Introduction, disclaimer, and a call to action
Similar disclaimer as the last time: I'm not a medical or a public health professional, but I am a data scientists. I deal with probabilities, statistics, and analyzing risks all the time. I've been looking at the coronavirus pandemic for some time now, looking at multiple sources of data. I consider myself to be well-informed, and my analysis to be sound. This is what I see, as of now (early morning hours of March 16th).
If we do nothing, this coronavirus will infect a large portion of the population (say, 50%), overwhelm our health care systems, and kill a significant portion of those it infects (say, 3%).
IF we do nothing, the numbers cited above results in 5 million deaths in the United States, and more than 100 million deaths worldwide. These numbers are so absurd that it doesn't even matter much if you somewhat disagree with my assumptions. You think the mortality rate will only be 1%, and only 25% will get it? It's still a complete catastrophe.
IF we do NOTHING, this will be the worst catastrophe in American history, and one of the worst in all of world history.
IF we do nothing.
The most important word in the above paragraphs is not "million", "death", or "catastrophe". It's "if". "IF we do nothing".
And that's why I DON'T think the above scenario will play out. But ONLY because we'll do something about it. We WILL ACT. We will not simply sit by and let one of the worst catastrophes in human history play itself out.
We will act to break the exponential propagation of the virus, limit its spread, and flatten its growth.
We will act to achieve what we already know is possible: China and South Korea have already broken the exponential growth of the virus, and they have successfully limited its spread to a tiny portion of their population. With any luck, Italy will soon see similar results, on the time scale of a couple of weeks (the incubation period of the virus).
We will act to save people, and bring our daily life back to normal as soon as possible. If we act strongly enough, it's still possible to keep the deaths below the numbers from last year's flu. Even if we have three major American cities blow up like Wuhan, that's still only about 10,000 deaths. And we will all be able to look back on this as merely a short, interesting time in our history.
But only because WE WILL ACT.
Looking into the future
To be sure, we have already taken some actions. But we're all wondering whether we've done enough, and how things will turn out in the future. After all, it's the future that's scary: people often report and comment on the current numbers, but I think this is a mistake. The current numbers, of themselves, are insignificant. It's what they portend for the future, under the assumptions of exponential growth, that's the cause for alarm. That's why it's so important to break the exponential, through our efforts of social distancing and better personal hygiene.
But will we succeed? Well, we are fortunate in this regard, because we can, in effect, look into the future. There are a number of countries that contracted this infection before the United States, and they're correspondingly ahead of us in the virus's growth curve. By examining these countries, we can effectively look at the multiple-choice future presented before us.
Taiwan is an ideal case: They've effectively succeeded in keeping the virus out of their country, and it's never reached significant numbers there. Of course, this scenario is closed off for the United States now. It's too late.
South Korea is also a really good case. They had a significant outbreak, but they've successfully broken the exponential, and their number of cases are flattening out. And they did it without having to lock down an entire city - instead using measures like contact tracing, aggressive testing, and tracking personal data.
China has also successfully broken the exponential growth, and they have very few new daily cases now. They did have to lock down Wuhan and several other cities to achieve this. This draconian measure is widely considered to have been a right, necessary move, although it might not have been necessary at all if the CCP didn't cover up the initial reports of the infection.
Italy locked down their whole country just a few days ago. Like in Wuhan, their health care system was overwhelmed, and their mortality rate is exceptionally high. Hopefully, they'll begin to see the results from the lockdown soon.
Meanwhile, Iran is digging mass graves. Reliable numbers from there are hard to come by.
So, those are the range of possible futures for the United States. Which one will we take? That depends on what we've done so far, and how we'll act going forward. Have we done enough? Should we do more?
United States status report
Here, I'm going to give a VERY ROUGH estimation of where I think we are, and whether we're doing enough. In the absence of other, more specific information, this could help you to inform your actions.
But again, I am not a medical or public health professional. I'm basing this only on broad, mostly publicly available data. If any local government or health authority gives out any specific information, advice, or order that contradicts anything I have to say below, please listen to them instead of me.
One thing that needs to be addressed right away is the appalling failure of testing in the US. This makes everything more confusing, and it means that we're significantly under-reporting the true number of cases, even compared to other countries. This makes everything harder, everything worse.
