On Tuesday 26th May Japan’s COVID-19 state of emergency ended, five days earlier than expected and with deaths down to low double digits every day. The state of emergency was accompanied by a voluntary lockdown that started on 8th April for Tokyo and six other prefectures, extending to the rest of Japan a week later and ending in the rest of Japan a week before the lockdown ended in Tokyo. This means that the lockdown affected Tokyo for just 7.5 weeks, and the rest of Japan for about 6 weeks. At its peak the epidemic generated about 1200 cases in one day (on 17th April), dropping from 1200 to 30 in just 5 weeks.

In contrast, the UK essentially introduced its lockdown on 23rd March and is still slowly relaxing the lockdown. The UK lockdown was stricter than that in Japan, with enforceable restrictions on movement and activities[1], it involved the complete closure of many businesses, and it effectively lasted 3 weeks longer than Japan’s. At its peak the UK saw 8700 cases in one day (on 10th April, a week before Japan’s peak) and dropped much slower, only going below 2000 cases on 25th May – the same day Japan reached 30 cases. This is a quite remarkable difference in pace of decline: dropping by 97.5% in 5 weeks for Japan, compared to 75% in 6 weeks for the UK. These differences show very starkly when plotted, as I have done in Figure 1. This figure shows daily new cases in the two countries by day since the 10th confirmed case, using data obtained from the Johns Hopkins School of Public Health coronavirus tracker[2]. From this figure it is clear that Japan saw its 10th case much earlier than the UK (on 30th January compared to 24th February) yet experienced a much more gradual increase and a much more rapid decline than did the UK.

Figure 1: Daily new COVID-19 cases in the UK and Japan by day since the 10th confirmed case

Why was Japan’s response to the coronavirus so much more effective than that of so many other high-income countries? In this post I will explore a little the key factors that affected the Japanese response, what made the numbers grow so slowly and why the lockdown was more effective than in many other countries. In particular I will compare Japan with the UK, as a model of the differences between an effective and an ineffective response.

Figure 2: Health education materials are essential to good pandemic prevention

A timeline of interventions

Japan saw its first case on the 16th January, compared to 31st January in the UK. However, Japan took action sooner and more aggressively. Here are some key actions and when they were taken by each country.

The difference in public response to the issue of mass events is a key example of the quality of the response in the two countries. While the UK was faffing about with discussion about which responses to take, Japan was already canceling and closing events. My own work events began to be postponed in the last week of February, but so did major public events:

  • J league (soccer) halted all games on 25th February (170 cases)
  • Japan National Pro Baseball league held all preseason games without an audience from 26th February (189 cases)
  • Japan boxing commission and pro-boxing association canceled or postponed all bouts from 26th February
  • Rise kickboxing was canceled on 26th February
  • Sumo was held without an audience from 8th March (502 cases) (5 days after Boris Johnson bragged about “shaking hands with everybody” (51 cases))

In contrast in the UK:

  • An England-Wales Rugby match was held on 7th March with a live audience and the PM in attendance (206 cases)
  • Premier league events were held on 8th March with a live audience (283 cases)
  • Cheltenham races were held on 10th – 14th March (382 – 1140 cases)
  • League one games were held on 10th March (382 cases)
  • UEFA champions league games were held on 12th March (in Scotland) (456 cases)

The UEFA champions league match brought a large number of German fans to Scotland, and a week earlier I think Liverpool visited Spain and another team visited Italy, where the epidemic was already booming. These events had huge numbers of fans – 81,000 people attended the England-Wales rugby match, and many soccer games host tens of thousands of fans. In contrast, the only major event to be held in March in Japan that I know of, with an audience, was K1 on 22nd March, which attracted 6500 fans who were all given a mask at the door (and this event still attracted huge controversy and anger in Japan).

Because of the slow growth of the epidemic the lockdowns also happened at different stages of the epidemic. Japan’s lockdown came on 8th April, when there were 5120 cases; the UK’s, on the 23rd March, when the UK had reached 6600 cases and was already on a much more rapid upward trajectory. It took 4 days from the announcement of lockdown for the UK’s case load to double, whereas it took Japan 8 days. The next doubling took the UK another 4 days, and never happened for Japan.

Finally of course there is the attitude of the leadership: on 3rd March Sadiq Khan announced no risk of catching coronavirus on the London Underground, the same day that Boris Johnson was bragging about shaking everyone’s hand at a hospital (and thus caught coronavirus himself).

It should be clear from this that while in some cases the UK government acted with about the same speed as the Japanese government, in general the Japanese government acted when it had much lower numbers of cases than the UK, and implemented more far-reaching and aggressive strategies that were likely to have greater impact. But beyond basic actions on mass events and action plans, there was one additional major difference in the Japanese government’s response: case isolation.

Contact tracing and case isolation

From the very beginning of the epidemic, Japan introduced a system of “test, trace and isolate” that follows WHO guidelines for emerging infectious diseases. Under this system, once someone was identified as a likely COVID-19 case and tested positive, they were immediately moved to a nominated hospital into a special management ward designed for highly infectious diseases, to have their condition managed by specialist medical teams. This case isolation reduces the risk that they will infect their family, and prevents them from spreading the disease through basic daily functions like shopping if they live alone and cannot be helped by others. This strategy was also used in China and Vietnam, and it is a core part of the reason why the lockdowns in these countries were so much more effective than they were in the UK, USA or much of Europe. When a confirmed case of COVID-19 self-isolates at home they are highly likely to infect family or housemates, who will then continue to spread the virus amongst themselves and to others. This is particularly bad in cities with high levels of inequality like London, where essential workers live in cramped share houses and lack the resources to stop working even if infected. These people infect their housemates, who must continue working as bus drivers, cleaners, care workers or shop assistants, and cannot help but infect others. If the first case is quickly isolated, this reduces the risk that subsequent cases will be infected. As stressed by the WHO, case isolation is key to cracking this highly infectious virus. Case isolation early in the epidemic slows the growth of the epidemic and buys more time to scale up testing and other responses, while case isolation once the lockdown is in place helps to push down the number of infections more rapidly, reducing both the severity and length of the lockdown.

Case isolation was key to Japan’s successful management of this epidemic, but many people have suggested that the epidemic was controlled also because of cultural and social factors that make Japan more successful at managing infectious diseases. I do not think these played a major role in Japan’s response.

Japan’s “unique” social and cultural factors

Some have suggested that Japan’s culture of hygiene, its long-standing mask-wearing habits, and high quality public infrastructure might have played a role in slowing the growth of the epidemic. It is certainly true that Japanese people have a tradition of washing their hands when they get home (and gargling), wear masks when they are sick, and have remarkably clean and hygienic public spaces, with readily available public toilets throughout the country. The trains are super clean and stations are also very hygienic, and it is never difficult to find somewhere to wash your hands. Japanese people also don’t wear shoes in the house (and in some workplaces!) and often have a habit of changing out of “outside clothes” when they come home. But I think these cultural benefits need to be stacked against the many disadvantages of Japanese life: Japan’s trains are incredibly crowded, and everyone has to use them (unlike say California, which was much worse hit than Japan); Japanese shops and public accommodations in general are very cramped and crowded, so it is not possible to socially distance in e.g. supermarkets or public facilities; because Japan’s weather is generally awful and its insects are the worst things you have seen outside of anime specials, most of Japan’s restaurants and bars are highly enclosed and poorly ventilated; and Japanese homes are often very cramped and small. When viewed like this, Japan is a disease breeding facility, a veritable petri dish for a rapidly spreading and easily-transmissible disease. Japan’s population is also very much older than the UK’s, which should suggest further high rates of transmission, and from mid-February we have terrible hay fever which turns half the country into snot cannons. Not to mention the huge outdoor party that is held at the end of March, where everyone gets drunk and nobody socially distances. Japan’s work culture also does not support home working, in general, and everyone has to stamp documents by the hour and we still use fax machines, so I really don’t think that this is a strong environment to resist the disease. I think these social and cultural factors balance out to nothing in the end.

