Exactly this! I kind of understand the WHO, the broad public, including media, doesn't care about models and such things. Providing to much details can have the opposite effect, instead of calming things down it could spark more fear.
On the other hand, online stuff like said growth hacker can draw a lot of attention. This will end up in the mainstream. That diseases aren't exponential, who cares when exponential curves fit so nicely early on.
What could, and should, be done by large tech companies is preventing this. Google could make sure that every Corona related search ends up showing the WHO on top, followed by local sources like the CDC, Robert Koch, John Hopkins and so on. They could support these parties in getting them up in the search results. Facebook could do the same, as does Twitter. In Germany, you have to explicitly include Robert Koch or RKI in your search for the link to show. Even by doing so, earlier today it still wasn't the tip link. The rest is reporting crap written every time a new case was found somewhere.
> That diseases aren't exponential, who cares when exponential curves fit so nicely early on.
Shouting this point does more bad than good. Outbreaks are exponential in their initial stage, to an extremely good level of approximation. Sure, they're ultimately s-shaped, but we're far from the bend point. That the growth starts to deviate from the exponent a tiny bit when half of your country is sick isn't a useful observation right now.
You don't have to wait until half the country is sick, though. If you restrict movement, you see a sharp reduction in transmission when you start getting neighborhoods hitting 50%. Some will get there faster than others.
So how do you explain South Korea? Their cases have decisively peaked. So one of three things happened;
1) Herd immunity has kicked in, meaning a majority of people have already been infected and are recovering/recovered
2) Containment measures were effective against a highly communicative virus which can live in the air for 3 hours and on surfaces for up to 12 hours.
3) They just stopped testing and/or are lying about the results and are hiding the resulting health care burden.
IMO the only one here that doesn’t require competency on the part of the government is #1, making it by far the most likely scenario.
If #1 is true to any extent, then it means IFR is actually quite low, more like 2009’s H1N1.
The other fundamental question I keep going back and forth on is the final total population infection rate. For H1N1 and other flus it’s usually on the order of 10-30% of the population. (There are arguments why this one might be higher, although I think some people confuse exposure numbers with infection numbers...)
Containment supposedly will not meaningfully reduce this ultimate number but would just slow down how long it takes for everyone to ultimately be exposed.
So while there are very few new cases in China (and they are closing their temporary hospitals) what happens when people go back to work?
When comparing countries (e.g. Italy against South Korea), you have to consider many factors.
Cultural factors: how quickly do people change their habits, to do e.g. social distancing. Do people in public wear surgical masks. Population density, temperature, weather,...
Lying governments: I don't think South Korea or Italy are lying, but Iran is for sure, and China up to some point (at least early on). Italy stopped testing at some point, but this is known. South Korea increased testing over time.
Herd immunity: maybe a part of the population was already immune before (too early to say), but it couldn't have "kicked in" during this year as there was only one wave yet.
There is no question whatsoever that this corona virus IFR is a lot higher than the 2009 H1N1 flu, but lower than the 1918 H1N1 flu. When comparing countries / regions, you should consider the population age pyramid (Italy has more old people than South Korea) and how overwhelmed the hospitals are (I think quite bad in Italy and Wuhan).
A co-worker from Italy told me. But you can find this for example here as well: https://www.aljazeera.com/news/2020/03/italy-south-korea-dif... "Italy started out testing widely, then narrowed the focus so that now, authorities do not have to process hundreds of thousands of tests." (I don't normally read Aljazeera... just found this using Google.) It matches what my co-worker told me. See also https://www.worldometers.info/coronavirus/covid-19-testing/ (I have no clue how reliable that source is)
I live in Italy and I'm not aware of any changes in the procedure for testing.
If I read the worldometer link you provided what I see is that both on March 2nd and on March 9th Italy was second only to Korea in number of tests performed and that we moved from 386 tests per million people to 1005 in the same period. What am I reading wrong?
Yup. But to make that point, you have to show the trend that the disease will follow if you won't restrict movement - and shouting that "it's an S curve, not exponential" isn't particularly helpful here.
But the early stages of disease spread _are_ exponential. And I find that people really fail to understand the meaning of that, and how scary numbers like "new confirmed cases doubling every two days, 500 new cases in France yesterday" truly are.
The problem is, exponential for how long?
For instance, all seems to indicate measures in Italy are taken too late: and the exponential growth is still happening there (almost 3 weeks after the problem started)
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
it = pd.read_json('https://raw.githubusercontent.com/pcm-dpc/COVID-19/master/dati-json/dpc-covid19-ita-andamento-nazionale.json',
convert_dates=True).set_index('data')
plt.plot(it[['deceduti', 'totale_casi']])
plt.xticks(it.index.values, rotation=90);
It's to early to say. The people who are popping up with symptoms now might have been infected up to two weeks ago.
