I heavily disagree on the doubling time being closer to 7 days.

If you have a look at Germany who is having a very good overview of the spread of the pandemic since testing is free, available, and done rapidly (5h turnaround time ) capacity for 12.000 tests a day ) you get a close to 3 day case doubling time currently if you look at the official German numbers from the Robert Koch Institute. And we'll start seeing in a week or two how good the drastic containment measures they are starting now are impacting the growth or viral spread.

11.03.2020 1,288.00

12.03.2020 1,567.00

13.03.2020 2,369.00

14.03.2020 3,062.00

15.03.2020 3,795.00

16.03.2020 4,838.00

In a country like the US where the Author makes his calculations the government frankly has zero clue how many people are infected already because testing is not free, not available and not rapid ( current turnaround 3 -5 days ) for most citizens. There is a chance that the case doubling time is worse, or bigger, but if Germany who had a lot better reaction to the viral threat is having problems reaching a case doubling time of 6+ days and if you think about that China is at 80.000 cases now but put the most drastic containment measures in at only 600 confirmed cases there is a huge probability we are all in for a very wild ride.

That said every day counts because there are promising randomized control studies going on in China which hopefully give doctors access to a drug they can actually help people with. Right now all they can do is support your breathing and pump you full with a cocktail of meds they have no idea if it will work for the specific patient or not. Everyone who lands into ICU with Covid-19 is basically a guinea pig for the rest of us healthy people at this point.

In the end all that matters right now is that we don't know enough about the illness to treat it effectively, and we are in desperate need of time because no government was prepared for a pathogen like this that usually is a once in a century event.

P.S: This is a current snapshot. If the containment measures like in China are working the case doubling rate rises quite fast. China is at over 21+ days now. But I think it's important to take this day by day and re-evaluate the numbers. The "doomsdays predictions" will most likely be wrong and just a theoretical numbers game.

You're probably right that Germany has the most trustworthy numbers. The numbers you give work out to 30% growth per day, a 2.6-day doubling time; https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pa... says Germany is at 6245 today, very close to the 6304 you'd predict from your numbers, although the Robert Koch Institut hasn't updated their page yet.

So, what accounts for the difference? The paucity of international travel (but then why is the spread so much slower in every other country — Germany is hardly famous for close physical contact with strangers)? Or is it just that Germany's comprehensive testing is allowing them to detect almost all the cases, while everybody else is underestimating by a factor of 10 to 50 or more — a constantly exponentially growing factor?

It seems unlikely that the pandemic was growing by 30% per day since December; it would have already infected 450 million people. Can we really impute that difference entirely to containment measures?

There is a simple explanation why the spread in Germany seems so much higher. If we look at how the virus spread in Germany we get a very good explanation.

It all started with a small cluster around Munich that showed up around the end of January ( 27th ) as the first confirmed case in Germany came back from business travel to China that was contained rather quickly as everyone involved did a great job isolating and breaking the infection chain and everyone involved recovered without severe symptoms just like any other flu for most mid-aged and healthy people. Then for a good month there were no confirmed cases, so no more drastic containment measures were taken.

After that the Government carelessly allowed Carnival in Germany to happen thinking they contained the virus and severely underestimating the threat it could pose. Carnival is one of the biggest celebrations in Germany each year with millions of people from all over the country coming to see, especially the Cologne Carnival on the 24th of February. While in general you are not wrong when you say "Germany is hardly famous for close physical contact with strangers” the carnival season and Oktoberfest are the two occasions where Germans do voluntarily have a ton of contact with strangers and party heavily. The Rhineland is famous for their carnival all over Europe and in some parts of the world. If you look at pictures of it you’ll see what kind of nightmare this is if you have a potentially deadly pathogen spreading silently during the celebration from an epidemiologist point of view.

Three days later a couple from the region were the second and third confirmed cases that heavily participated in the celebrations while already being sick. Remember Covid-19 can be contagious up to 14 days before a patient shows symptoms. On top of that there was no chance to break the infection chain because the man is still in critical care and couldn't talk to officials and the woman had no idea where they could have been infected because they had contact with hundreds, possibly thousands of people over the course of the celebration days until the husband fell critically ill. So the lack of care from the Government together with gathering of hundreds of thousands of people from all over the country in close proximity, kissing, drinking and standing head to head in a crowd paired with that there were no tests done on people with covid-19 symptoms for a whole month between the munich and heinsberg cases is most likely the reason for the explosion in case numbers.

Also remember we are basically looking into the past up to 14 days as people who need hospitalization now have been infectious for up to that timeframe and just now start getting very sick. This is an incredible different pathogen to deal with and easy to underestimate because of this. To fight a pandemic you need to know the number of infected people, if you know someone is infected that gives you a fighting chance to break the infection chain if you isolate all people they have been in contact with. Unfortunately because of the huge celebrations this was impossible to do and we are where we are now.

"while everybody else is underestimating by a factor of 10 to 50 or more" this could very well be the case. With the numbers of infected people we see travelling outside Iran there are estimatons that a large part of the population is already infected. 7.5 Million people registered on an Iranian website that allowed for symptom screening. You usually don't register for such a site if you don't have any symptons that could be related to Covid-19. Just to show the difference between the real reported numbers and what could be likely.

If you ask about the containment measures, yes they work incredibly well, but at the cost of gigantic economic damage and right now I don’t want to be in the shoes of any leader in any country that basically has to decide between saving lifes now and that there also needs to be a good future for the survivors of this crisis afterwards. It’s horrible to think that up to 25% of a certain population and age could die. But it’s equally frightening to think that depending how long this takes millions of people and their families could lose their homes, jobs and potentially starve because we have an almost complete economic shutdown across all sectors.