Differences in Personal Protective Equipment

I do not know what the general situation for PPE was in Japan, but certainly the hospital attached to my university, which is a major nominated infectious disease university, sent around a circular in mid-February describing our state of readiness, and at that time we had 230 days’ supply of COVID-rated gowns at the current infection rate, as well as ample stocks of all other PPE and plans in place to secure more. There was a shortage of masks for public use in March, which was over by April, but I do not get the impression that there was such a shortage in the designated hospitals. Japan also has a very large number of hospital beds per capita compared to other high-income countries, but this figure is misleading: most of these beds are for elderly care and not ICU, and in fact its ICU capacity is not particularly large. However, by keeping the new cases low and moving isolated patients to hotels once the hospitals became full, Japan managed to mostly avoid shortages of ICU beds (though it was touch and go for a week or two in Tokyo). I think in the Japanese hospital system the lack of ventilators and ICU beds would have become a major problem long before the country ran out of PPE.

Inequality and disease transmission

One way that Japan differs from a lot of other high-income countries is its relatively low levels of inequality. In particular it is possible for young people to live alone in Tokyo even if they do not have high incomes, which means share housing does not really exist here, and all the young people who move to the big cities for work mostly live by themselves where they cannot infect anyone. Although it is a very densely-populated country and houses are much smaller than in the UK, there is less overcrowding because housing is affordable and there is a lot of it. Most people can afford health care and have ready access to it (waiting times are not a thing here). This low inequality plays an important role in elderly care homes, where staff are better paid and treated than in the UK care sector, and less likely to move between facilities on zero-hour contracts as they do in the UK. There is a higher level of care paid to basic public facilities like hospitals, railway stations, public toilets and other facilities which ensures they are relatively hygienic, and cleaning staff here tend to be paid as part of a standard company structure rather than through zero-hours contracts, with good equipment and basic working rights. Also there is a much lower level of obesity here, and obesity is not as class-based, so there is less risk of transmission and serious illness through this risk factor. There is a very high level of smoking, which is a major risk factor for serious illness and death from COVID-19, but it is the only risk factor that is comparable to or higher than those in the UK. In general I think Japan’s low level of inequality helped in the battle against this disease, by preventing the country from developing communities where the disease would spread like wildfire, or having strata of the population (like young renters) at increased risk, or forcing increased risk onto the poor elderly as we saw in the UK.

A note on masks

I think masks are a distraction in the battle against this disease. I think most people don’t know how to wear them properly and use them in risky ways – touching them a lot, reusing them, wearing them too long, storing them unsafely, and generally treating them as part of their face rather than a protective barrier. I think that this can create a false sense of security which leads people to think that opening up the economy and dropping lockdown can be safely done because everyone is protected by masks. This is a dangerous mistake. That is not to say one shouldn’t wear them, but one should not see them as a solution to the more basic responsibility of social distancing and isolation, and one definitely should not drop one’s hand hygiene just because one is wearing a mask: hand hygiene is much more important for protecting against this disease. It’s worth remembering that on the days that Japan was seeing 300 or 500 or 1000 cases a day everyone was wearing masks, but somehow the disease was still spreading. They are not a panacaea, and if treated as an alternative to really effective social measures they may even be dangerously misleading.

Conclusion: Early, sensible action and strong case isolation are the key

Japan took an early, rapid response to the virus which saw it screening people at airports, educating the population, and implementing sensible measures early on in the epidemic to prevent the spread of the disease. The first measures at airports and in case isolation were taken early in February, major events were cancelled and gatherings suspended from mid- to late-February, and additional social distancing measures introduced in March. Throughout the growth of the epidemic the Japanese response focused on the WHO guideline of testing, tracing, and isolating, with case isolation a routine strategy when cases were confirmed. This case isolation slowed the growth of the epidemic and once lockdown was in place helped to crush it quickly. This in clear contrast to the countries experiencing a larger epidemic, which typically reacted slowly, introduced weak measures, and did not implement case isolation at all or until it was too late. Lockdowns with self-isolation will work, but as Figure 1 shows, they are much less effective, causing more economic damage and much slower epidemic decline, than lockdowns with case isolation.

Finally I should say I think Japan ended its lockdown a week early, when cases in Tokyo were still in the 10s, and we should have waited another week. I fear we will see a resurgence over the next month, and another lockdown required by summer if our contact tracing is not perfect. But it is much better to end your lockdown prematurely on 10 cases a day than on 2000 a day, which is where the UK is now!


fn1: With certain notably rare exceptions, of course…

fn2: I have had to do a little cleaning with the data, which contains some errors, and I think the JHSPH data doesn’t quite match that of national health bodies, but it is much more easily accessible, so that is the data I have used here. All case numbers are taken from that dataset, unless otherwise stated.

As I write this many countries are beginning to end their lockdowns and make plans to reopen. The UK has already begun to reopen, the US is opening state by state and much of Europe is beginning to return to work and play. Japan has ended its state of emergency in 40 prefectures, leaving the 7 hardest hit prefectures another two weeks of lockdown before they can resume normal activity. Different countries and states have different guidelines and rules about how to reopen, and are reopening at different stages of the epidemic. Let’s look at the circumstances in some of them.

  • United Kingdom: 2,400 new cases on 19th May, down from a peak of about 6,000 a day. A major epidemic still seems to be raging in elderly care homes, but people have begun returning to work. There is debate about whether to reopen schools, but some universities have decided to conduct the entire 2020/21 academic year online. Quarantine rules will be introduced for inbound overseas travelers from early June. Still recruiting staff to do contact tracing.
  • Germany: 513 daily cases on 19th May, down from a peak of 6,000 a day. Shops have reopened, Bundesliga has restarted without crowds and schools will soon reopen. The end of lockdown began on about May 10th, when there were about 670 cases a day
  • USA: 19,662 daily cases on 19th May, down from a peak of about 35,000 a day. States are reopening at their own pace with some being strict and some being very relaxed. Most states have ongoing daily cases in the hundreds, and there are signs that the decline in daily cases has stopped in states like New Jersey and Washington, or that case numbers are rising in states like Maryland, after seeming to plateau. In some states like Texas the number has been constantly increasing and the state is reopening after completely failing to stop the growth of the virus. Major problems with the testing infrastructure and large state-by-state differences in public health infrastructure.
  • Japan: 31 daily cases on 19th May, down from a peak of about 700 cases, with 5 in Tokyo. Only some prefectures are reopening, rules remain regarding mass events, schools have not yet reopened, and things aren’t going straight back to normal. Full reopening of the country is currently planned for 31st May but could be postponed if the trajectory changes

New Zealand, of course, began to reopen only when there were 0 cases. These countries seem to have starkly different ideas about when and how to reopen, with the USA and UK really nowhere near the bottom of their incidence curves, and still huge numbers of cases being discovered every day. Most of these countries claim to have pushed the reproduction number of the virus below 1, which means that they think the epidemic is under control. But what is the best metric for determining when to end a lockdown?

Metric 1: Daily number of cases

One way to judge whether to exit lockdown is the daily number of cases. You can calculate this as a percentage of your total active cases and from that estimate the amount of time it takes to double the number of cases, and if you think this is low enough you can reopen. Under this metric New York is ready to reopen, since it saw 1,474 new cases yesterday out of 353,000 total cases, which suggests a growth rate of 0.4%, which in theory should mean it will take another 100 days or more for case numbers to double.  By this metric Arkansas should be okay too – it had 110 new cases yesterday out of 4,923 existing cases, giving a 2% growth rate that suggests about a month or more to double. You need to show a little caution with this calculation though, because many states that have experienced slow growth in long epidemics have a large number of recovered cases. In fact in Arkansas there are only 1,184 active cases, so basically yesterday it saw a 10% increase in case numbers, which means the number of cases will double in a week. It should probably stay closed by that metric! But a lot of states don’t seem to be recording or reporting recovered cases. Also if we use the metric of not opening if your cases will take a week or less to double (say, a 10% increase per day), then New York now could open even if it had 30,000 daily cases, since that is less than 10% increase a day. But I think everyone would agree a single city opening when it still has 30,000 cases a day would be a bit silly.

