simsim314 wrote: March 28th, 2020, 9:17 am
I'm also believing corona will continue for half a year so new economical opportunities with the internet technologies should come up, as the market always adapts to new situation. If free market is trying to emulate evolution, so now it's the time when the meteor hits.
It may last until a vaccine or some other effective treatment exists, which is longer than half a year. If we get the raging pandemic under control, we may have something like a new normal of fighting brush fires around the globe with localized lockdowns. There will be new economic opportunities, of course, and already are. But it will be a long time before those opportunities make up for the losses, and many people will be left out.
I am very confident (rightly or not) I could get this virus and survive. However, I have an immune-suppressed family member who I need to protect, and an aging mother on the east coast in her late 90s and susceptible to just about any kind of health risk. For all that, I think what I fear most is a breakdown of the social contract, and the sense that even many people who think they are prepared for this have no idea what they're really in store for.
The sanguine view of just riding out the mortality rate is completely ludicrous unless people suddenly stop demanding modern medical care. A society that could promise nothing better than bedrest and noodle soup for COVID-19 could avoid the worst of the disruption and just carry on with some weeping and extra funerals. But we have higher expectations than that, and we should. The nightmare is that the cases and not just fatalities overflow our ability to handle them.
It amazes me when I see the stock market change daily, because I do not understand what they think they are pricing. It is like Feynman's analogy of "guessing the length of the emperor's nose." Collect enough opinions, and you get an aggregate value. But what does it have to do with reality? Nobody can see to the other side of this event.
Political leaders are uniquely unqualified for a variety of reasons, but even the smart ones among them are not usually smart about math. Even the so-called "business people" who at least should know how compound interest works. Nobody seems to react until it is at least two weeks later than their best shot of controlling spread. That is more forgivable at the beginning than now, when you can literally look into the future and find another country that looks like you're going to look in two weeks. The response in the US at a federal level has been so bad that I'm frankly ashamed of it.
True story: back in January, I thought of how we would not be building field hospitals like China because, well, first it's really tough to build anything on that scale in the US today with permit requirements, NIMBYism, etc.
But I comforted myself with the idea that we must have something better like super-high tech medical FEMA trailers. I just assumed, because I'm American, that we would address this competently if we needed to, just in a leaner more mobile way. Now I see how wrong I was about that. Italy looks bad today, but it will be sheer luck if the US escapes the fate of overcrowded hospitals and morgues. I don't see what we are doing to stop it.
I think there has been some attenuation in the growth curve, which was rising at a terrifying 35% per day at one point. The cases we see are the detected cases, and it's the actual cases, visible or not, that result in spread. (In fact, the visible ones can at least avoid further spread once detected.)
With that in mind, I was trying to come with a simple model of what these attenuated curves should look like. Obviously, the pure exponential is easy, but there are two other things I want to understand. First, we don't detect all the cases, and the curve I can see in the news is just the detected cases. Second, lockdown measures eventually have an effect, but there is a lag due to onset of symptoms. I am not an epidemiologist, so please don't see this as anything but a toy math problem.
Assume there is 1 "patient zero", that there is some rate of increase (capturing "basic reproduction number"), that detected patients stop spreading immediately when they are detected. Assume that once a quarantine is put in place, all further spread ends. Also, rather than try to model the actual lag in symptom onset, let's just say that anyone with the virus has a certain probability of detection on any given day. This is a gross oversimplification, but maybe it's enough to capture qualitatively how to see these charts. The visible part is simply the number of new cases
detected per day, or the cumulative number detected.
The interesting question is how bad is it really compared to how it looks. Also, how long after a quarantine is declared does it take to really see results (here the model deviates from reality because reality includes a step function of symptom onset).
The parameters are r (new cases as fraction of current undetected), s (detected cases as fraction of current undetected), Tq (time in days when quarantine starts). Pseudocode (does this work? got anything better? i.e. simpler, more faithful, or both).
Code: Select all
Start with n_hidden = 1
for t = 0, 1, 2, ...
n_new_cases = r * n_hidden if t<Tq else 0
n_new_detected = s * n_hidden
n_hidden = n_hidden + n_new_cases - n_new_detected
I started fiddling with this in a spreadsheet. I don't think it is good enough to bother fitting to real data. It is just to develop some intuition about the lag between taking measures and seeing significant results.
Update: Here is some Python code for the above. One trivial observation that if r=s, i.e. the percent of new cases is the percent of detected cases, then you get a linear growth model even without a quarantine. I.e., if we could just chase down these cases immediately, we might be able to keep things under control. Once again,
I am not an epidemiologist, and this speculation is for amusement only.
repl.it link to python
https://repl.it/repls/IntelligentTrivialServers
Code: Select all
n_hidden = 1
n_detected = 0
r = 0.1
s = 0.1
t_q = 200
for t in range(0, 100):
n_new_cases = r * n_hidden if t < t_q else 0
n_new_detected = s * n_hidden
print("%15.0f %15.0f %15.0f %15.0f" %
(n_hidden, n_new_cases, n_new_detected, n_detected))
n_hidden += n_new_cases - n_new_detected
n_detected += n_new_detected
Update 2: Of course, the quarantine doesn't have to be 100% effective. Instead of 0 spread, you could model it as anything below detection rate. However, I am trying to keep this very simple.
Update 3: The n_hidden curve up to the quarantine is simple exponential growth based on a recurrence n_hidden = n_hidden * (1 + r - s). After that, it is exponential decay n_hidden = n_hidden * (1 - s). The curve we expect to see reported n_detected is proportional to the integral of this piecewise function. It has an inflection point where the quarantine starts, and eventually flattens to horizontal. This is similar to China's curve of confirmed cases, which is a bit choppy around the transition.
https://www.worldometers.info/coronavir ... try/china/
South Korea's curve is interesting because instead of flattening, it continues on with linear growth.
https://www.worldometers.info/coronavir ... uth-korea/ Can they have really reached a steady-state where they detect new cases at exactly the rate they appear, so they do not stop the contagion, but catch just in time to keep it constant?