Nine proposals for combatting the coronavirus pandemic in the UK

 

The following proposals have been suggested by a combination of world-renowned scientists (in several different fields), and ordinary people. As I believe they will be of great importance in combatting the pandemic, I’ve taken the liberty of collecting them together and sharing them publicly, in the hope that policymakers (and others) will act on them, or at least seriously consider them.

Proposal 1: Introduce a complete and compulsory Spain-style lockdown in the UK as soon as possible, and ramp up testing capacity as fast as possible.

An overwhelmingly strong case for this (both in the UK and the US) is made in the brilliantly researched article of Tomas Pueyo and his team, here. The weight of expert scientific opinion now supports Pueyo’s conclusion; an open letter, sent to the UK government on Thursday 19th March and signed (as of today) by 627 UK public health specialists, epidemiologists, scientists in relevant fields, and healthcare professionals, also calls for an immediate lockdown and extensive testing. The behaviour of many people in the UK over the last weekend (ignoring the government’s plea for social distancing), combined with the critical situation in Intensive Care Units (particularly in London, but it will soon happen in most other places), implies that government ‘guidelines’ are no longer enough: new rules with strict enforcement are needed, with enforcement by the police and maybe even the army if the police lack the manpower.

Proposal 2: While there is a limited supply of testing-kits available, try to test those whose positive diagnosis would do most to prevent new infections and deaths.

This won’t be easy and will involve some difficult trade-offs, but it could save a very large number of lives if it is done right. NHS staff and other key workers should presumably be prioritized to a large extent. NHS staff obviously cannot work from home and, if they are infected but do not realize, they have the potential to infect a very large number of other key workers (NHS staff) and also a large number of vulnerable people (patients with other conditions) who are more likely to die. Those in essential parts of the food industry, and delivery drivers, should also be given fairly high priority. Finally, while there is still a shortage of testing-kits, testing should not be spread too thinly in the rest of the population: if it can be concentrated to good effect in a particular district to stop an outbreak at a very early stage, or to suppress outbreak in an area where the NHS is being completely overwhelmed, then this should be seriously considered, even if it means less testing temporarily in some other districts. If they aren’t already, the NHS and the UK government should be taking advice on this specific problem from mathematicians specializing in probabilistic and computational modeling, as well as from epidemiologists and public health experts.

Proposal 3: Speed up the development of treatments, by loosening the rules.

In ordinary times, newly invented treatments have to go through more than 18 months of testing before becoming available, to make sure they don’t interact badly with any one of a vast number of other treatments that are available on the NHS. But these are not ordinary times – every day of delay in the availability of a treatment will almost certainly lead to thousands of deaths, many of which could have been averted by a treatment becoming available sooner. The government has to weigh these things up, even if adverse reactions to the treatments will result in some deaths – the question is, which course of action will result in the fewest deaths, and the least suffering?

Proposal 4: Speed up the development of a vaccine, by loosening the rules.

In ordinary times, vaccine-testing (like treatment-testing) is also subject to very strict rules, which slow it down. The government’s scientific advisors should perform a cost-benefit analysis of loosening these rules, even if there are some negative consequences of loosening the rules. Every day in the delay of the availability of a vaccine, could cost thousands of UK lives. There will be tough trade-offs, as discussed here, but we shouldn’t simply assume that the existing regulations are appropriate to this unprecedented situation; they almost certainly aren’t.

Proposal 5: Loosen the rules around privacy to allow more effective contact-tracing.

Today, South Korea reported the lowest daily number of new cases (64) in the last four weeks. For the last two weeks, the growth in the number of cases in South Korea has been linear (rather than the exponential growth Europe is seeing), and it has a very good chance of being successful in suppressing the outbreak. A key part of South Korea’s strategy was to relax the laws around individual privacy and surveillance, enabling detectives to trace the contacts of people who have tested positive, and to ensure that those contacts get tested; those who had been in close proximity with a known case received text-messages informing them of this. The ordinary rules on privacy and surveillance can be restored when the outbreak is over, but a temporary relaxation of the rules in the UK could well save a large number of lives (and help prevent catastrophic socioeconomic damage).

Proposal 6: Develop an instant contact-tracing app that people can download voluntarily, which notifies them if (in the last 14 days) they have been in close proximity with a newly-confirmed case.

A multidisciplinary team of researchers at Oxford University, in work published last week, used computer modelling to show that a mobile phone app for instant contact-tracing, would be capable of stopping a coronavirus epidemic (if used in combination with other measures). Prof. Christophe Fraser, who leads the team, describes the idea as follows. ‘The instant mobile app concept is very simple. If you are diagnosed with coronavirus, the people you’ve recently come into contact with will be messaged advising them to isolate. If this mobile app is developed and deployed rapidly, and enough people opt-in to use such an approach, we can slow the spread of coronavirus and mitigate against devastating human, economic and social impacts.’ An app along these lines was rolled out yesterday by the Israeli Ministry of Health, on both Apple and Android platforms. It has the advantage of not uploading any location information to government servers, thus avoiding the ‘big brother’ problem. The full code of the app is open-source, and it was endorsed by a large number of security and privacy researchers in Israel who assured the public that it is safe to use, since it does not upload any information to government servers. Within 12 hours it had already been downloaded hundreds of thousands of times (and bear in mind that the total population of Israel is only about 8 million). In the light of the findings of the Oxford team, the UK should implement something similar, as soon as possible.

Proposal 7: Recruit people who are immune to COVID-19, to work in care homes.

This would work well if immunity generally persists for a long time. It will take some more time for reliable data on this to be available, as the pandemic is only three months old, but when reliable data is available, a cost-benefit analysis of this proposal should definitely be performed.

Proposal 8: Introduce rationing (and government-controlled distribution) of several types of essential goods.

Supermarkets in the UK are currently completely unable to cope with demand, which has spiked tenfold since early March. If supply-chains become disrupted due to agricultural and delivery workers falling ill, this problem will become even worse. The government should step in to make sure everyone gets enough of the essentials. There will be enough to go around, provided the more fortunate don’t hoard everything. Professor Tim Lang, one of the UK’s leading food-supply experts, argues for these measures in this article, published today.