Metric 2: Reproduction number

Everyone is becoming familiar with the effective reproduction number, Rt, now that the epidemic is all the news we can read about. Rt is the number of cases that will be generated by a single infected person. Rt measures this number over time, so it can change as policies change, and is slightly different to R0, the basic reproduction number. R0 measures Rt at the beginning of the outbreak, when there is only 1 new case and the population has no special measures in place. I estimated R0 for COVID19 to be 4.4, meaning that each case will generate 4.4 new cases. Because the disease has an incubation period when people are asymptomatic of about 4-5 days, we can expect those 4.4 new cases to occur between 4 days and two weeks after the initial infection, so we might expect that an approximate rule for this virus is that 100 cases today will generate 400 cases after a week, suggesting that unrestrained it doubles every 3-4 days. That’s nasty! But after policies are put in place we can drive Rt down to 1, and once it’s below 1 we should expect that the epidemic will begin to die out. This seems to be the primary metric the UK government is using – their politicians are always on TV talking about “the R number” and everyone is eager to get it below 1. The big problem with using Rt is that if you have enough daily cases, an Rt below 1 will still mean you generate a lot of new cases. For example, the US has 20,000 cases a day and most Rt values are near 1. If Rt is 0.8 then given the incubation time we should expect 16,000 daily cases after a week, 12,800 after two weeks, and so on. That suggests a half-life for the disease of perhaps 2-3 weeks, and it will take another two months to disappear. A lot of deaths will happen in that time.

Another problem with Rt is that once the economy opens we should expect it will go up. If Rt keeps fluctuating above and below 1, are we to keep closing and opening the economy? What if it’s 0.8 for a week, then goes up to 1.2? Do we close down? Or wait as the epidemic begins to spread again? If it is fluctating like this we may end up with an epidemic that is constantly varying around 20,000 cases a day: one week it’s 15,000 a day, then we loosen our measures and it’s 22,000 a day, and so on. Also there is a lot of uncertainty in estimates of Rt – if it’s 0.9 then in theory we are in epidemic elimination territory, but actually if the confidence interval is 0.7 to 1.1 there’s some chance we aren’t there at all.

Metric 3: Health system capacity

Unless we do as NZ has done and exterminate the virus completely before we reopen, we can be confident there will still be some cases when we reopen. In this case we will need to deal with them by testing, contact tracing, and if possible isolating the cases. Contact tracing one case when they’re in lockdown is easy – you just test the people they live with. But once they’re working and socializing one positive case will likely mean tracking down and testing 5 or 10 more people. This is hard work and it needs to be done quickly with a disease like this, especially if even a small number of people are asymptomatic but able to spread. Basically you need to find and test all 10 contacts and get their results back to them – and if necessary isolate them – within 4 days of the onset of symptoms in the index case, and even less time if the index case delayed presentation to hospital. This means if you have 500 cases a day you need to track 2500 to 5000 people daily, and potentially have to isolate 2000 of them. To do this requires a lot of boots on the ground and a lot of hotel rooms. Furthermore, the more cases you have the less room there is for error. If you have 5 cases a day and a 10% error rate in contact tracing you’ll miss 5 people, 1 of whom might be infected. With 500 cases a day you’ll miss potentially 500 people, of whom 100 might be infected. Those slip ups will help the virus continue to spread until it finds a super spreader like the Korean bar scenario (or in America, a meat packing plant).

To me this is the best guide for when to open: do you have the logistics to cope with cases as people begin to socialize and spread the disease again? If you have 50 cases a day and 500 contact tracers then you can probably handle it; if you have 500 cases a day and 500 contact tracers then it’s not going to work, and you’re going to lose control of the epidemic. Rather than judging by the rate at which the virus might double, or the reproduction number, you should look at whether you can rigorously and effectively stamp out every single case that could be generated after you reopen, and not ease your lockdown until you’re well within the logistic capacity to do so. That means looking at testing capacity, the number of people able to contact trace, your population’s willingness to share contacts and engage with health workers, your hotel capacity for case isolation, and your hospital bed capacity (and in-hospital infection risk!) for those you miss. If any aspect of that process could break, you need to wait.

Unfortunately, a lot of policy makers and politicians have been focused on the reproduction number, as if crossing the reproduction threshold will automatically end the epidemic. It’s an easy number to focus and gives an easy story to tell the press and the public, and it’s nice to have a target to aim for, but although a scientifically valid measure of the epidemic’s dynamics it is of little use in deciding how to deal with the epidemic. Much more important is the ability to control the cases you have, and a long term plan for getting rid of them, than a spot judgment about whether you “have the epidemic under control” based on a number that is both uncertain and ultimately not very practically informative.

The consequences of losing control a second time

The big problem with losing control of the epidemic a second time is that you have a lot more cases floating around than the first time it happened. It took the UK two weeks to rise from 152 cases a day to 4,500 cases[1], so if the UK opens up on 2,500 cases and loses control the consequences will be dire. If the week after opening up there are 2,000 cases, and the contact tracing misses 152 of them (<10%!), then in theory within two weeks the UK will be back to 4,500 cases a day. Furthermore, it will be much harder to go back into lockdown a second time, because the population will no longer see it as an effective strategy and it will be political suicide for any government contemplating it. Socially and politically, you can’t let this genie back out of its bottle. And although we like to hope that the population will observe social distancing rules and other niceties, in reality this will slide quickly, and if the cases aren’t under control by the time people return to their normal ways, another explosion will follow. This is without considering unknown and potentially catastrophic risks, such as school openings. The UK government is pushing to reopen schools because they say there is little risk of spread among children, but the ONS survey found much higher proportions of young people with antibodies in the community than are recorded in confirmed hospital cases. If the virus was quietly spreading in young people when it started at 1 case, how explosive will its growth in this cohort be if it starts from 2000 cases? These low-risk groups are highly likely to have many social contacts and to be an excellent infection vector for high-risk groups such as their parents and teachers.

Watching the data from the USA, I think this is already happening in some states in the USA now. Texas, Maryland, Minnesota, maybe New Jersey, North Carolina, maybe Tennessee are already beginning to see either growth or a distinct flattening of previous downward curves, and other states that are reopening like Florida and Wisconsin will likely see this in a week or two. I don’t think any of these states have the contact tracing capacity for the cases they are currently seeing, and they don’t have any plan to isolate cases, nor do they have well-functioning or affordable health systems. The same is true in the UK, which is nowhere near having its contact tracing infrastructure in place, and is playing with all kinds of deadly scenarios (like reopening schools and soccer games). I think this is partly because they’re fixated on Rt as the metric for reopening, partly because they’re incompetent, and partly because of political and economic pressure, but regardless, a disaster is in their near future if their health system capacity is not ready – and I think it’s not. In two weeks we are going to see the second wave hit these unready countries, and it’s going to make the first wave seem like a bad cold.


fn1: But it has taken 5 weeks to get from 4,500 back to below 4,000. This shows the incredible urgency of stopping this epidemic during its upward rise, not once it has really spread. The government’s faffing in the early days has made every subsequent decision harder, less effective and more deadly. The entire crew should resign immediately and hand government over to some adults to manage the place properly.

In early March, when COVID-19 was starting to spread in the UK, the government announced a strategy of “herd immunity” in which they would shield vulnerable people (such as older people and people with pre-existing conditions) from the disease, and aim to slowly allow the rest of the country to be infected up to some proportion of the population. This policy was based on the idea that once the disease had infected a certain proportion of the population then this would mean it had naturally been able to achieve herd immunity, and after that would die out. The basics of the strategy and its timeline are summarized here. This strategy was an incredibly dangerous, stupid and reckless strategy that was built on a fundamental failure to understand what herd immunity is, and some really bad misconceptions about the dynamics of this epidemic. Had they followed this policy the entire UK population would have been infected, and everyone in the UK would have lost at least one of their grandparents. Here I want to explain why this policy is incredibly stupid, and make a desperate plea for people to stop talking about achieving herd immunity by enabling a certain portion of the population to become infected. This idea is a terrible misunderstanding of the way infectious diseases work, and if it takes hold in the public discourse we are in big trouble next time an epidemic happens.