If you look at the Wuhan data, you see that the lockdown worked, but the number of confirmed cases at the time continued to rise dramatically until 12 days after the lockdown went into effect. We are only three days in on the Italy lockdown.
Yes, but extrapolating the early exponential phase is, plain and simple, mathematically wrong. No idea why data scientists aren't going the first mile and look up the relevant functions before spitting data out. Total fail on their part, IMHO.
It's not wrong: it has produced extremely good predictive results day after day for total cases outside of China for months now. Using a simpler approximate function in place of a more complicated exact function is far from wrong, it is bread and butter for getting practical results in all areas of science.
Countries that implemented extreme measures to slow the spread of the virus. It will be different for countries which haven't. The WHO and other health officials around the world are saying the same thing. This will spread to a large number of people. It's too late for containment, you can only hope to flatten the curve. That's why it's now a pandemic.
Unless you simultaneously ramp up your healthcare resources (what China did), even as "low" as 100 cases/day still has very real potential to go exponential (R0=2.5), overwhelm your healthcare, and kill 10% of our population if not more (especially if your population is aged).
I hear that, what I'm saying is, follow that logic through... If it's crucial to maintain strict protocols even during a rate of only 100 new cases/day, that means these protocols stay in place roughly... indefinitely.
Counting individual cases and deaths in a country of 300 million is nonsensical. You could do the same thing with the flu and you'd hit 20,000 deaths a year and you'd destroy the economy in the process.
IMO, the solution is best preparing to treat the number of people who do become severely ill from it, and getting the rest of the country fully back to work as quickly as possible.
Although I disagree strongly on the "kill 10% of your population" bit, which is just fear-mongering, it's kind of besides the point.
>Although I disagree strongly on the "kill 10% of your population" bit, which is just fear-mongering, it's kind of besides the point.
If every case went untreated, 10% is a reasonable guess about what the death rate would be. Unchecked growth would lead to almost every case going untreated. That's the penalty for allowing the number of active cases to rise above five times the number of open beds/ventilators.
Mathematically wrong is not a relevant category here. There is no "ground truth" that is approximated by an exponential growth. Every disease model is counterfactual "spread of the disease if no countermeasures were taken", etc...
Modelling the beginning of an epidemic as exponential growth is useful, sensible and empirically validated. As, countermeasures are taken during the beginning of the epidemic, for discussions of the effect of countermeasures, exponential is the correct model.
In fact, hopefully the countermeasures taken will be sufficient that the intrinsic disease dynamic will never get past the exponential stage...
If you find any source, idealy scientific papers on the subject, that shows that contagious diseases can be modelled with simple exponential functions, please share them. I am not an expert on that matter, so I would be really interessted to see some reliable sources confirming the use of exponential functions.
Notice that the rate of change in the infected population (dI/dt) is proportional to the current number of infected (I) and the current number of susceptible (S).
In the early stages, when S is large and I is still small, this acts just like an exponential function in I.
For example, think about what happens when you double I the first several times. S stays relatively unchanged, and so dI/dt roughly doubles each time you double I.
Yeah, exactly. In the beginning exponential, later on not anymore. Without changing the equation. So, no, not exponential. Because, you know, very early on an exponential graph can approximated by something non-exponential. Would be utter BS, sure, so nobody does it.
Exponential growth. It's the growth phase that matters.
People keep mentioning the exponential because both of these curves, at an important point in time, grow very fast. Much faster than anything you're likely to encounter in daily life, so the public really doesn't have the requisite intuition.
But I can see you're not interested in understanding the point. You asked for equations, I gave you equations. Good day sir.
We are, I think, not disagreeing at all. May sound crazy, but bear with me a second here. I know that the initial phase of any epidemic is exponential. Key are these three small words, initial growth phase. Because they make all the difference, as every epidemic will ultimately peak.
These three words are simply to often drowned out in discussions about COVID-19. That's we you see extrapolations of this growth against, for example, the population of Italy. And this is dangerous. And I don't think we disagree here, I never disputed the exponential nature of the early phase.
We just shouldn't make the mistake in assuming everybody catches these three little words, especially not online.
The most critical question everybody is trying to answer right now is, when the peak will be. And whether this peak will to high for our medical infrastructure. With all the measures being taken, the conclusion seems to be the point will be too high. Hence the counter measures. So we should all do what we can to flatten the curve as much as possible. I never said anything else, and honestly, I don't see where are disagreeing here.