Proposal 9: Institute a Universal Basic Income for the duration of the outbreak.

Many jobs are under threat, particularly in the hospitality, catering, events, tourism and clothing sectors, but also in many other sectors impacted by social distancing; many have already been made redundant. The administrative load of means-testing financial relief for everyone in this situation would be completely unmanageable. A Universal Basic Income is the best solution (indeed, the only viable solution) for preventing mass-hardship – as argued powerfully by the Oxford economist Daniel Susskind in this FT article. (Skeptics should note that, before the pandemic, Susskind was not in favour of a Universal Basic Income.)


Further discussion on the above proposals (and others), as the situation develops.

[Some of the most important updates/additional proposals have titles in red.]

Update 1 (24th March): On the new UK lockdown.

Yesterday evening, the UK Prime Minister announced measures that almost amount to a Spain-style lockdown, effective immediately. It is permitted for citizens to leave home only for the following reasons:

  1. Shopping for basic necessities, such as food and medicine – which should be as infrequent as possible.
  2. One form of exercise a day, for example a run, walk, or cycle – alone or with members of your household.
  3. Any medical need, or to provide care or to help a vulnerable person
  4. Travelling to and from work, but only where work absolutely cannot be done from home.

Government instructions state that ‘These four reasons are exceptions – even when doing these activities, you should be minimising time spent outside of the home and ensuring you are 2 metres apart from anyone outside of your household.’ Gatherings in public of more than two people are prohibited (unless those two people belong to the same household), and all non-essential shops and businesses are required to close.

Analysis. It remains to be seen whether people will abuse the second exception (being allowed to leave home to take exercise), e.g., whether people will comply with the requirement to only exercise alone or with members of their own household, and whether they will stick to the ‘once-a-day’ rule and stay two metres from others while doing it. If they don’t, there could be a strong case for forbidding it; most people will not be seriously at risk from having to exercise indoors for three weeks. One should note that the second exception was not allowed in Spain.

The police do not yet have the required powers to enforce these measures (e.g. to fine those who violate the instructions), so legislation allowing enforcement will need to be passed with the utmost speed. Widespread testing is still urgently required, and as mentioned in the post, the police may require the support of the army, if enough people defy the instructions, or if the police suffer critical manpower shortages. The Metropolitan Police today reported that 19% of its police officers, civilian staff and community support officers did not report for duty because of contracting the coronavirus or because of having to self-isolate after being in contact with a known case.

Gil Kalai (an internationally-renowned mathematician with expertise in graph theory, among other areas) has today communicated to me a very good point about the UK lockdown. To delay the peak of the coronavirus outbreak in the UK (and reduce the maximum number of simultaneous infections), it will be important to minimise travel of people between different communities, so that, for example, the very serious outbreak in London (which already on Saturday was seeing Intensive Care Units in North London being overwhelmed) is not immediately transmitted to other districts and regions, many of which are currently less hard-hit; this will buy the government time for its emergency preparations. In mathematical (graph-theoretic) terms, minimising unnecessary contacts between different communities prevents the Transmission Graph from being an expander; this is important for suppressing the epidemic near the beginning, as pointed out for example in this study. Kalai observes that car-travel by individuals between different communities will be a particular danger (particularly if they visit ‘hubs’),  but car-travel is not specifically mentioned in the UK government instructions. Some car-travel will be necessary (for those in more isolated areas to buy food and medicines, for example, and for critical-sector workers to take their children to school if they don’t live within walking or cycling distance of the school). But it may be worth the UK government adding penalties for violations of the lockdown that involve unnecessary car-travel between communities.

A London-specific problem is that even today, workers from non-critical sectors were still defying the government’s instructions and using the London Underground, leading (for the second day this week) to crowded carriages where it was impossible to keep 50 centimetres (let alone 2 metres) from the nearest other occupant. This poses a great risk to critical-sector workers, in particular to NHS staff who have to use the Tube to get to work, and to the many patients and colleagues they will subsequently come into contact with. (As has been pointed out many times, due to the close proximity of commuters for 15 minutes or longer at a time, the Tube is an ideal environment for the spreading of the virus.) Substantial penalties should perhaps be introduced for people using the Tube in defiance of government instructions; Transport for London could also consider blocking the contactless/Oyster accounts of those who do not provide evidence (within a few days) of being a critical sector worker – though the administrative burden of this might be substantial.

If the UK lockdown is successful in initially suppressing the outbreak (possibly after it has been made more stringent), the next stage will be to prevent a ‘second peak’ by rapid containment action to suppress any new outbreak (this is the phase that Pueyo refers to as ‘The Dance’). In this phase, I expect Proposal 6 to be of crucial importance. But the sooner an instant contact-tracing app is rolled out, the better.

Update 2 (25th March, re Proposal 1): On NHS staff getting to work safely.

Several of my colleagues have suggested promising strategies to avoid a situation where significant numbers of NHS staff contract COVID-19 while using the Tube. One is to encourage cycling where possible (perhaps by distributing free bicycles, bicycle locks, bicycle lights and helmets to NHS staff who live a certain distance from their place of work). Another is to offer free or subsidised emergency accommodation within walking-distance of hospitals (though another solution would be needed for those with families). Finally, as of today, parking charges have been lifted for all Scottish hospitals, and in my opinion this should be done (for staff) in England too – as per this petition, already signed  in the last two days by over 380,000 people. (Update, 26th March: free hospital parking for NHS staff in England has now been announced.) When COVID-19 testing kits become widely available to NHS staff, it could also make sense for the NHS to offer free minibus transport to its staff, but this could be counterproductive (with NHS staff passing the virus to one another, e.g. if they are seated close together on journeys longer than 15 minutes), while testing-kits for NHS staff are still in short supply.

Update 3 (26th March). The need for systematic testing to determine the true COVID-19 infection-rates in each region of the UK; misleading headlines generated by an Oxford study. 