I will explain here what herd immunity is, and follow this with an explanation of what the UK’s “herd immunity” strategy is and why it is bad. I will call this “herd immunity” strategy “Johnson immunity”, because it is fundamentally not herd immunity. I will then present a simple model which shows how incredibly stupid this policy is. After this I will explain what other misconceptions the government had that would have made their Johnson Immunity strategy even more dangerous. Finally I will present a technical note explaining some details about reproduction numbers (the “R” being bandied about by know-nothing journalists at the moment). There is necessarily some technical detail in here but I’ll try to keep it as simple as possible.

What is herd immunity?

Herd immunity is a fundamental concept in infectious disease epidemiology that has always been applied to vaccination programs. Herd immunity occurs when so many people in the population are immune to a disease that were a case of the disease to arise in the population, it would not be able to infect anyone else and so would die out before it could become an epidemic. Herd immunity is linked to the concept of the Basic Reproduction Number, R0. R0 tells us the number of cases that will be generated from a single case of a disease, so for example if R0 is 2 then every person who has the disease will infect 2 other people. Common basic reproduction numbers range from 1.3 (influenza) to about 18 (measles). The basic reproduction number of COVID-19 is probably 4.5, and definitely above 3.

There is a simple relationship between the basic reproduction number and the proportion of the population that need to be vaccinated to ensure herd immunity. This proportion, p, is related to the basic reproduction number by the formula p=1/(1-1/R0). For smallpox (R0~5) we need 80% of the population to be vaccinated to stop it spreading; for measles (R0~18) it is safest to aim for 95%. The reason this works is because the fundamental driver of disease transmission is contact with vulnerable people. If the disease has a basic reproduction number of 5, each case would normally infect 5 people; but if 4 of every 5 people the infected person meets are immune, then the person will only likely infect 1 person before they recover or die (or get isolated). For more infectious diseases we need to massively increase the number of people who are immune in order to ensure that the infection doesn’t spread.

If we vaccinate the correct proportion of the population, then when the first case of a disease enters the population, it’s chances of meeting an infectable person will be so low that it won’t spread – effectively by vaccinating 1-1/R0 people we have reduced its effective reproduction number to 1, at which point each case will only produce 1 new case, and the virus will not spread fast enough to matter. This is the essence of herd immunity, but note that the theory applies when we vaccinate a population before a case enters the population.

What is Johnson Immunity?

There is a related concept to the basic reproduction number, the effective reproduction number Rt, which tells us how infectious the virus currently is. This is tells us how many people each case is infecting at the current state of the epidemic. Obviously as the proportion of the population who have been infected and recovered (and become immune) increases, Rt must drop, since the chance that they will have contact with an infectious person goes down. Eventually the proportion of the population infected will become so large that Rt will hit 1, meaning that now each case is only infecting another case. The idea of Johnson Immunity was that we would allow the virus to spread among only the low-risk population until it naturally reached the proportion of the population required to achieve an Rt value of 1. Then, the virus would be stifled and the epidemic would begin to die. If the required proportion to achieve Rt=1 is low enough, and we can shield vulnerable people, then we can allow the virus to spread until it burns out. This idea is related to the classic charts we see of influenza season, where the number of new infections grows to a certain point and then begins to go down again, even in the absence of a vaccine.

This idea is reckless, stupid and dangerous for several reasons. The first and most serious reason it is dangerous is that the number of daily new infections will rise as we head towards Rt=1, and by the time we reach the point where, say, 60% of the population is infected, the number of daily cases will be huge. At this point Rt=1, so each case is only infecting 1 other case. But if we have 100,000 daily new cases at this point, then the following generation of infections will spawn 100,000 new infections, and so on. If, for example, the virus has an R0 of 2, and takes 5 days to infect the next generation, then the number of new cases doubles every 5 days. After a month we have 64 cases, after two months we have 4100 cases, and so on. By the time we get to 30 million cases, we’ll likely be seeing 100,000 cases in one generation. So yes, now the virus is going to start to slow its spread, but the following generation will still generate 100,000 cases, and the generation after that 90,000, and so on. This is an incredible burden on the health system, and even if death rates are very low – say 0.01% – we are still going to be seeing a huge mortality rate.

The second reason this idea is reckless and stupid is that it is basically allowing the disease to follow its natural course, and for any disease with an R0 above about 1.5, this means it will infect the entire population even after it has achieved its Rt of 1. This happens because the number of daily cases at this point is so large that even if each case only infects 1 additional case, the disease will still spread at a horrific rate. There is an equation, called the final size equation, which links R0 to the proportion of the population that will be infected by the disease by the time it has run its course, and basically for any R0 above 2 the final size equation tells us it will infect the entire population (100% of people) if left unchecked. In practice this means that yes, after a certain period of time the number of new cases will reach a peak and begin to go down, but by the time it finishes its downward path it will have infected the entire population.

A simple model of Johnson Immunity

I built a very simple model in Excel to show how this works. I imagined a disease that lasts two days. People are infected from the previous generation on day 1, infect the next generation and then recover by the end of day 2. This means that if I introduce 1 case on day 1, it will infect R0 cases on day 2, R0*R0 cases on day 3, and so on. This is easy to model in Excel, which is why I did it. Most actual diseases have incubation periods and delayed infection, but modeling these requires more than 2 minutes work in a real stats program, and this is a blog post, so I didn’t bother with such nuance. Nonetheless, my simple disease shows the dynamics of infection. I reclaculated Rt each day for the disease, so that it was reduced by the proportion currently infected or immune, so that for example once 100,000 people are infected and recovered, in a population of 1 million people, the value of Rt becomes 90% of the value of R0. This means that when it reaches its Johnson Immunity threshold the value of Rt will go below 1 and the number of cases will begin to decline. This enables us to see how the disease will look when it reaches the Johnson Immunity threshold, so we can see what horrors we are facing. I assumed no deaths and no births, so I ran the model in a closed population of 1 million people. I ran it for a disease with an R0 of 1.3, 1.7, and 2.5, to show some common possible scenarios. Figure 1 shows the results. Here the x-axis is the number of days since the first case was introduced, and the y-axis is the number of daily new cases. The vertical lines show the day at which the proportion of the population infected, Pi, crosses the threshold 1-1/R0. I put this in on the assumption that the Johnson Immunity threshold will be close to the classical herd immunity threshold (it turns out it’s off by a day or two). The number above the line shows the final proportion of the population that will be infected for this particular value of R0.

Figure 1: Epidemic paths for three different reproduction numbers, with Johnson Immunity threshold

As you can see, when R0 is 1.3 (approximately seasonal influenza), we cross the approximate Johnson Immunity threshold at 44 days after the first case, and at this point we have a daily number of cases of about 40,000 people. This disease will ultimately infect 49% of the population. Note how slowly it goes down – for about a week after we hit the Johnson Immunity threshold we are seeing 40,000 or so cases a day.

For a virus with an R0 of 1.7 the situation is drastically worse. We hit the Johnson Immunity threshold after 23 days, and at this point about 140,000 cases a day are being infected. Three days later the peak is achieved, with nearly 200,000 cases a day being infected, before the disease begins a rapid crash. It dies out within a week of hitting the Johnson immunity threshold, but by the time it disappears it has infected 94.6% of the population. That means most of our grandparents!

For a disease with an R0 of 2.5 we hit the Johnson Immunity threshold at day 13, with about 140,000 cases a day, and the disease peaks two days later with 450,000 cases a day. It crashes after that, hitting 0 a day later because it has infected everyone in the population and has no one left to infect.

This shows that for any kind of R0 bigger than influenza, when you reach the Johnson Immunity threshold your disease is infecting a huge number of people every day and is completely out of control. We have shown this for a disease with an R0 of 2.5. The R0 of COVID-19 is probably bigger than 4. In a population of 60 million where we are aiming for a herd immunity threshold of 36 million we should expect to be seeing a million new cases a a week at the point where we hit the Johnson Immunity threshold.

