Tokyo Zombie Movie
The novel coronavirus (COVID-19) continues to spread globally, and at this point in its progress very few high-income countries have escaped its grip. On a per-capita basis Spain has 38 times the rate of infection of China, the US 10 times and Australia 3 times, but plucky Japan has only 0.3 times the infection rate of China. Until now the rate of growth has been low, with only tens of cases per day being recorded over much of February and March, but since last week the alarm has been sounding, and the government is beginning to worry. We had our first lockdown on the weekend, a voluntary two days of 自粛 in which everyone was supposed to stay inside, and this week discussion of lockdown began. This is because the previous week was a bright, sunny weekend with the cherry blossoms blooming, and all of Tokyo turned out to see them despite the Governor’s request for everyone to be cautious. Over the two weeks leading up to that weekend, and for perhaps two days afterwards, the train system returned to normal and Tokyo was being its normal bustling, busy uncaring self. But then on the week after that event the numbers began to climb, and now the government is worried as it begins to watch the numbers slide out of control. I am also now hearing for the first time stories of doctors having to find alternative ICU beds for COVID patients – still not a huge deal, because any one hospital does not have a large supply, but enough cases are now appearing to force doctors to seek empty hospitals elsewhere.
It is possible to see the effect of this party atmosphere in the data, and it offers a strong example of how important social distancing is. Using the data from the Johns Hopkins Coronavirus tracker (and making a few tiny adjustments for missing data in their downloadable file), I obtained and plotted the number of new cases each day, shown in Figure 1 below. Here the x axis is the number of days since the first infection was identified, and the y-axis is the number of new cases. Day 70 is the 1st April. The red line is a basic lowess smooth, not a fancy model.
Figure 1: Daily new cases by time since the first case
It is clear from this figure that things changed perhaps a week ago. New case numbers were up and down a lot but generally clustered together, representing slow growth, but since about a week ago the gaps between each dot are growing, and more dots are above than below the line. This is cause for concern.
However, it is worth remembering that each day the total number of cases is increasing, which means also that if you add the same number of new cases on any day, it will have a proportionately smaller effect on the total. We can estimate this by calculating the percentage change each day due to the new cases added on that day. So for example if there are 10 cases in total and 10 new cases are detected we see a 100% change; but 10 new cases with 100 existing cases will lead to only a 10% change. From this we can calculate the daily doubling time: the time required for the number of cases to double if we keep adding cases at the same percentage increase that we saw today. So, for example, if there are 100 cases on day 9 and on day 10 there are 10 more cases, the percentage change is 10%, and from that I can estimate that the number of cases will double after 7.2 days if that 10% daily change continues. This gives a natural estimate of the rate at which the disease is growing, adjusting for its current size. Figure 2 shows the doubling time each day for Tokyo, again with the number of days since the first infection on the x-axis. I have trimmed the doubling time at 20 days, so a few early points are missing because they had unrealistically high doubling times, and added a lowess smooth to make the overall pattern stand out. The vertical red line corresponds with Friday March 20th, a national holiday and the first day of the long weekend where everyone went cherry blossom viewing.
Figure 2: Daily time required for case numbers to double in Japan
Since the infection hit Japan the doubling time has been growing slowly, so that in February it would take almost two weeks for the number of cases to double. The doubling time dropped in March[1], which was also the time that the government began putting in its first social distancing guidelines (probably about late February); work events were being canceled or postponed by early March, probably in response to government concern about the growing number of cases, and this appears after two weeks to have worked, bringing the doubling times back up to more than two weeks. And that was when the sunny weather came and everyone went to hanami, marked on the red line, at which point the doubling time dropped like a stone. Back in the middle of March we were seeing between 10 and 40 cases a day, slow changes; but then after that weekend the number of cases exploded, to 100 or 200 a day, pretty much 4-6 days after the long weekend started. The following weekend was when the government demanded everyone stay in, and the city shut up shop; but we won’t begin to see the effect of those measures until tomorrow or this weekend, and right now the number of new cases is still hovering around 200 a day.
It’s worth noting that not all of these cases are community transmission. About 10% are without symptoms, and another 20% are having symptoms confirmed (probably because they’re very mild), which indicates the effectiveness of contact tracing in tracking down asymptomatic contacts. A lot of these cases are foreigners (something like 20-25%), and this is likely because they’re residents returning from overseas, and likely identified during quarantine/self-isolation (so not especially risky to the community). But still, even 70% of 200 is a lot of cases.
It’s instructive to compare this doubling time with some heavily-affected countries. Figure 3 shows the smoothed doubling times for Japan, the US, Italy and Australia. It has the same axes, but I have dropped the data points for clarity (I make no promises about the quality of these hideous smooths). The legend shows which country has which colour. Italy and Australia start slightly later in this data because their first imported case was not at day 0.
Figure 3: Doubling times for four affected countries
As you can see, Italy’s doubling time was almost daily in the first week of its epidemic, but has been climbing rapidly since they introduce social distancing. Australia’s doubling time was consistently a week, but began to increase in the last two weeks as people locked in. The US tracked Japan for a couple of weeks and then took a nose dive, so that at one point the daily doubling time was 3 days. Italy provides a really instructive example of the power of social distancing, which was introduced in some areas on February 28th and nationally in increasingly serious steps from 1st March to 9th March. Figure 4 shows Italy’s doubling time over the epidemic.