This week, a team of researchers at Oxford (Lourenço, Paton, Ghafari, Kraemer, Thompson, Simmonds, Klenerman and Gupta of the Department of Zoology / Nuffield Department of Medicine) released a preprint (not yet peer-reviewed) stating that, according to their models, the current coronavirus data is consistent with around 50% of the UK population having been infected (at some stage) by COVID-19 by 19th March. (Though, as they say and as explained here, the data is also consistent with much lower proportions than 50% having been infected, hence the need for systematic testing to determine the true prevalence.)

The preprint generated some unfortunate headlines reporting stronger claims than the Oxford team actually made. Many experts (including other expert epidemiologists) are concerned that these headlines could encourage complacency and a lack of compliance with measures to suppress the UK outbreak, and a group of them wrote this letter to the Financial Times today, pointing out that the hospitalisation-rate among infected cases assumed by the Oxford team to get the 50% figure (0.1% of infections requiring hospitalisation) seems to lack empirical justification, and seems too low compared to the data from Italy. As the letter points out, Lombardy has a total population of 10,060,574. Despite stringent control-measures (a lockdown of the worst-hit provinces starting 21st February, and a complete nationwide lockdown starting 9th March), the total number of people in Lombardy hospitalised with coronavirus is 10,905. Hence, the number of hospitalised cases of coronavirus per head of the population in Lombardy is 0.108%. So the 0.1% estimate for the hospitalisation rate would only be close to the truth in Lombardy, if almost 100% of the population had been infected at some stage. (The letter also points out that their Italian colleagues Prof. Walter Ricciardi and Prof. Anna Odone have data indicating much higher hospitalisation-rates per head of the population than 0.108%, in some Lombardy towns.)

There is also the issue that the SIR model used by the Oxford team assumes that infected people are ‘well mixed in’ with uninfected people, in the general population. This is not quite true, since infections in the UK appear to have been concentrated in various hotspots (such as London) where infected individuals have a lower probability of infecting those from other parts of the country (such as Lincolnshire), where the proportion of infected people was much lower. In mathematical terms, the SIR model works perfectly if the transmission graph is highly pseudorandom, but this is not quite true for the actual transmission graph: there will be geographical concentrations of personal connections, for example. As pointed out by Gubbins (of the Pirbright Institute) and Hunter (of UEA) here, this will lead the SIR model to overestimate the number of infected people. But it will only be a slight overestimate, since (particularly in the early stage of the UK outbreak, before 19th March, which the Oxford team use to calibrate their model), very many of the contacts of infected people will have been uninfected.

It is worth remarking that even under the assumption that the hospitalisation-rate per infection is 3% (and given the data from South Korea, the UK rate will almost certainly be no higher than this, even accounting for the UK’s more elderly population), the Oxford model would still predict that about 15% of the UK population had probably already been infected (at some stage) by 19th March, so the predictions are somewhat robust with respect to quite large changes in hospitalisation-rate. (Though the calculations will need to be checked in the peer-review process.) Note that, even if the 50% figure were correct, it does not mean that those 50% will have long-lasting immunity; it is impossible to know at this stage how long immunity will typically persist for, and it will be of crucial importance for tackling the outbreak to perform repeated tests on recovered individuals to find out how long immunity typically persists for. (Some patients have reportedly recovered and then become ill with COVID-19 a second time, but it is possible that the testing may have been faulty; at this stage there is simply not enough evidence to know whether it is possible to catch coronavirus twice, as pointed out yesterday in this New Scientist article.)

The main conclusion we should take from the Oxford study (as the Oxford paper/preprint says itself) is that systematic testing is urgently needed to determine the prevalence-rate of COVID-19 infections per head of the population, in each region of the UK. (Note that this prevalence will be higher in some regions, for example London, than others, so systematic testing is needed in each separate region.) This could be done either by randomised testing, or (if this proves impracticable), testing all the inhabitants of one small district or town, in each larger geographical area. (The Italian authorities, for example, tested all the inhabitants of the town of Vò, in Lombardy – including those without any symptoms.) As the Government Chief Scientific Advisor Sir Patrick Vallance said yesterday, we simply do not know at this stage what proportion of the UK is currently infected. And we will have no way of knowing (for some time) whether immunity persists for a short time or a long time.

(NB: this update previously contained a calculational error, now corrected thanks to a comment below. The main conclusion, that systematic testing is urgently needed to determine the prevalence rates in each region of the UK, still stands.)

Update 4 (26th March): On closing non-essential construction sites.

It has been pointed out many times that construction-sites are an environment where COVID-19 can spread easily (it is impossible to maintain a 2-metre distance from coworkers in many situations, for example). UK Government instructions do not yet mandate that construction-sites close. Several companies have decided to close their construction sites anyway (e.g. Barratt, Belway and Tayor Wimpey; Persimmon is stopping ‘all but essential work’). But several have announced they are not suspending work (e.g. Cairns Construction, Berkeley, Crest Nicolson and Balfour Beatty). (See this BBC article and this Guardian article.) There could be a strong case for the government mandating that all but essential work is stopped (essential work includes, for example, the building of emergency temporary hospital capacity, or making other sites safe for closure as soon as possible).

Update 5 (26th March): On encouraging safe shopping; an issue with Sainsbury’s opening hours.

Most UK supermarkets are still unable to offer online delivery slots to customers under 70 years old (and not in strict isolation because of a suspected coronavirus case), due to being overwhelmed by the huge demand, so it is still necessary for many people to shop occasionally for essentials. Supermarkets and shops should take measures to minimise the risk of transmission during shopping; this could include providing a supply of disposable latex gloves at the entrance, encouraging people to wear their own disposable or washable gloves where possible, and incentivising contactless payments (perhaps by a discount). These ideas were suggested by the mathematician Prof. Darij Grinberg, in a comment below on this blog.

There is also the issue that the special Sainsbury’s shopping slot for NHS workers and carers only (7:30am-8am Monday to Saturday), comes right before their special hour for the elderly and vulnerable (8am-9am Monday, Wednesday and Friday), three days per week. This does not seem to be a very good way of arranging things, as the half-life of the virus in air is approximately one hour (and longer on plastic surfaces), the elderly are of course especially vulnerable, and at present there are high rates of infection among NHS staff (due to the lack of testing-kits). It would probably be advisable for Sainsbury’s to separate their slots for the elderly, from their slot for NHS workers and carers, by a greater length of time. Reversing the order of the two slots on Mondays, Wednesdays and Fridays could make sense if most NHS workers can shop later than 8am on those three days (and this would presumably not be an issue for hospital workers working 7am-7pm shifts). Some stock can be kept back for the elderly-only slot if this is placed a few hours after the slot for NHS staff (if panic-buying and stock shortages persist).