This is an incredibly stupid policy!

Other misconceptions in the policy

The government stated that its Johnson Immunity threshold was about 60% of the population. From this we can infer that they thought the R0 of this disease was about 2.5. However, the actual R0 of this disease is probably bigger than 4. This means that the government was working from some very optimistic – and ultimately wrong – assumptions about the virus, which would have been catastrophic had they seen this policy through.

Another terrible mistake the government made was to assume that rates of hospitalization for this disease would be the same as for standard pneumonia, a mistake that was apparently made by the Imperial College modeling team whose work they seem to primarily rely upon. This mistake was tragic, because there was lots of evidence coming out of China that this disease did not behave like classic pneumonia, but for some reason the British ignored Chinese data. They only changed their modeling when they were presented with Italian data on the proportion of serious cases. This is an incredibly bad mistake, and I can only see one reason for it – they either didn’t know, or didn’t care about, the situation in China. Given how bad this disease is, this is an incredible dereliction of duty. I think this may have happened because the Imperial College team have no Chinese members or connections to China, which is really a very good example of how important diversity is when you’re doing policy.

Conclusion

The government’s “herd immunity” strategy was based on a terrible misunderstanding of how infectious disease dynamics work, and was compounded by significantly underestimating the virulence and deadliness of the disease. Had they pursued the “herd immunity” strategy they would have reached a point where millions of people were being infected daily, because the point in an epidemic’s growth where it reaches Rt=1 is usually the point where it is at its most rapidly spreading, and also its most dangerous. It was an incredibly reckless and stupid policy and it is amazing to me that anyone with any scientific background supported it, let alone the chief scientific adviser. Britain is facing its biggest crisis in generations, and is being led by people who are simply not competent to manage it in any way.

Sadly, this language of “herd immunity” has begun to spread through the pundit class and is now used routinely by people talking about the potential peak of the epidemic. It is not true herd immunity, and there is no sense in which getting to the peak of the epidemic to “immunize” the population is a good idea, because getting to the peak of the epidemic means getting to a situation where hundreds of thousands or millions of people are being infected every week.

The only solution we have for this virus is to lockdown communities, test widely, and isolate anyone who tests positive. This is being done successfully in China, Vietnam, Japan, Australia and New Zealand. Any strategy based on controlled spread will be a disaster, and anyone recommending it should be removed from any decision-making position immediately.

Appendix: Brief technical note

R0 (and Rt) are very important numerical qualities of an infectious disease but they are not easily calculated. They are numbers that emerge from the differential equations we use to describe the disease, and not something we know in advance. There are two ways to calculate them: Empirically from data on the course of disease in individuals, or through dynamic analysis of disease models.

To estimate R0 empirically we obtain data on individuals infected with the disease, so we know when they were infected and when they recovered down to the narrowest possible time point. We then use some statistical techniques related to survival analysis to assess the rate of transmission and obtain statistical estimates for R0.

To estimate R0 from the equations describing the disease, we first establish a set of ordinary differential equations that describe the rates of change of uninfected, infected, and recovered populations. From this system of equations we can obtain a matrix called the Next Generation Matrix, which describes all the flows in and out of the disease states, and from this we can obtain the value of R0 through a method called spectral analysis (basically it is the dominant eigenvalue of this matrix). In this case we will have an equation which describes R0 in terms of the primary parameters in the differential equations, and in particular in terms of the number of daily contacts, the specific infectiousness of the disease when a contact occurs, and the recovery time. We can use this equation to fiddle with some parameters to see how R0 will change. For example, if we reduce the recovery time through treatment, will R0 drop? If we reduce the infectiousness by mask wearing, how will R0 drop? Or if we reduce the number of contacts by lockdowns, how will R0 drop? This gives us tools to assess the impact of various policies.

In the early period of a new infectious disease people try to do rough and ready calculations of R0 based on the data series of infection numbers in the first few weeks of the disease. During this period the disease is still very vulnerable to random fluctuation, and is best described as a stochastic process. It is my opinion that in this early stage all diseases look like they have an R0 of 1.5 or 2, even if they are ultimately going to explode into something far bigger. In this outbreak, I think a lot of early estimates fell into this problem, and multiple papers were published showing that R0 was 2 or so, because the disease was still in its stochastic stage. But once it breaks out and begins infecting people with its full force, it becomes deterministic and only then can we truly understand its infectious potential. I think this means that early estimates of R0 are unreliable, and the UK government was relying on these early estimates. I think Asian governments were more sensible, possibly because they were in closer contact with China or possibly because they had experience with SARS, and were much more wary about under-estimating R0. I think this epidemic shows that it is wise to err on the side of over-estimation, because once the outbreak hits its stride any policies built on low R0 estimates will be either ineffective or, as we saw here, catastrophic.

But whatever the estimate of R0, any assumption that herd immunity can be achieved by allowing controlled infection of the population is an incredibly stupid, reckless, dangerous policy, and anyone advocating it should not be allowed near government!

Since just over a week ago we have begun to see reports of changes to figures on deaths due to COVID-19 in many countries. The changes typically lead to upward revision of the death figures, and usually this seems to occur either because the daily reporting of deaths has not incorporated deaths occurring outside of hospitals, or because national organizations are catching up on deaths that are not due to COVID-19 and discovering large changes in non-COVID death patterns. For example, on 17th April we started to see reports that Wuhan city had increased its death count by about 50%, and today we find the BMJ reporting that deaths in care homes in the UK have increased rapidly. Of course as soon as China revises its figures we see accusations of cover-ups, and no doubt people are also wondering if the institutions in some hard-affected countries are competent enough to accurately report death figures. So in this post I want to explain a little about how these mortality data are collected, how deaths are reported, why figures can be suddenly revised, and what some of the data we’re seeing means, using British data revisions as an example.

How death data is collected

For people living in high-income countries it may come as something of a surprise to learn that vital registration systems – the systems that record births and deaths – are not actually very sophisticated or high-tech, and that for many countries they do not exist at all. In high-income countries these systems are often legacy systems, based on a network of paper-based reporting that is still quite far behind the needs of modern information-hungry media, and many countries have no such systems in place: the WHO estimates that 2/3 of all deaths that occur every year are not recorded in any registration system. In a pandemic like this, where media organizations want to report daily death numbers, the traditional systems in place to register deaths often cannot keep up.

Typically a vital registration system takes some time to update. After someone dies a doctor has to assign a cause of death, which in many cases will be recorded on a piece of paper that has to then be input into a computer system and slowly passed up a chain to a central authority, where it will be checked and certain data cleaning activities undertaken. In many cases the doctor’s original cause of death recording doesn’t make sense, so some checks have to be conducted to make sure that things are working. Then whatever the doctor wrote down has to be converted into a standardized cause of death (under the International Classification of Diseases) and entered into a database by its code, along with whatever local codings (for place of death, geocoding, etc) that the national jurisdiction calls for. Figure 1 (taken from the UN Stats handbook) shows the stages of the flow of vital registration.

Figure 1: Flow of data through the vital registration system

Many countries lack some or all stages of this process: for example, China still does not have a complete vital registration system, and mortality estimates are based on sample surveys outside of major cities[1]. In many countries deaths occurring in different locations may be processed at very different speeds, with death in prison, homes or elderly care facilities being reported much more slowly than in hospitals, and rural hospitals or smaller clinics reporting more slowly than major regional or teaching hospitals. When people want to know rapidly how many people are dying in a fast-evolving situation it is unlikely that we will get complete mortality estimates, and usually the only data that the health service can aggregate quickly is data on in-hospital deaths. It can take weeks, months or even a full year to obtain a full, accurate snapshot of mortality figures across the entire community. As an example, this Kaiser Foundation report on care-home deaths due to COVID-19 in the USA makes clear that there are very large differences in how completely death data is collected between states in the US, and differences in how rapidly that data is reported. Oregon, for example, presents fairly comprehensive data on cases and mortality in residents and staff, but only on a weekly basis. But 55% of deaths reported in Oregon occurred in care facilities, which likely means that the death data in Oregon is delayed by a week and there will likely be revisions to earlier totals that slip by in the rush to report information.