However, some people have used this as an excuse to postulate that there are a truly vast number of undetected cases out there. I am not much moved much by such a postulate, for two reasons: 1) I find it unlikely, and 2) if true, it would actually be good news in an unexpected way.
First, I find it unlikely because the number of deaths here in the United States have are still fairly limited - and deaths are much less likely to go undetected. Again looking at the data across countries, we see that the US has about the same number of deaths as South Korea. And we know that South Korea has 1) had extensive testing, and 2) has the infection mostly under control. So their number of reported cases must be somewhat close to the number of true cases. This implies that if the US also had extensive testing, we'd also have roughly 8000 reported cases, and that the total cases would not be too much larger than that, order-of-magnitude wise. You can do a more sophisticated calculation taking into account things like doubling time and time-to-death, but I don't think the numbers will change very much for this order-of-magnitude calculation. The United States probably has something like 20,000 - 90,000 actual cases, but probably not 500,000 or a million. Other estimates, for example from this excellent article, also puts the estimates at 5 to 30 times the number of reported cases, in its estimates from San Francisco Bay Area, Washington state, and Wuhan.
Secondly, if we really did have a million undetected cases, then that would actually be good news, because that would imply a very low mortality rate for the virus. Apparently most of these million people were largely asymptomatic and never in any real danger of dying. This remains true even if you back out the typical time-to-death after contracting the virus. A million undetected cases, after backing out the time to mortality, would imply a mortality rate of about 100 deaths / 100,000 cases = 0.1%. That would mean we can go back to treating this like a bad flu.
So, the most cautious and reasonable approach would be to assume roughly 10 times the reported number of cases. This is good enough for my rough, order of magnitude calculations below, and I'll proceed with that number going forward.
Other numbers I'll use here are:
2% mortality rate, multiplied by 3.5 to account for the mortality of the 2.5 other people you're likely to infect. So if you get infected, the chance of you dying, or directly getting someone killed, is roughly 7%.
15% of active cases generate new cases every day, if we do nothing. This is in accord with a doubling time of 5 days, and a R0 of about 2.5.
Then your personal risk of causing death - your own or the ones you directly infect - on a given day can be estimated by:
fraction of population that's reported to be infected
* 10 (to account for true vs. reported cases)
* 0.15 (15% growth rate per day)
* 0.07 (chance of causing death, given infection)
All this again assumes we do nothing to avoid infection. These number and calculations are, again, rough, but they're serviceable for an order-of-magnitude estimation. Note that there's a single parameter that largely determines how bad things are - the fraction of population that's reported to be infected.
Let's work through how things change as we increase this number. This will tell you how much danger you're in, and whether you're doing enough. Again I remind you that this is only a ROUGH ESTIMATE, under the assumption that we do nothing, and that you should defer to any information from local governmental and health authorities.
But with all that said, if the fraction that's reported to be infected in your city is:
At this level, your daily risk of causing death is about 1 in 10 million. This is less than your chance of dying in a car accident in a given day (1 in 3 million)
So there isn't a whole lot of risk to your personal safety at this level. The risk is less than driving. But you should still pay attention, stay vigilant, and prepare. Governments, being larger than individuals, needs to start acting at this level or sooner, because If we do nothing, in just a few weeks, the fraction will become...
Daily risk of causing death: 1 / 1 million.
Other fatality rates for reference:
car accident: 1 / 3 million days
sky diving: 1 / 160,000 jumps.
sky diving has about the same life-expectancy loss as smoking a pack of cigarettes.
You should definitely take personal precautions at this stage, beyond just "wash your hands" and "don't cough on people". After all, when you drive, you put on a seat belt and make sure you're not drunk or tired. You put your kids in a car seat. You get insurance, and pay thousands of dollars for extra safety features on your car. But at 0.001%, if we do nothing, the level of danger due to the coronavirus is distinctly higher than just driving.
America, as a whole, is at this level (4000 cases / 330 million population = 0.001%). But your numbers for your city are more important. They'll affect you more directly.
Los Angeles county is slightly below this level (70 cases / 10 million = 0.0007%. All local case numbers come from here).