Update 6 (26th March): On (not) banning outdoor cycling for exercise. 

Some have pointed out that the Spanish lockdown includes a ban on cycling. This may not be a very good idea, as the typical distance between cyclists (unless they are cycling in a big group in defiance of government regulations) is greater than the typical distance between pedestrians; added to which, it is many people’s main form of exercise, and preventing the taking of exercise has important costs, in terms of both physical and mental health. This, like the previous point, was observed by Darij Grinberg in a comment below. The UK lockdown at present permits cycling for exercise (and it is permitted to go outside to take exercise once a day, for up to two hours); as far as I can judge, this is probably sensible and proportionate.

Update 7 (26th March): On encouraging people to exercise at different times of the day in areas with a high population density.

The current UK government instructions allow people to leave their homes to take exercise once a day, for at most two hours per day. In cities with a high population density, such as London, this could lead to concentrations of people exercising at certain times of the day (e.g. the early morning or early evening), which is undesirable. A solution to this would be to encourage those who can to exercise at a time of the day based on e.g. the letter their surname begins with (or some other criterion that is independent of where one lives). This would be voluntary, as some people can only exercise at given times, due e.g. to childcare commitments, being a key worker or being a shift worker. This was suggested in a comment below.

Update 8 (26th March): On reciprocal agreements between countries to alleviate ICU staff shortages and equipment shortages.

As the well-known historian (and author of Sapiens and Homo Deus), Yuval Noah Hariri, pointed out in his F.T. article on 20th March, there will be significant advantages to cooperative actions between countries, in many aspects of tackling the pandemic – advantages to all the countries concerned in the relevant cooperative action. For example, many countries with early outbreaks are projected to shortly suffer a critical lack of ICU-trained staff (especially given high levels of staff sickness) – or indeed are already suffering such a shortage (as reported in London today, by the BBC).  On the other hand, several countries either have very small outbreaks currently, or appear to have successfully contained their outbreak. If country A has a serious outbreak and is projected to soon suffer a critical shortage of ICU-trained staff, whereas country B has no serious outbreak currently, an agreement whereby ICU-trained staff from country B will work in country A for a specified length of time (in return for some form of current or assistance), would be of great advantage to both countries. (One obvious form of future assistance would be as follows: if country A is able to suppress its outbreak, and country B subsequently suffers a serious outbreak, there could be a transfer of ICU-trained staff who are well-trained in tackling COVID-19, from country A to country B.)

In many cases it will also be advantageous for large groups of countries to agree on the joint procurement of certain types of equipment in which there is an acute global shortage, as larger blocs typically have more buying power than smaller ones and can also hedge more effectively against acute shortages. To explain the latter point, suppose that a particular product is crucial for tackling the epidemic, and three countries each have their own independent supply, and each supply will fail with a probability of 1/10 (independently). The probability that a particular country’s supply will fail is 1/10, but if each country agrees to help supply the two other countries should their supply fail, the probability that the bloc as a whole will ever suffer a failure of supply is only (1/10)3=1/1000. The (small) disadvantage to the most well-resourced country is that if all the supplies simultaneously fail, then the most well-resourced country would presumably have to share some of its remaining stock with the other two countries – but this event of simultaneous failure has a probability of only 1/1000, so the disadvantage is small. This is a simplistic analysis, of course (the independence assumption will not always hold exactly, and the failure-probability of 1/10 is for illustrative purposes only), but it conveys the idea.

In his article, Hariri outlines several other mutually advantageous cooperative actions between countries, some of which I will discuss below.

Update 9 (27th March): On international flights.

If the UK is successful in suppressing the current outbreak (through the lockdown, and other measures), but other countries are not, it will make sense to impose (temporary) restrictions on international flights arriving in the UK. (On 17th March, for example, the European Union suspended all non-essential travel into the bloc by non-EU nationals; the Canadian government announced a similar measure on 16th March, and announced on 25th March that, effective from midnight, international arrivals would have to self-quarantine for 14 days on entering Canada.) One mistake made early on by Italy was imposing restrictions only on flights from China; this meant for example that some flew to Italy from China via third countries, making it much more difficult for them to be identified and potentially tested for COVID-19 (or its symptoms), on landing in Italy. Hence, if restrictions are imposed, they should probably be imposed on flights regardless of their country of origin. Moreover, as pointed out by Hariri in his article, it will of course be necessary to maintain some capacity for international flights to and from the UK, throughout the crisis, for emergency purposes: the transport of medical staff and other critical personnel, and of medical equipment and other critical supplies, for example. As pointed out by Hariri, an international agreement by which emergency passengers were tested for COVID-19 before departure would be of great utility (the disease can of course be readily transmitted during air travel, due to the close proximity of passengers for a long period of time), though I differ from Hariri in believing that testing on arrival would also be of additional utility, until it is proven that the UK has the capability of suppressing and limiting the damage from a new outbreak.

Assuming the current outbreak is suppressed, in the medium-term, until it is fairly certain that the UK has the capability to suppress (and limit the damage from) future outbreaks that might occur in the event of reintroduction, it will make sense to consider restrictions (e.g. testing or self-quarantine) on international arrivals, though the benefits of such restrictions (given that there are other means of reintroduction) must be balanced against their socioeconomic costs and their (geo)political costs. If a vaccine or effective treatment is developed, or if a large enough proportion of the population develop immunity, or suppression measures become extremely effective, such restrictions would no longer be needed.

Update 10 (28th March): On avoiding ‘hubs’ where large numbers of people come into contact, and the urgent need for supermarkets to increase their home delivery capacity (if necessary with government aid).