Figure 4: Doubling time for Italy
It is very clear that as measures stepped up the doubling time gradually increased. In this figure day 40 is the first of March, the first day that national measures were announced. Despite this, we can see from Figure 3 that it took Italy about a month and a half from the first case to slow the spread enough that further doubling might take a week, and early inaction meant that a month of intensely aggressive measures were needed to slow the epidemic, at huge cost.
It is my hope that Japan’s early measures, and aggressive investigation of clusters at the beginning of the outbreak, will mean that we don’t need to go into a month-long lockdown. But if Japan’s population – and especially Tokyo’s – don’t take it seriously now, this week and this weekend, Tokyo will go the same way as London and Italy. It’s time for Tokyo to make a two week sacrifice for its own good. Let’s hope we can do it!
fn1: Which the smooth doesn’t show, by the way, it’s an awful smooth and I couldn’t improve it by fiddling with the bandwidth[2]
fn2: A better model would be a slowly increasing straight line with a peak at the hanami event and then a rapid drop, but I couldn’t get that to work and gave up[3].
fn3: Shoddy jobs done fast is my motto!
Compromise and Conceit 
April 2, 2020 at 11:26 pm
I am hearing about the first test of a large random sample of the population of a continental European country other than Italy this week. If they publish the results that should be educational.
April 3, 2020 at 8:38 pm
I think Iceland did this and the results vindicated my research and theory – only 10% of cases are reported. I look forward to a larger sample!
April 4, 2020 at 8:33 pm
First result: of 1,161 workers in supermarkets, old-age homes, and hospitals in Austria tested on 29 and 30 March, six tested positive. That is a rate of 5 case per thousand population: on that date about 1 case per thousand had been identified in Austria (the national and regional figures don’t agree but it was about 10,000 cases in a population of 9 million).
April 10, 2020 at 11:31 pm
The tests of a random sample of 1,544 residents in Austria from 1 to 6 April for covid-19 by an agency called SORA suggests that between 10.200 and 67.400 residents were infected in that period. There were 12.200 known cases by 6 April. I can’t find estimates of false positive and false negative rates, they were using a PCR test called cobas® SARS-CoV-2.
https://www.sora.at/nc/news-presse/news/news-einzelansicht/news/covid-19-praevalenz-1006.html
April 12, 2020 at 2:02 pm
Just how important testing is: a comment on another blog sent me poking around in the US CDC stats database. US deaths from pneumonia and flu usually run between 1300 and 1600 weekly. From the first week of February this year they run over 4000 weekly. This tells us first that estimates in the absence of testing almost certainly under-estimate mortality a lot and second that the disease reached the US in early January – probably at about the same time that the Chinese identified it.
April 12, 2020 at 2:51 pm
Just how important testing is: a comment on another blog sent me poking around in the US CDC stats database. US deaths from pneumonia and flu usually run between 1300 and 1600 weekly. From the first week of February this year they run over 4000 weekly. This tells us first that estimates in the absence of testing almost certainly under-estimate mortality a lot and second that the disease reached the US in early January – probably at about the same time that the Chinese identified it.
The official US death count is 20,000. It is probably more like 45-50,000.
April 13, 2020 at 9:58 pm
Peter T, while the disease definitely reached the US in January I don’t think it was circulating to the extent that it was killing 2500 people weekly in February. I have seen an (excellent) conspiracy theory video about how the virus actually escaped from a lab in Maryland (I don’t believe the conspiracy; I say it is excellent in the same sense that Stranger Things is excellent) which makes the same point that flu cases have been very high this season; it also makes the point that similar over-active seasons have been seen before (I can’t remember the year, but I think the video said 2014 was another such year).
Pretty soon I think we will start to see robust research on mortality databases from some of these countries, and then we will really be able to see how widespread this disease was. I think we are going to find that the deaths due to this disease are contained to exactly when we confirmed it entered the country, and we are going to be staggered by how many people it has killed. Once the full mortality profile is known – which can take months, because of the time it takes to compile, clean, check and register deaths – only the craziest crackpots are going to be pretending it’s not a big deal, or that it can be confused with influenza.
But getting back to the testing issue, I don’t know how many cases in the various affected countries are being confirmed by testing and how many by clinical diagnosis. I think in some countries (the UK?) they’re no longer testing people who die at home or in care homes, and I read that in NY hospitals now they just assume everyone with a respiratory problem is COVID-19, because it’s dangerous for medical staff to assume otherwise. I don’t know if they’re testing those people or just sending them straight to ICU – I read also that it doesn’t change the treatment strategy and they don’t have time to mess around. If so I’m guessing a lot of cases of flu would be being misdiagnosed now. But those misdiagnoses will be a tiny part of the burden of COVID-19 in any case, and flu season is now almost over in any case, and peaked in February. There’s an enormous amount of time and energy being spent on debating testing strategies and who should be tested and why, but for many countries they don’t have the time or the staff to do it, so it’s irrelevant. In that case I think in many countries the number of cases at the peak of the epidemic is going to be massively underestimated as the health system focuses all its effort on dealing with the waves of patients coming in, and reserves testing for health care workers and other essential staff (if it can even do that!)
On the topic of the epidemic in Japan, yesterday there were >700 cases in Japan and 166 in Tokyo; today there seem to be about 520 in Japan and 97 in Tokyo, so it appears that the social distancing and partial lockdown introduced two weeks ago are beginning to work. I’m hoping this means we can eliminate this stupid virus in Japan in the next month, and move to helping other countries.