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.