It is intuitively clear that a dangerous obstacle to suppressing the current UK outbreak is the presence of ‘hubs’ (such as supermarkets and schools) where large numbers of people (who don’t otherwise come into contact) visit on a given day. This is confirmed by mathematical modelling, e.g. here. In fact, the presence of just one ‘hub’ in a community leads to a much higher (and sooner) spike in the number of simultaneously infected people, and this effect is considerably more serious than the effect of e.g. car-travel between different communities that avoids ‘hubs’ (e.g. children being moved from one parent’s house to another). Avoiding a situation where large numbers of people are simultaneously infected is obviously of critical importance in preventing the healthcare system from being overwhelmed, and therefore in keeping the number of deaths down. This is no doubt part of the thinking behind the updated government instructions that people should exercise locally if possible – e.g. they should not be visiting beauty-spots that require a car-journey, and other places that are generally popular with large numbers of people who don’t otherwise come into contact with each other.

[It is important to note that restricting car-travel between communities – even where this car-travel avoids hubs – is also important to buy time for the government’s emergency preparations – it will help delay the peak in the number of infections in less-hard-hit communities that are a greater distance from London, for example.]

The closure of schools (to children of people who are not critical workers) will help to cut down the risk posed by ‘hubs’, though schools must necessarily remain open to children of critical workers, and they cannot of course be closed for too long without very significant down-sides. But the danger posed by ‘hubs’ does imply that it is important to do more to minimise people’s need to visit supermarkets. Even if people are able to keep a distance of 2 metres or more from others while shopping, there is still a risk of infection – the half-life of the virus in air is a little over one hour, and its half-life on plastic surfaces (for example) is longer. Cashiers are also at particular risk of contracting the disease or inadvertently (and through no fault of their own) passing it on (if they display no symptoms). It is therefore of high importance for supermarkets to rapidly increase their capacity for home deliveries, even for those who are not elderly. Short-term government aid to facilitate this would be worth serious consideration – for example, through the emergency provision of refrigerated delivery vehicles (a particular bottleneck) and delivery staff. It may be necessary and appropriate to increase salaries for delivery staff, to aid and accelerate recruitment and to compensate for the risk they are at.

As of today (28th March), Sainsbury’s, Tesco and Waitrose are still unable to take new registrations/orders for home delivery in most areas of the UK, except for those classed as particularly vulnerable (e.g. the elderly) or those in strict isolation due to a suspected COVID-19 case, but the younger and less-vulnerable can also spread the disease, and in fact are more likely to do so, as there are many more of them and they leave their homes more often. (The fact that around 70% of cases are asymptomatic or quasisymptomatic, is relevant here; younger and less-vulnerable people will not necessarily know they have the disease, but can still be infectious in the asymptomatic period.)

Another means for supermarkets to increase their home-delivery capacity would be to make a temporary agreement with wholesalers with unused/under-used refrigerated delivery vehicles (such as wholesalers who generally supply the now-defunct hospitality industry, and/or restaurants), for a short-term loan of vehicles (and/or delivery drivers). This would presumably be of mutual advantage. Some wholesalers are already using some of their underused capacity (which is ordinarily used e.g. to supply restaurants, now closed to dine-in customers) to offer home deliveries, but an alliance with supermarkets such as I describe would enable them to use more of their spare capacity (as well as ensuring that the extra home-delivery capacity they provide is not restricted mainly to the wealthy).

Update 11 (3rd April): On emergency free / low-cost accommodation for NHS workers, in universities, hotels and vacant short-term lets.

In the last two weeks, reports have emerged that some NHS workers who lodge with their landlords have been requested to leave their accommodation at short notice, by live-in landlords worried that NHS workers are at a higher risk of infection. (The temporary suspension of evictions for 90 days, a.k.a. ‘eviction ban’, which took effect on 1st April, does not apply to lodgers.) Such requests, while often distasteful, might sometimes be understandable when the landlord is in a particularly high-risk group, so making them illegal would be problematic. (Though penalties could be considered for landlords not in a high-risk group.)

To help NHS workers in such situations, some hotels, some universities, and thousands of landlords are now offering free or very low cost emergency accommodation to healthcare workers. (Many hotels are all but empty, the short-term letting market is now down by 90%, and UK universities are currently operating only via distance-learning, so that much of their student accommodation is currently vacant.) Other universities and hotels should perhaps be strongly encouraged to do this. A fortnight ago, Merilee Karr set up a new website, NHS Homes, to put healthcare workers in touch with landlords and hotels willing to offer free accommodation for healthcare workers; as of today, about 400 homes are listed, worth a combined total of £1.2 million per month in rent. The government could consider introducing financial incentives to increase the number of homes offered (by hotels and by landlords). In the short-term, particularly while there is still a shortage of covid-19 tests for NHS staff, the need for emergency accommodation for NHS workers will only increase – for example, when NHS staff with a suspected case of covid-19 need to self-isolate from their families in separate accommodation. Incidentally, these problems underline the urgent need for ramping up testing-capacity.

Update 12 (5th April): On the possible exit-strategies for exiting the UK lockdown.

The first objective of the ‘suppression’ strategy that the UK government has adopted is to get the number of new infections per day down to a level that will not overwhelm NHS capacity. This essentially involves getting the ‘infectivity’ (defined as the average number of people each infected person infects) down to a number that is below one. About two weeks after this has been achieved, the number of newly confirmed cases per day will start to fall. (The delay is because of the incubation period of covid-19, and a delay in testing and getting the results.) But until it has been achieved, the number of new infections per day will continue to rise.

The following graph shows the number of newly confirmed cases in the UK, each day, up until yesterday (4th April):

Screen Shot 2020-04-05 at 12.29.32

Not too much should be read into day-to-day variation in the number of new confirmed cases; it appears the number tends to drop slightly at weekends for example, possibly because of reduced testing-capacity at weekends. It is still too soon to know whether the UK lockdown has succeeded in achieving a fall in the number of new infections per day; if it has not yet succeeded in doing this, the government will need to introduce further measures (such as mass-testing and contact-tracing, or stricter enforcement) until it does fall, to prevent the NHS from being overwhelmed. It is even a bit too soon to know (with a high degree of certainty) whether the Italian lockdown (introduced earlier) has succeeded in this, though we should know with more certainty in about a week’s time.