The state of New York, and the San Francisco Bay Area, are both ABOVE this level (700 cases / 20 million population = 200 cases / 7 million population = 0.003%). Santa Clara - the hardest hit county in the Bay Area - is higher still, at 0.005%. In these areas, going about your day normally, without any precautions, is about as dangerous as skydiving. Would you go out to eat if you had to skydive to get there? And smoke a pack of cigarettes on your way back? Then don't go out. I personally have started working from home. If you must leave your house, take a LOT of precautions.
If we do nothing, in a just few weeks, the fraction will become...
Daily risk of causing death: 1 / 100,000
about the same life-expectancy loss as smoking 2 packs of cigarettes.
Wuhan went into lockdown at around this level (1000 cases / 10 million population = 0.01%). This makes perfect sense: As a city leader, if every citizen in your city started smoking 2 packs a day, would you not do something? Especially when faced with the prospect that this number will double every 5 days or so?
Another way to think about it is that this is the last level where some kind of "normal" life is possible. The levels above this one - 0.1% and above - rapidly approach the worst case scenario I described at the very beginning, where a good chunk of your population dies. 0.1% reported infection rate would mean about a 1% actual infection rate, and it's hard to see how you can stop that from growing to a significant portion of the population. So there isn't a whole lot of time left at this 0.01% level. Drastic actions are required.
Seattle (King and Snohomish counties) is ABOVE the 0.01% level (460 cases / 3 million population = 0.015%). Meaning, the ONLY thing that'll keep Seattle from going Wuhan is its social distancing/personal hygiene efforts up till now.
Has that been enough? Well, in order to break the exponential, the R0 (reproductive number for coronavirus) needs to drop from 2 - 2.5 down to below 1: that is, a reduction to 50%-40% of its normal value. Everyone needs to reduce their chance of infection to those values, through social distancing or better personal hygiene. Now I've looked at some data on this, and it seems like Seattle is just at the cusp of that 50%-40% value: that is to say, SEATTLE MAY NOT BE DOING ENOUGH. No American city is doing enough yet, but at least the other cities have a little more time. For Seattle, the time for drastic action is NOW.
I'll not say whether Seattle needs to go into total lockdown, like Wuhan or Italy. I remind everyone that this is only a rough estimation, made under the assumption that we do nothing. And Seattle has certainly been doing things. They're engaged in extensive social distancing measures, and many of their citizens are aware of what's at stake. But even that may not have been enough. Right now, every option - including total lockdown - should very much be on the table for Seattle.
For the rest of America - watch Seattle. Pay very close attention. Remember, this is effectively looking a couple weeks into our future. If it turns out that Seattle hasn't done enough, then we'll all know that we need to redouble our efforts.
Italy, as a whole, is distinctly above this level (25,000 cases / 60 million population = 0.04%). It's not at all surprising that they shut the whole country down.
If we do nothing, in just a few weeks the fraction will become...
Daily risk of causing death: 1 / 10,000
Taking on this level of risk every day is very likely to cause a premature death (on the order of 50%). This is therefore a completely unacceptable level of risk, and any city or country that finds itself in this situation needs to do everything they can to get themselves out.
If we do nothing, in just a few weeks the fraction will become...
Daily risk of causing death: 1 / 1000
This is effectively the worst case scenario detailed at the beginning of this post. A big chunk of your population will die. Everyone keeps saying "don't panic", but if ever there is a time to panic, this would be it.
An important takeaway here is how quickly we progress up these levels IF WE DO NOTHING. From 0.001% (where we are as a country) to 0.01% (where cities and countries start shutting down) is only a matter of weeks. Seattle is there already. And if we go much above that, we quickly approach the completely unacceptable, worst-case scenario.
Another important takeaway is that no American city may be doing enough. We need to break the exponential growth. We need to reduce R0 - from 2 or 2.5, down to below 1. That's a reduction to 50%-40% of its normal value. My best guess right now is that we're hovering around 50% in our major cities - not enough to be certain of breaking the exponential. Seattle is taking this the most seriously, but they also have the least time.
It may be that Seattle turns out to be an example and a warning to the rest of the American cities. It may need to completely lock down, and that may cascade into other cities to taking equally drastic measures.
But now is still not the time to panic. Keep calm. Stay safe and healthy. And take the necessary actions to safeguard yourself and your community.
You may next want to read:
On the coronavirus
The intellect trap
Another post, from the table of contents
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