When media report daily deaths, what they are really doing is taking data in a relatively raw form from the first orange box (“Health services”) in figure 1, before a proper civil registration and vital statistics quality control process has been implemented. Then, subsequently, national statistical authorities release the actual figures, which can be much larger than those initial estimates, and require some large and rather embarrassing changes to the numbers. This is particularly likely if – as in the UK – care homes are understaffed and use primarily unskilled labour. During a pandemic that targets elderly people, those facilities are likely to be way too busy to process mortality data in the timely fashion the media demand!

How deaths are recorded

Another important part of the puzzle is how deaths are actually recorded. Death statistics are recorded in three different forms: the direct cause of death, which actually made the person die; contributing causes of death, which may have helped them along the line; and the underlying cause of death, which is the real reason they died. This is a matter of medicine and biology, not always easily determined: for example diabetes might be the underlying cause of death, there may have been a contributing factor from pneumonia, and the direct cause may have been some kind of organ failure. You can see this process in action in the example blue forms provided by the CDC. When a death is finally reported by the government the underlying cause will be reported, not the contributing cause; but in the case of a major pandemic we may have good reason to think that the death would not have happened without the contribution of COVID-19. Furthermore, deaths are certified by doctors, and there is not necessarily a common agreement on when something is underlying, direct or contributing, and death certificates can be notoriously low quality. This creates problems for assessments of mortality patterns generally, but it is particularly important when giving rapid assessments of mortality due to a disease that we still don’t properly understand, since a judgment about whether something contributed to or was the underlying cause of death requires a basic understanding of how that cause works. This can lead to repeated reassessments of numbers of deaths, as doctors change their understanding of how the disease kills and what comorbidities might be vulnerable to the disease.

When you see a change in mortality figures it will be because of either or both of these problems. It could arise because a new source of causes of death has finally been cleaned and added to the data; it could be that a computer system had to be updated to allow daily death records to include COVID-19; or it could be because experts decided that certain events that had previously seemed independent of COVID-19 were actually related; or it could be because the government decided to include (or exclude!) deaths where COVID-19 was a contributing (rather than underlying) cause of death.

Another possible reason for changes in death figures, and a very serious one, is that the daily figures media received were those on deaths due to confirmed COVID-19, which are accurate and precise, but that after a few weeks the statutory authorities realized that there had been a huge increase in non-COVID deaths due to pressure on the health system, and started recording those too. This is what has started to happen in Europe, and this is what we will examine using the UK as our base.

Sudden huge increase in mortality in the UK

The Office of National Statistics has finally been able to compile, clean and release the data on all causes of death in the UK over the past few weeks, and the findings are stark. In week 16 of this year (11-17 April) there were 22,351 deaths in the UK. This is 11,854 more deaths than the five year average for that week. Basically, the number of deaths in the UK in that week doubled. There were 8,756 deaths due to COVID-19 in that week, which suggests about 3,000 deaths occurred due to non-COVID causes, an excess mortality rate of about 30%. So in one week in April, the number of deaths in the UK doubled, and only 70% of those excess deaths were due to COVID-19: the other 30% were other causes which, I think it’s safe to assume, occurred because of pressure on the health system.

This ONS report also notes that for the whole year so far there have been 22,000 or so excess deaths compared to the five year average, an increase of about 10%. COVID-19 has been in full force in the UK for just 3-4 weeks, and it has already increased the year-to-date mortality rate by 10%. That was based on figures that are already basically two weeks old, so we can expect that with 3-4 more weeks of deaths still to come, the year-to-date mortality rate will increase even more – but we won’t know for a few more weeks because of the delay in reporting at-home deaths. Figure 2 (taken from the ONS report) shows this in stark relief.

Figure 2: Weekly mortality figures for the UK

 

I hope those lines in Figure 2 make very clear that COVID-19 is not “just flu” and that its impact on the UK population has been staggering. Had the government pursued its foolish “herd immunity” strategy things would have been much, much worse.

I hope this two-week-after-the-fact revision will help my reader(s) to understand that the adjustments that were made to Wuhan’s mortality figures 10 days ago are not unusual or evidence of any kind of cover up: it’s natural that a health system that is struggling to deal with a sudden massive surge in hospitalizations and deaths, and which already does not have a well-functioning mortality registration system, is going to miss some deaths on the initial pass, and is going to need a bit of time to collect all the data and make it available in a comprehensive format. Over the next few weeks we will see this happening in a lot of health systems, and additional components of COVID-19 mortality will become clearer as time passes. This does not reflect incompetence or dishonesty, just the efforts of a system that was designed for slow, annual stocktake-type processes to adapt to a rapidly-changing pandemic situation.

This also means that we should expect that the figures we see now are not the final toll of this virus. Whatever numbers we’re seeing now from the USA, for example, we should expect to grow considerably once the CDC has had the chance to compile all the separate, confusing sources of data and put together a comprehensive report.

And when they do that, it’s going to be bad. Very, very bad. This disease is very dangerous, and without major action on the part of every country it is going to exact a terrible toll.

Stay home and stay safe, people!


fn1: Like all things in China, this is changing rapidly, and the quality of mortality statistics regularly improving. The linked article is from 2015 and is probably already out of date.

There is a lot of pressure at present for the expansion of testing for COVID-19 to enable better understanding of the spread of the virus and possibly to help with reopening of the economy. Random population surveys have also been conducted in many countries, with a recent antibody survey in California, for example, finding 50 times more people infected than official estimates report. The WHO recognizes testing as a key part of the coronavirus response, and some countries are beginning to discuss the idea of “immunity passports”, in which people are given an antibody test and enabled to return to work if they test positive to antibodies and are well (since this indicates that they have been infected and gained immunity). The WHO advises against this approach because there is no evidence yet that people who have experienced COVID-19 and recovered are actually immune. But in addition to this virological concern, there is a larger, statistical concern about COVID-19 tests (especially antibody tests) and the consequence of widespread use of these tests as a policy guide: how reliable are they, and what are the consequences of deploying poor-quality tests?

My reader(s) may be familiar with my post on the use of Bayesian statistics to assess the impact of anti-trans bathroom laws on natal women. This study found that, since being transgender is a very low prevalence phenomenon, if we tried to actually enforce birth-gender bathroom laws almost everyone we kicked out of a woman’s toilet would actually be a cis woman. This is a consequence of Bayes’ Law, which basically tells us that when a condition has very low prevalence, any attempt to test for that condition will largely produce false positives unless the test is a very very accurate test. This applies to any attempt to discriminate between two classes of things (e.g. trans women vs. natal women, or coronavirus vs. no coronavirus). It is a universal mathematical theory, and there is no escaping it.

So what happens with testing for coronavirus. There are a couple of possible policies that can be enacted based on the result of testing:

  1. People testing positive are isolated from the rest of the community in special hospitals or accommodation, to be treated and managed until they recover
  2. People testing positive self-isolated and all their potential contacts are traced and tested, self-isolating as necessary
  3. People testing negative are allowed to return to ordinary life, working and traveling as normal
  4. People testing positive to antibodies with no illness are issued an “immunity passport” and allowed to take up essential work
  5. Health workers testing negative are allowed to return to hospital

Obviously, depending on the policy, mistakes in testing can have significant consequences. This is why the WHO has quite strict diagnostic criteria for the use of testing, which requires multiple tests at different specified time points with rules about test comparison and cautionary notes about low-prevalence areas[1]. Now that some antibody tests have achieved marketing status, I thought I would do a few brief calculations using Bayes’ rule to see how good they are and what the consequences will be. In particular let’s consider policy options 1, 3 and 4. I found a list of antibody tests currently being marketed or used in the USA here, and information on one PCR test, from Quantivirus. I assumed a testing program applied to a million people, and for each test under this program I calculated the following information:

  • The number of people testing positive and the number who are actually negative
  • The proportion of positive tests that are actually positive
  • The number of people testing negative and the number who are actually positive
  • The estimated prevalence of COVID-19 obtained from each of these tests