Obviously, a full lockdown cannot last indefinitely; the socioeconomic costs of continuing it for a very long time would become too great (leading eventually to societal collapse). When the number of new cases per day has been reduced to level that is manageable by the NHS, the two most vital questions the UK government has to decide will be (1) when should the full lockdown be lifted?, and (2) what measures should it be replaced by to ensure that the number of new infections per day doesn’t simply start to rise again in such a way as would overwhelm NHS capacity (i.e., a so-called ‘second peak’)?

Four possible answers to the second question have been proposed, each of which I believe are worth serious consideration.

Approach (1): The suppression (or ‘Hammer and Dance‘) strategy proposed by Pueyo. Lift the lockdown when the number of new infections per day has fallen to a very low level, and then subsequently stamp down hard on any new outbreak in order to suppress it, using a combination of contact-tracing, rapid and extensive testing (possibly of the whole population), rapid and effective isolation of known cases, and other measures such as Pueyo describes in his influential article. These measures would need to last, in some form, until a vaccine or an effective treatment has been developed, or until the capacity of the NHS has been sufficiently built-up to deal with a ‘second peak’.

Approach (2): The ‘Adaptive Triggering‘ strategy: alternate between lockdown and ordinary life, lifting a lockdown when the number of new infections per day falls below a certain pre-decided number N, and introducing a new lockdown when the number of new infections per day rises above another pre-decided number, M. Proposed by Ferguson et al. in their influential paper that caused a major shift in UK government policy.

Approach (3): The two-day working week, i.e. two days of ordinary life followed by five days of lockdown, repeated weekly until there is no longer any need to do so. Proposed by the systems biologists Alon, Dudovich, Karin and Korem, in this article.

Approach (4): A fortnightly variation on (3), with four days of ordinary life followed by ten days of lockdown, repeated fortnightly until there is no longer any need to do so. Also proposed, as a safer alternative to (3), by Alon, Dudovich, Karin and Korem, in this article.

Here, it is important to clarify that the days of ‘ordinary life’ in (2), (3) and (4) above would not be completely ordinary (by pre-pandemic standards). To prevent an uncontrolled growth in the number of cases on those days, the days of ‘ordinary life’ would still need to involve extensive testing, the prompt and effective isolation of symptomatic cases, and strict hygiene practises (such as regular hand-washing and the regular disinfection of workplaces, public places and vehicles of public transport). Those most at risk could also continue to be shielded from non-essential contact with others to a large extent. However, most workers would go to work as usual, and schools, kindergartens and universities would open as usual.

On ‘lockdown’ days, however, the situation would be broadly the same as it is in the UK currently, under lockdown: schools, kindergartens and universities would be closed, and most (except for key workers) would work from home. Most people would leave their homes only to shop for essentials (such as food and medicine), or to take exercise (and then only once per day).

Many experts (as well as many ordinary people) favour trying approach (1), as (if it goes according to plan) it would avoid further lockdowns (with their high socioeconomic costs) and it would simultaneously avoid future large increases in the number of cases. However, it is too soon to know whether approach (1) will definitely work, for the following reasons.

Approach (1) has not yet been fully and successfully implemented in any country that suffered a major outbreak. So far, it has been partly implemented in South Korean (but only partly, as schools remain closed, for example). Among all the countries that have suffered large outbreaks, South Korea is the only country (except for China) that has seen a consistent and long-term daily decline in the number of active cases:

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South Korea has never in fact imposed a lockdown; the social-distancing rules in force are milder than those in the UK, and many shops, cafes and other businesses remain open. Instead, it has opted for a combination of mass-testing and intensive contact-tracing. It has made extensive use of drive-through centres for testing, and also tests asymptomatic people, estimated to be around half of all carriers of the disease. As of today (5th April), more than 460,000 tests have been performed in South Korea, compared to about 196,000 in the UK, whose population is 1.2 times larger.

It is important to note, however, that South Korea has not yet returned to normal life, properly speaking. Kindergartens, schools and universities remain closed, for example, greatly restricting the ability of parents to go to work. It was announced on 31st March that the reopening of schools (which had been due to take place on 6th April, after two delays) would be delayed for a third time (with online lessons starting on 9th April, instead).

As I said above, approach (1) has not yet been successfully implemented at all in any other country that suffered a large outbreak. (Singapore and Taiwan did adopt it with some success, but neither ever suffered a large outbreak. Also, the Singaporean government decided on 3rd April to close schools and most businesses, after seeing a recent increase in the number of new cases.) China imposed highly draconian measures that would not be possible in Western European countries, unless perhaps the disease were many times worse.

Moreover, while mass-testing on South Korean levels can certainly be replicated in the UK within weeks, it is not clear whether the UK would be able to achieve democratic consent for relaxing privacy laws to the extent that will allow for effective contract-tracing. Jung Won Sonn outlines in this article that contact-tracing as practised in South Korea has involved a level of surveillance and exposure of individual information that would currently be illegal in all Western European countries – as well being very resource-intensive. (In South Korea, large teams of detectives examine CCTV footage to track the movements of confirmed cases and identify their contacts, who are then notified by text-message of their proximity to a known case, and are asked to visit a testing centre. Text-messages are also sent by district authorities to the general public, listing the locations – including shops and restaurants – visited by individuals who subsequently tested positive.) There are of course less invasive and less resource-intensive methods of doing contact-tracing (such as the development of a voluntary contact-tracing app, described in Proposal 6 above). But we do not yet know for sure how effective these less invasive methods will be in reducing transmission of covid-19 in Western Europe. (The effectiveness the app will depend on the level of uptake, and how effectively people make use of the information the app provides, for example, as well as how fast transmission is taking place, given the suppression or mitigation measures we have in place.) 