France has officially announced that it's doubling every 3 days as well. Definitively not 7 days now.

> closer to 7 days (10% growth in cases per day) than to 3 days (41% growth in cases per day).

A doubling time of 3 days corresponds to 26% growth per day (not 41%), because 1.26^3 ≈ 2.

You are of course correct. I don't know how I made such a glaring calculation error in the first place or how it slipped past me. That explains why Italy's doubling time is so close to 3 days (it's doubling every 4 days) despite being so much less than 26% growth per day. Thank you for the correction.

Could you expand on your observation regarding the true growth rate? I don't think that's accurate. Italy's outbreak is entering its fourth week, they have a very constant daily factor of ~1.33. Most countries are on the same trajectory. The only ones to have slowed down are China, South Korea and possibly Iran, though I really doubt the Iran numbers.

You can see that here, all the others are linear in a log plot: https://studylib.net/coronavirus-growth

Even Italy hasn't been over 23% in over a week; over the last week they've averaged 19% growth per day, far from the constant 33% you allege:

    >>> (24747/7375.0)**(1/7.0)
    1.188799592827802

That's a 4-day doubling time, which is how they've outdistanced every other country in the world. Presumably if the Italians would put on some masks and kiss each other less† they'd get down to the same kind of rate as China, Korea, and Iran.

More broadly, we're currently at 167676 confirmed cases worldwide; the first day we have numbers for is January 16th, when there were 45 cases. It's been 59 days since then (31-16+29+15) giving a 15% daily growth rate

    >>> (167676/45.0)**(1/59.0)
    1.1495551283620273

but some of that 15% is the discovery of several thousand existing but previously undetected cases over the next several weeks. So the overall growth rate is a little lower than that 15%.

(If the Italians were to keep spreading the disease at this rate, by mid-May they'd have more cases than the entire rest of the world; unfortunately for the plausibility of this prediction, their case count would have to be over half a billion people at that point, requiring vast influxes of guest patients from the rest of the world to meet such a quota.)

I did projections at the beginning of February based on a 3.5-day doubling time (22% daily growth) which was what we seemed to be seeing at the time. They said it would infect the majority of the world's population in February. That didn't happen.

† Hey, I'm guilty of this myself; the last time I kissed somebody I'd just met that day was, like, Tuesday. Here in Argentina we can expect rapid contagion.

Given 1% IFR for the people from the cruise ship, where everybody was able to be treated properly (or properly enough for this paper's estimate):

https://cmmid.github.io/topics/covid19/severity/diamond_crui...

and the current number of deaths in Italy: 1809 one could come to the estimate of actual number of infections in Italy being around 180K people. That big number is real only if Italians managed to treat that many cases as good as it was possible before the hospitals were overwhelmed. What's probably true, however, is that their hospitals already reached their limits and now the number of deaths per infection raises compared to the ideal case, lowering the number of actual infections.

But even not using that estimated "bigger number" Italy reports 24747 actually confirmed cases.

And assuming that the DNA analysis of this Italian researches is right, Italy's strain must have reached Italy not before January 19th:

https://www.reuters.com/article/us-health-coronavirus-italy-...

Even starting from one person at that date we get, for the number of confirmed cases a factor of close to 1.2 per day, or for the assumed cases (a bigger number) 1.24 per day. That gives doubling time between 3 and 4 days, and never longer than that.

Note that even a difference of using 24K or 180K infected can't give the factor you suggest: 1.15.

That's only observing Italy. I don't know if you are combining Chinese development, where they indeed contained the spread on their territory, with Europe and the rest of the world, where no comparable actions happened (and the actions taken still haven't significantly slowed down the growth), but if you do, that's not proper use of the data available.

These are good points. I hope the disease's course in the world to date proves more typical of the pandemic from here on out than its course in Italy, which is substantially more alarming.

Yeah, I misremembered the growth rate in Italy. But check out the reference that I provided, most countries are in the high 20s / low 30s, many of them for multiple weeks.

If there really was a 10% "true" growth, and higher growth was just testing capacity ramping up, you would see very few straight lines in that plot. Yet that is what you see in all cases except for China, South Korea and Iran.

Also, you can't look at the world-wide growth rate since January like that, since that includes a period where the total number of cases was totally dominated by Chinese cases, but China had slowed already. Actually, the fact that you get 15% by using this approach which substantially underestimates the growth shows that 10% is way too low.

Maybe, you could be right. Certainly Italy and Spain have already exceeded South Korea's cases per capita, as well as deaths per capita: Italy, Spain, and South Korea have respectively 1809, 335, and 75 deaths†, with populations of 60.3 million, 46.7 million, and 51.7 million, for rates of 3.0, 0.7, and 0.145 per 100,000 population to date. So it's implausible that South Korea's dramatic improvement is due to a much larger number of subclinical cases saturating the population and preventing further spread, and I understand that their testing is quite comprehensive as well, so it probably isn't due to underreporting either (which in any case is less likely for death rates); if that's true, it would seem that the only plausible conclusion is that containment is working in South Korea.

I think it's reasonable to expect that similar containment measures will be put in place in most countries soon, though, so perhaps it's not unreasonable to take them into account when trying to estimate future growth rates.

† https://en.wikipedia.org/w/index.php?title=Template:2019%E2%...

The distinction 'kragen is making is between actual cases (total number of people with the virus) versus cases confirmed via testing. The daily growth of ~33% probably reflects increase in testing capacity more than increase in actual cases.

Here are some studies supporting the doubling time estimate of 6-8 days:

https://wwwnc.cdc.gov/eid/article/26/5/20-0146_article

https://www.nejm.org/doi/full/10.1056/NEJMoa2001316

https://www.thelancet.com/journals/lancet/article/PIIS0140-6...