S = N - I - R, and lets used normalized ratios, so i = I/N, r = R/N, etc... so the dynamics of i are given by:
di/dt = beta (1 - i - r) i - gamma i
di/dt = (beta - gamma) i - beta (i^2 + ri)
At the beginning of the disease, the ratio of infected and recovered is very small, say 1e-5 for 100 cases in a population of 10 million. So initially the second term is 1e-10 whereas the first is 1e-5. The initial dynamics of a new disease are given by:
di/dt ~ (beta - gamma) i
exponential growth. It will start deviating from exponential growth once i becomes large enough. If 10% of the population have had the disease it will deviate from exponential growth by 10%. Once it gets to half the population being infected or recovered you start seeing a real deviation.
In reality this might never happen, because we are taking a lot of measures to get beta down. So really you have something like
di/dt ~ (beta(t) - gamma) i
where beta(t) will capture all the countermeasures people take. If the countermeasures are effective and manage to push beta(t) below gamma before a large chunk of the population is infected, we might never see non-exponential behaviour from the disease. It will have an exponentially growing phase, and then an exponentially shrinking phase.
---
Here is just one paper I found with two seconds of google that looks at this, very recent, a bit basic:
"The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic, and is also closely related to the basic reproduction number."
"Classical compartmental transmission models assume exponential growth during the early phase of a well-mixed population"
Key word, initial. Later on, not so much. Which is the whole point, pandemics aren't exponential over the complete run time. So, why not using these formulas at least in the models instead of using exponential equation limited by world population?
Edit:
"It will have an exponentially growing phase, and then an exponentially shrinking phase"
Confirming the point above. Math is a precise science, it's a while since I did stuff like that, but getting equations right or not used to be a big deal back than. And now we talking more serious things than just a grade in an exam.
Okay you're just trolling now. We are very much in the initial exponential phase of Covid-19. As I derived above, once you get to 10% you might start seeing deviations from exponential in the SIR model. The bump that you saw in China is not due to this deviation from exponential growth behaviour. We luckily never got close to 10% infection. It's due to getting to negative exponential growth. The beta(t) part of my answer above.
You're free to use whatever sensible model you want in your analysis, but you are criticising people for using exponential models. You have no arguments for that. Then you throw out Wikipedia, falsely claiming that exponential models are nowhere to be found there. Then you demand peer reviewed studies that use an exponential model, which I provide. But somehow that is not enough either.
In fact there are numerous assumptions in the SIR/exponential growth model. These might not hold. We might get slightly sub-exponential growth in some diseases. There is vast literature on that. But the base line in all the vast literature on this is that the most natural, obvious and common behaviour is exponential.
> The rest is reporting crap written every time a new case was found somewhere.
This is the problem. Not that our institutions are failing to deal with the problem, but that our media has vastly overblown the whole situation in order to scare everyone witless so they'll keep clicking on news updates and watch those ads.
With the secondary effect, of course, that all searches for information end up at a media outlet trying to scare people, and not the appropriate primary source of suitable information.
And the tertiary effect that an institution presenting non-sensationalist data based on research is dismissed as an "inadequate response" if it doesn't match the hyperbolic media frenzy.
We should be shutting down newspapers, not schools.
People keep turning to the media because our institutional outlets provide inadequate information for the majority of the population. The institutions default to saying nothing useful because they are scared of blow-back.
I check my city, county, state, and world health sites and there is simply inadequate for my needs. I want to know what closures are in place in my community. I want to know if asymptomatic transmission is real. I want to know if there is a plan to widen the testing criteria.
That's the problem, yes. I still ignore the media, others don't. Both approaches are fine. The thing is, the media doesn't have any other sources, do they? But the have to produce content, so they do. Not very helpfull in the quality department if you ask me.
I would say that broadly speaking, media is better than the institutional outlets for providing information.
You have to sift through the garbage, but the content exits. to use the topics I listed above as an examples, I can find more details on local closures and outbreaks in the local news the local department of public health. Similarly, I have found coverage and links to medical journal publications embedded in articles. Lastly, the institutions are avoiding disclosure of next steps or plans like the plague ( no pun intended). Either they have no plan for the days to come, or they are intentionally withholding information. On the other hand, there are a number of media outlets, mostly non-traditional, that are providing projections based on other counties.
That is true and I agree. I would just point out that the unfortunate reality we live in is that the government sites are doing a terrible job of informing.
+1! And just to be sure, I would add social media.
But in all seriousness, I am absolutely disappointed with the reactions of Google, Facebook, Twitter and YouTube on this. Everybody made a well deserved fuzz about the 2016 US election. So these companies are absolutely aware of this. Now that the stakes are much higher. Still no response, no action.