Since we do not yet know whether approach (1) will work, it is worthwhile to consider approaches (2), (3) and (4). The computer modelling of approaches (3) and (4) by Alon et al (see their article) suggest that approach (4) could well be capable of gradually reducing the fortnightly total number of new cases, and that approach (3) would also be capable of  doing this, though approach (4) would achieve it faster since it takes advantage of the fact that people infected on workdays would be at their most infectious on lockdown days (under the fortnightly cycle). However, the assumption they make on the effective transmission rate of covid-19 under lockdown (RL), namely that RL is close to 0.3, is rather optimistic. This study reported a figure of approximately 0.3 for the (highly draconian) lockdown in Hubei province, but it is not yet clear whether such low rates have been replicated by the European lockdown. A recent (30th March) study by Ferguson et al found estimates for RL (for the current lockdowns in Europe) all being at least 0.98 (though with a high degree of uncertainty); the probability that the UK lockdown achieved RL < 1 is estimated at 0.4. Further days of data (consisting of the number of new cases per day, probably for a further week or more) will be needed to properly estimate the effective transmission rate under the UK lockdown. Assuming the UK lockdown achieves RL < 1 (at which point the number of new infections per day starts to decrease; this is certainly needed before a lockdown is lifted), it may be necessary to slightly adjust the model of Alon et al to account for a higher value of RL than in Hubei province. This might lead, for example, to a need to replace the fortnightly cycle of 4 ‘ordinary’ days and 10 ‘lockdown’ days by a fortnightly cycle of 3 ‘ordinary days’ and 11 ‘lockdown’ days, to achieve the desired reduction in the fortnightly infection rate.

Compared to approach (2), approaches (3) and (4) have the advantage that they provide a predictable schedule around which people can plan their lives; they also make it easier for people to keep track of which regulations are in force on which days, which would improve compliance. Approach (2), on the other hand, is better-suited to responding to the current infection-rates, e.g. if these rise too high too suddenly during a period without a lockdown. It would also be worth considering a combination of approaches (2) and (3) – starting with approach (3), and then switching to approach (2) if the fortnightly number of new infections rises too fast. Similarly, a combination of approaches (2) and (4) could be used. The last combination would perhaps be better, as approach (4) is safer than approach (3), and at present I think it would be my preferred option if approach (1) fails.

Update 12 (11th April): On the possible non-persistence of immunity.

A preliminary study released on MedRxiv on Monday 6th April by a team of researchers at Fudan University (Shanghai) examined blood-samples from 175 (recovered) coronavirus patients who had suffered ‘mild’ symptoms (which may include a fever or continuous cough but do not include dyspnea, high respiratory frequency and low blood oxygen saturation), and had subsequently been released from Shanghai Public Health Clinical Centre. The study found that 30% of the patients exhibited levels of antibodies that may be too low to provide future immunity. (Most of those with low antibody levels were young; the patients in the 60-85 age-group had on average more than three times the antibody levels of those in the 15-39 age-group.) The paper will need to be peer-reviewed, and other scientists will need to attempt to replicate the findings, before we can draw any firm conclusions. But if the findings are confirmed, they may (for example) reduce predictions as to the future levels of population immunity that would arise from certain levels of infections. The study also raises the possibility that a vaccine might not provide effective protection for part of the population: if the immune system of some individuals does not produce antibodies in response to the actual virus, it might not do so in response to the vaccine either. Of course, all this is rather speculative at this stage; even if the findings are confirmed, they wouldn’t rule out the possibility of an effective vaccine. More research, and more data, is certainly needed on the persistence (or otherwise) of immunity, particularly in view of the tentative proposal to provide UK citizens with ‘immune passports’.

Update 13 (17th April): First systematic serological study enables a crude estimate of the percentage of the UK population exposed to covid-19 by 24th March.

The first systematic serological study (to my knowledge) was completed last week in Germany; the preliminary report is here. A representative sample of about 1000 inhabitants (not necessarily known to have been exposed to covid-19) was drawn from the town of Gangelt (a particularly hard-hit town, due to a carnival in February). For a preliminary result, blood samples from 500 people were tested. 14% of them were found to contain covid-19 antibodies (using a test claimed to have >99% specificity, though its sensitivity is not mentioned). Individuals who are currently ill with covid-19 do not always have antibodies and so the proportion of these individuals was estimated using the usual PCR tests, at 2%. The final estimate for the number of exposed individuals was 15% of Gangelt’s population. This enabled the researchers to estimate the case-fatality rate in Gangelt, at 0.37%. The case-fatality rate should be independent of the fact that Gangelt was particularly hard-hit (given that the healthcare system there wasn’t overwhelmed, which it wasn’t).

Now, assuming the case-fatality rates (in each of the various age-groups) in Gangelt is similar to the case-fatality rates in the UK as a whole (in each of the various age-groups) – which I think is a fair assumption as none of the healthcare systems in any of these countries/towns have been overwhelmed at any stage – one can use the case-fatality rate in Gangelt (together with the number of fatalities and the population histograms) to estimate roughly the true number of people exposed to covid-19 in the UK, by the beginning of the UK lockdown.

I’ll do this fairly crudely. The official UK data on covid-19 deaths for the last two weeks does not include covid-19-linked deaths outside hospitals (e.g. in care homes). The UK’s Office for National Statistics reports that there were 6,235 covid-linked deaths in England and Wales up until 3rd April (of which 4313, i.e. 70%, were in hospitals), but thereafter only figures for deaths in hospitals have been published. Assuming that in the last two weeks also, across all of the UK, 70% of covid-19-linked deaths took place in hospitals, one gets an estimate of a total of 13,729/0.7 = 19,600 covid-19-linked deaths in the whole of the UK, up until yesterday (16th April). About 88% of covid-19 fatalities in the UK have been people over the age of 65. Now, very crudely, assuming Gangelt contains roughly the same proportion of over-65’s as Germany as a whole, and bearing in mind that the proportion of the German population over 65 is 1.3 times that in the UK, one might expect the case-fatality rate in the UK to be around 0.0037/1.3 = 0.0028 = 0.28%. Assuming this, and also given that the average time between infection and death is about 23 days, one can estimate crudely that on 24th March, the first day of the UK lockdown, around 7.3 million inhabitants of the UK, i.e. 11% of the UK population, had previously been infected with covid-19.

