth very little. The cycle, process new data, update the model, produce a new forecast, needs to be repeated daily. That will cause forecasts to bounce around some, but they will stabilize. Examining how the forecasts react to recomputing with new data can introduce judgmental factors that can improve them greatly.
i saw somewhere that the early models assumed that each sick person would infect between 2 and 3 others. The measured, and that's got to be way below survey-grade, numbers are looking more like between 1 and 2. Things like this is where judgment comes in. Is this a trend that's going even lower or is it an anomaly that's going to reverse?
i see the infection rate slowing in NC and for the US as a whole. But that's not the case in New York or Louisiana. Neighboring states are locking down their borders with those states, probably the right thing to do, but scary.
So, forecasts are unreliable but totally necessary. Let's hope that the ones we're seeing now are biased toward the high side.
@holy-cow My daughters employer is covering her cable bill for the next three months or when the WHO determines this pandemic is over. Good for them.
Then I went to work on a concrete crew
Davy Crockett and Jim Bowie were standing at the wall at the Alamo. They see 10,000 Mexicans coming up over the hill. Jim turns to Davy and says, "Are we pouring concrete today"?