I used the current number of cases in the USA on 24th April (870,000), multiplied by 10 to include asymptomatic/untested cases and a US population of 330 million to estimate the true prevalence of coronavirus in USA at 2.6%.  Note that with 2.6% prevalence the true situation is 26,000 cases of COVID-19 and 974,000 people negative. I then compared the estimated prevalence for each test against this. Here are the results

Beckton-Dickinson/Biomedomics Covid-19 IgM/IgG Rapid Test

This test has 88.7% sensitivity and 90.6% specificity, and has been given emergency use authorization by the FDA. If used to test a million people in the context of disease prevalence of 2.6%, we would find the following results:

  • 114,906 people testing positive of whom 91,521 are actually negative
  • Only 20.4% of tests positive
  • 885,903 people testing negative, of whom 2,979 are positive
  • An estimated coronavirus prevalence of 11.4%

This would mean that under policy 1 (isolation of all positive cases) we would probably increase prevalence by a factor of 5, since 80% of the people we put into isolation with positive cases would be negative (and would then be infected). If we followed policy 3 or 4, we would be releasing 2,979 people into the community to work, get on trains etc., and infect others. We would also recalculate the case fatality rate of the virus to be 50 times lower than the actual observed estimate, because we had observed deaths among 870,000 cases (prevalence 0.26%) but were now dividing the confirmed deaths by a prevalence of 11.4%. This would make us think the disease is not much worse than influenza, while we were spreading it to five times as many people. Not good! Curing that epidemic is going to need a lot of bleach injections.

Cellex qSars-CoV-2 IgG/IgM Cassette Rapid Test

This test has also received emergency use authorization, and has 93.8% sensitivity and 95.6% specificity, which sounds good (very big numbers! Almost as good as Trump’s approval rating!) But if used to test 1,000,000 Americans with prevalence of 2.6% it still performs very poorly:

  • 67,569 people testing positive of whom 42840 are actually negative
  • Only 36.5% of tests positive
  • 932,430 people testing negative, of whom 1,635 are positive
  • An estimated coronavirus prevalence of 6.8%

This is still completely terrible. Isolating all the positive people (policy 1) would likely increase prevalence by a factor of 3, and we would allow 1,635 people to run around infecting others blithely assuming they were negative. Not a good outcome.

CTK Biotech OnSite Covid-19 IgG/IgM Rapid Test

This test has not yet received emergency use authorization, but has 96.9% sensitivity and 99.4% specificity. With this test:

  • 31,338 people test positive of whom 5,841 are actually negative
  • About 81% of tests are actually positive
  • 968,611 people test negative, of whom 817 are positive
  • An estimated coronavirus prevalence of 3.1%

This is much better – most people testing positive are actually positive, we aren’t releasing so many people into the wild to infect others, and our prevalence estimate is close to the true prevalence. But it still means a lot of people are being given incorrect information about their status, and are taking risks as a result.

Conclusion

Even slightly inaccurate tests have terrible consequences in epidemiology. As testing expands the ability to conduct it carefully and thoroughly – with multiple tests, sequenced tests, and clinical confirmation – drops, and the impact of even small imperfections in the testing regime grows rapidly. In the case of a highly contagious virus like COVID19 this can be catastrophic. It will expose uninfected people to increased risk of infection through hospitalization or isolation alongside positives, and if used for immunity passports significantly raises the risk of positive people returning to work in places where they can infect others. In comparison to widespread testing with low-quality tests, non-pharmaceutical interventions (e.g. lockdowns and social distancing) are far more effective, cheaper and less dangerous. It is very important that in our desire to reopen economies and restart our social lives we do not rush to use unreliable tests that will increase, rather than reduce, the risk to the community of social interactions. While testing early and often is a good, strong policy for this pandemic, this is only true when testing is conducted rigorously and using good quality tests, and not used recklessly to end social interventions that, while painful, are guaranteed to work.

 


fn1: It’s almost as if they know what they’re doing, and we should listen to them!

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!

Conspiracy theories about Japan’s approach to the coronavirus (COVID-19) are beginning to spread online, as people find it very difficult to believe that the country still has only 1000 cases of the virus even though it has not been testing a great deal. This has led to suggestions that Japan is covering up the true number of cases, and the epidemic is out of control in Tokyo.

This isn’t true: Japan has actually tested quite a lot of people, the epidemic is not out of control here as it is in so many other countries, there is no cover up, and what is happening in Japan is an example of what can be achieved with careful, early interventions. I will explain this here a little.

What is Japan’s epidemic situation?

According to the Ministry of Health, Labour and Welfare there were 1193 confirmed cases of COVID-19 on 25th March, of whom 272 had recovered,  43 had died and 57 required ventilator support. Japan’s first death from COVID-19 occurred on 13th February, about 41 days ago, a lot earlier than in other countries such as Germany (15 days ago), Italy (34 days ago) or the USA (25 days ago). For a disease as infectious as this one, these small differences in number of days should lead to huge differences in case numbers: Japan has had 16 days more than the USA to see this epidemic grow, but on day 9 the USA had only 645 cases – now it has 64,661 cases. It is obviously mystifying to many people that the US could see a 100-fold increase in the number of cases in the same time period that Japan saw only a two-fold increase. The obvious suspicion is that since Japan hasn’t tested that many cases, they must be hiding something. There are two reasons this theory doesn’t work: 1) Japan is actually testing more than people recognize and 2) you would definitely be able to tell if there was a 50-fold undercount of cases.

What is Japan’s testing situation?

Testing data can be obtained here. Japan has tested about 22,000 people, of whom 1193 have been confirmed positive. In contrast Germany has tested 167,000 and the UK has tested 65,000. This certainly seems like a lot of missed tests in Japan, but it is worth bearing in mind that the number of tests per positive person is actually about the same in these countries: 18.4 per positive in Japan, 19.7 per positive in the UK, and 25.5 per positive in Germany. In South Korea the number is unusual: 350,000 tests for about 9,000 cases, or 38.9 tests per positive case, but South Korea was dealing with a unique situation where a particular population group was known to be at risk (the weird religious group) and an aggressive testing policy could be targeted based on a social identity. In other countries the number of tests has approximately mapped the scale of the epidemic. This strangely stable ratio of tests to positive patients arises from the limitations on the test: it can only work on people who currently have the virus (it’s a PCR test) and it is expensive and still limited, so population-level testing cannot yet be conducted, and if done partially would miss cases. Basically every country is using passive case-finding to identify the disease, and only using the test where the symptoms suggest it, in order to conserve tests and avoid the social consequences (isolation and clinic shutdowns) associated with false positives. Japan is doing no differently here than Germany or the UK, it’s just that there are less people with symptoms, and less people to test as a result.

It’s worth noting that Japan set up a call centre for people with COVID-19 concerns on the 28th January, and since the middle of February it has been receiving about 3000 calls a day (also, somewhat cutely, 0-2 faxes per day: don’t ever change, Japan!), so there have been about 150,000 calls over the period of testing. In a country of 120 million this doesn’t seem to be a sign of a massively out of control epidemic. I can’t find statistics on the NHS 111 line but there are many stories out there about how it is congested with calls.

Why is Japan following this policy?

There are several levels of testing that can be conducted for any disease, ranging from population screening (seen in breast cancer programs) through voluntary testing (seen in HIV prevention programs), active case finding (where community health organizations target particular groups known to be at risk of a disease, usually used for TB) to passive case finding, which is used in almost all non-fatal sexually transmitted infections, influenza, and other infectious diseases. Screening is usually only conducted if the disease course can be changed by early detection. Passive case finding is useful when there is no identifiable group to target, or the disease prevalence is low so the chance of a positive test is low, or the test is rare/expensive/invasive. In this case the test is still restricted in availability, and the disease prevalence is low so you need to use a lot of tests to find one case. This is complicated in the case of COVID-19 by the possibility that the testing process itself will infect the tester, and so it’s better not to go charging out into the community exposing testers to large amounts of potentially infected people. South Korea conducted a kind of active case finding program, but that is because they knew where to look.