What are you suggesting exactly? Do you want them to delete "alarmist" posts? That sounds like a recipe for a total collapse in trust in public institutions.
No, just giving the top search spots to updates from WHO, followed by the national, regional and local sources. Play with the search algorythm to push the more alarmist ones further down.
Help the above mentioned institutions to write their "content" in a social media optimized way. That would be agreat opportunity for these tech giants to gain trust they lost since 2016. Not doing anything right now moght very well have the opposite effect.
The WHO waited an extra month before declaring a pandemic, and US national sources are generally considered by experts to be understating the severity of the issue. What you want is the top slots to go to the experts, who are not necessarily ranked correspondingly to the hierarchy of political bodies. For example the top virologists are probably in labs and universities, not the Cabinet.
WHO has been shouting “take action now” the whole time and the official stance was “it could be stopped if governments act now.” Governments didn’t listen, so here we are. I fail to see what good declaring a month earlier would achieve, as governments clearly don’t give much of a crap about WHO advice unless the situation is seemingly spiraling out of control. One likely outcome of declaring one month earlier is being taken even less seriously; they can’t just re-emerge a month later and declare it’s really a pandemic this time.
That's why I didn't inlcude the cabinets, did I? Just in Germany, the relvant data comes from the WHO (global picture), Robert Koch Institut (national), state health ministries (regional) and community health authorities (locally). All are relevant, the international numbers show the large picture, inlcuding the declining cases in China. The national ones provide more detailed insights into the country in question, while the regional and local ones are the most actionable for you. Which schools are closed, which policies are in place and whay. Stuff like that.
I would prefer to not get these from some journalist writig his tenth article today.
Personally, I am also very cautious with virologists taking the cable news and talk show turs right now. Where are they taking the time from to do so? If they are spokes people from institutions, it is different. But if their function is "professor at university X", my gut feeling tells me that they might like the public attention a tad too much.
>But if their function is "professor at university X", my gut feeling tells me that they might like the public attention a tad too much.
This is a very interesting perspective, which is very different from my own. Being in the US, my attitude is that officials are usually chosen based on criteria other than their skills in the domain they are administrating, and I would expect the best knowledge on any subject to be found among low-level people who deal with it professionally. I am also suspicious that officials might prioritize maintaining public order over disseminating true information, which caused many unnecessary deaths during the Spanish Flu.
>I would prefer to not get these from some journalist writing his tenth article today.
That's true enough. But I would rather have information from front-line experts than administrative officials.
Second that, I would love to hear from the frontline guys. But I don't. It is either elected officials (fair enough, that's part of their job) using input from said experts.
You don't hear from the frontline people / orgs, I assume because the are simply too busy right now. Which brings me back to the professor acting basically as a free agent. That should change.
The professor is the front-line guy. I'm talking about epidemiologists, not physicists. If he wasn't acting as a "free agent," then you would be back to hearing from elected officials, who are mired in compromises and not entirely trustworthy.
if you think the WHO are not the best people to be dealing with this problem, that's a different problem than thinking that the WHO are not the best organisation to be dealing with this problem.
The WHO are literally the organisation we specify to deal with this problem. If they're staffed with the wrong people, that's a different problem.
I think it would have been terribly irresponsible to forcibly give the WHO top billing back when they were arguing nobody should restrict travel, or to suppress news of the preparations starting to take place in SV when official US authorities were universally saying it’s not a big deal.
Exactly. This. It's a Big Deal because of the media frenzy, not because of the inherent lethality or virality of the disease. We've seen similar pandemics before, without this media frenzy.
The WHO is making science-based responses, which are then perceived as "inadequate" by a public stoked into a frenzy by the media. The media are not motivated by public good, but by profit. The more scared you are, the more times you hit refresh.
We should definitely give WHO top billing on search results, because these are the people we've entrusted to do exactly the right thing in response to this situation. Giving top billing to profit-driven media companies is utterly irresponsible.
Or if we've got this wrong, then sack the WHO and appoint a half-dozen billionaires to their role. Same same.
On the other hand, online stuff like said growth hacker can draw a lot of attention. This will end up in the mainstream. That diseases aren't exponential, who cares when exponential curves fit so nicely early on.
What could, and should, be done by large tech companies is preventing this. Google could make sure that every Corona related search ends up showing the WHO on top, followed by local sources like the CDC, Robert Koch, John Hopkins and so on. They could support these parties in getting them up in the search results. Facebook could do the same, as does Twitter. In Germany, you have to explicitly include Robert Koch or RKI in your search for the link to show. Even by doing so, earlier today it still wasn't the tip link. The rest is reporting crap written every time a new case was found somewhere.
And yet, nothing like that happens.