In this sense Japan’s policy is really no different to that in other countries. Japan has focused its efforts up until now on finding cases through cluster investigation: a lot of cases in Japan up until recently have arisen from cluster’s connected to specific events, and finding the people connected to these clusters and isolating them is super important. A single live music event in Osaka, for example, was responsible for 48 cases (about 5% of all the cases in Japan!), and had those cases not been tracked they would have turned into a huge outbreak. You can see the effect of this cluster approach in the statistics: often new cases (particularly in rural Japan) are asymptomatic, which indicates they were caught as part of a contact tracing effort; and even today with 40 new cases in Tokyo about half have a known contact already, which suggests they were tracked down (or their contacts will be). Quite a few cases are also imported: 5 of today’s 40, for example, have an overseas travel history. Focusing on clusters means targeting testing at people who need it, which avoids clogging up testing facilities and ensures that the test follow up is good quality.

Another reason for Japan’s low number of tests is its basic advice to people with suspected COVID-19. The advice from the government to citizens and medical institutions alike is: don’t come in for a consultation unless you have a fever >37.5C and coughing/chest tightness for at least 4 days (unless you’re pregnant or otherwise at risk). Until then you should self-isolate and avoid travel. This advice is super important in Tokyo, where most people travel by public transport, and ensures sick people aren’t infecting others on the train, and it avoids over-burdening health facilities with people who just have a cold. Two of my role-playing group have gone through this process; one went to the doctor after 4 days and was diagnosed with a cold based on x-ray and influenza tests, and the other self-isolated until her symptoms faded after 3 days. We’ll never know if she is immune to the virus now, but it doesn’t matter because she wasn’t at risk and she did not infect anyone else by getting on a train. Given that a lot of cases in Italy are now being  reported as hospital-acquired, this is good advice – but it also leads to the use of less tests.

So how do we know the size of Japan’s epidemic?

If we aren’t testing, how do we know what’s happening? First, we can assume given the ratio of positive results to tests is the same as in other countries that the process is working the same way here, and less tests are needed because less people have the virus. Second, though, we can look at the state of hospital emergency and intensive care wards, and make a judgment about the epidemic from the burden those wards are facing. In New York, for example, we now have horrifying accounts of emergency wards overflowing with cases and doctors working without breaks as their hospitals become basically COVID zones. In Italy new triage guidelines are being released for rationing ventilators. I am sure that is not happening (yet) in Japan, for two reasons: I work with doctors at a major hospital, and I am regularly visiting that hospital for medical care.

I have worked in and around hospitals for my whole career, doing data management and research, including in Japan, and I am familiar with how a hospital feels when it is working well and when it isn’t. You can tell from the way the doctors and nurses are working, the state of the physical environment, and what they complain about when they talk to you during your work day, whether they are struggling. Doctors are often wrong about epidemiology but they have an eye for when things are changing in their case load, and when they talk to you about it you can tell if things are going wrong. I don’t get that impression from my day job, or from any of my research colleagues from other hospitals here. There is not yet any pressure on emergency or intensive care services. I also receive the circulars for the medical staff in my work email, and so I can see how they are preparing for a surge that has not yet happened (today for example I received reassuring news about the stockpile of emergency equipment that my hospital has, the kind of news that would probably make an American very angry at how ill-prepared their system was). It’s not complacency or a lack of care: the wave just hasn’t hit yet.

The second reason I know this is that I have had to visit a lot of different parts of this hospital for medical care for my stupid knee, which I dislocated at kickboxing four weeks ago and have subsequently discovered has been missing some major components for the past 30 years. I only discovered this through multiple x-rays, MRIs, and CT scans (which I guess Aussie doctors didn’t feel I deserved over the first 30 years of my life!) As we all know, X-rays play a very important role in COVID-19 care since they enable doctors to see what kind of damage is going on. There is no way I would have sat just 10 minutes in the x-ray queue, watching orthopaedic patients hobble in and out calmly, if my hospital were overrun with COVID patients – I would probably be sent off to an external private provider or forced to wait all day. There’s also no way the CT scanner would be available for me to use 15 minutes before my appointment.

Unless Japanese people are uniquely able to resist this virus, the surge isn’t here yet, which means the epidemic is still in its infancy here – but that may all be about to change.

Japan’s prevention policy and what is coming soon

Japan has avoided major lockdowns yet, because it acted early and sensibly in light of warnings from China. The Japanese government listened to China, sent help early on, and paid careful attention to what was happening. The first advice from the Ministry of Health, Labour and Welfare was sent early – probably in early February – and the first restrictions on public behavior were instituted probably two weeks after the first death in mid February. My work events were being canceled by the end of February, and instructions were being disseminated throughout Japan to avoid large events. New advice about self isolation was issued early, and the National Institute of Infectious Diseases began its epidemiological investigations early. Japanese companies already have seasonal flu policies in place, and it is quite common for people to self-isolate if they have influenza, and those who don’t self-isolate will wear masks and behave responsibly with their disease. Japan is also not a touchy-feely huggy kind of country, and bowing is the standard greeting. In contrast, the UK was still considering what to do about large events in early March, and hand-shaking was still being discussed. It’s incredible that the day before the UK experienced its first coronavirus death, when Italy was starting to go pear-shaped, and in light of China’s experience, the British government still had no opinion on large events or shaking hands, one of the most disgustingly unhygienic ways you can greet someone.

This early action has served Japan well – even though it at no point closed its border to China! – but it may not be enough. Yesterday there were 40 new cases in Tokyo and 95 new cases in the whole country, and the Tokyo governor asked people to stay inside all weekend and not travel at all unless it was an emergency. There has been general uproar that a large kickboxing event (K1) was held on Sunday, and also consternation at the large numbers of people still going to parks and gardens for ohanami (it’s the season). If counter-measures aren’t stepped up it’s likely that Japan will lose a grip on this. It’s my expectation that by next weekend the Ministry of Health, Labour and Welfare will announce a lockdown, at least of the major cities, and an extended closure of restaurants and bars (to be clear, I have no inside knowledge of this – it’s just my judgment). The 40 cases we saw in Tokyo today were at least partly a result of last weekend’s ohanami madness, and we won’t know the effect of a weekend shutdown until next week, so my guess is the government will increase the restrictions next weekend. Given the small number of cases at present and the slow daily growth they probably only need to maintain a couple of weeks’ shutdown, not the extended horror we have seen in some cities, but my guess it is coming. If the Japanese government does what it’s very good at and dithers, expect Tokyo to become a zombie survival game show within a month. But so far the Japanese response has been measured and careful and effective, so I hope they will continue this and will get this right.

A note on conspiracy theories and racism

It’s worth recognizing that the European and Anglosphere countries (except perhaps for New Zealand) had two months’ warning of what was coming, they watched everything that was happening in China and they basically ignored it. Even Boris Johnson’s rapid turnabout on his irresponsible and inhumane “herd immunity” policy wasn’t driven by the clear knowledge available to the whole world from China; he waited until some white dudes at the University for Killing People and Stealing their Shit had had time to update their model with the Italian experience before he realized what a disaster he was unleashing. It seems that no one in the west at any point considered Chinese experience, Chinese struggle or Chinese lives worth anything, and ignored all the warnings they were being given until it was too late. Japan, on the other hand, listened to China and bought itself a month of slow growth as a result.

The conspiracy theories you see online about China and Japan are grown in the same fertile racist soil as the European policy mistakes. There is a long-standing image of Asians as shifty, untrustworthy, authoritarian and narcissistic, and that is exactly the racist image that drives these conspiracy theories. It’s not possible for white people to imagine that Asians could be doing something better than them, so they simply imagine that Asians are lying and covering up the truth. Inscrutable, untrustworthy and impenetrable societies are hiding the numbers and pretending everything’s okay for their own nefarious ends (or to “save face”).

Needless to say, it’s all bullshit. There is no conspiracy, and nobody is covering anything up. Asia is just doing it better, and the west needs to start listening to what’s happened over here, if they want to escape this with any of their grandparents alive.