It’s also worthwhile to do the same calculation for London, a major coronavirus infection hotspot (with significantly more confirmed cases per head of the population than any other part of the UK). The number of covid-19-linked deaths in London hospitals up until 16th April was 3,522. ONS and NHS data up until 3rd April suggests that in London, 90% of covid-19-linked deaths in London occurred in London hospitals. Hence, we may estimate the total number of covid-19-linked deaths in London up until 16th April (inside and outside hospitals) at 3,522/0.9 = 3910 deaths. Bearing in mind that the proportion of Germany’s population over 65 is 1.8 times higher than in London, one may estimate the case-fatality rate in London at 0.0037/1.8 = 0.00205, or 0.205%. Assuming, as before, that the average time between infection and death is 23 days, one can estimate crudely that on 24th March, the first day of the UK lockdown, around 3910/0.00205 = 1.9 million Londoners (i.e., 20% of London’s population) had previously been infected with covid-19.

One should do the above a bit more carefully using the distribution of times from infection until death, and the full population histograms of the UK, London and Gangelt (which was chosen, however, partly because it had a similar population histogram to Germany as a whole), but this won’t change the result much. Until we know the sensitivity of the German test, one should treat the 11% figure as a crude lower bound. But I wouldn’t be surprised if it was pretty close to the truth. Much too low for herd immunity, lower than the Oxford (Lourenço et al) ‘estimates’ of 15%-50%, but higher than the Imperial (Ferguson et al) estimates of 3-4%. The fact that herd immunity is almost certainly still a very long way off, provides (additional) evidence in support of the UK government’s decision yesterday to extend the lockdown for at least a further three weeks.

The (preliminary) results of the Gangelt study are consistent with the (preliminary) results of this (much larger) Stanford study released on 17th April on medRxiv in preliminary form, a serological study of 3,330 individuals in Santa Clara County in California. There is quite a lot of uncertainty over the sensitivity and specificity of the Stanford test, leading to prevalence estimates for Santa Clara County that differ by a factor of about 1.7, depending on which sensitivity & specificity assumptions are used. (Note that this is not a statement about confidence intervals; under one sensitivity-specificity scenario one gets a point estimate of 2.49% for the prevalence of covid-19 in Santa Clara County, and other another sensitivity-specificity scenario one gets a point estimate of 4.19% for the prevalence of covid-19 in Santa Clara County.) So the Stanford estimate for the case-fatality-rate in Santa Clara County is either 0.12% (for one sensitivity-specificity scenario) or 0.2% (for another sensitivity-specificity scenario). Given that the proportion of over-65’s in Santa Clara County is about half that in the UK, this leads (crudely) to an estimate for the case-fatality rate in the UK of either 0.24% or 0.4%. The figure of 0.28% used above is certainly between 0.24% and 0.4%. (To refine these estimates it will be necessary to estimate more precisely the sensitivity of both the Gangelt and the Stanford tests.)

It should also be reiterated that we cannot know from these studies (or any studies publicised so far) what level/concentration of antibodies typically provides immunity, or more importantly how long immunity will typically last for. It is important to conduct longitudinal serological studies, examining the same group of patients over a long period of time, to estimate how long immunity typically lasts for.

Update 14 (17th April): New UK cases by day, and the government’s decision to extend the lockdown.

The following graph shows the number of new lab-confirmed cases of covid-19 in the UK, each day. It strongly supports the government’s decision (announced yesterday) to extend the lockdown for another three weeks. The number of new cases appears to be plateauing, but only just.

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It is usual to take 7-day moving averages in order to account for the fact that less testing typically takes places at weekends. This yields the following curve, which gives a similar picture of the situation.

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It is hoped that the number of new cases per day will now start going down. This has already happened in Norway, which introduced a lockdown similar to the UK, much earlier (on 12th March):

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It is to be hoped that the UK lockdown will eventually achieve the same decrease as has been observed in Norway. For the benefit of the small number of people still skeptical of that the lockdown has made a difference, it is instructive to compare the decrease in the number of new cases per day in Norway with the steady growth in the number of new cases per day in Sweden (a very similar country that has still not introduced a lockdown):

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Update 15 (23rd April): On ways of tackling the shortage of PPE equipment in UK hospitals and care homes.

There is currently much discussion in the media over the shortage of PPE in UK hospitals and care homes. Some hospitals last Friday (17th April) reportedly had only around 24 hours’ worth of supply of certain key items (e.g. full-length, fluid-repellent gowns), and guidance was changed that day to enable re-use of PPE and to enable the wearing of aprons rather than full-length gowns if the latter ran out, which is certainly not optimal. This has been in spite of the UK’s relatively large initial stockpile. There have been reports that the government did not join the EU-wide scheme for procurement of PPE, for political reasons, even though it had that option. (Though the UK government has denied these claims, and has stated instead that the UK had not joined the scheme due to a communications delay.) Be that as it may, assuming that the EU procurement scheme proves successful (as of yesterday, the first deliveries were expected shortly but had not taken place), I do not see why the UK government should be unable to apply to join it at a later stage, at an appropriate buy-in price. At any rate, I am not sure why the possibility appears not to be under consideration, on either side.

Update 16 (30th April): On the value of surgical masks for healthcare workers in all staff-patient interactions in hospitals.

On 25th March, as reported here, Brigham and Women’s Hospital in Boston introduced a rule that all clinical staff were to wear surgical face-masks for all their interactions with patients (not just with patients known to be infected) — unless, of course, an N95 respirator, or similar, was being used instead. After just a few days, the number of new covid-19 infections confirmed per day among healthcare workers in the hospital had gone down from 12-14 per day (before the rule was introduced) to an average of around 8 per day – a reduction of about 50%. When, on 6th April, the hospital introduced an additional rule that all patients were to wear surgical masks during examinations by clinical staff, the number of new covid-19 infections confirmed per day among healthcare workers dropped further, to an average of around 6 per day. During the same period, the number of new covid-19 infections confirmed per day in the surrounding area (of Boston, and also in the state of Massachusetts as a whole) continued to increase. Very early in its outbreak, Singapore instituted the same rule in its hospitals, that clinical staff were to wear surgical masks in all interactions with patients (unless, of course, they were wearing an N95 respirator, or similar). According to this article (of 21st March) in the New Yorker, up until the time of writing (21st March), not a single healthcare-related transmission of covid-19 was known to have taken place in Singapore, despite the hundreds of cases that its medical system had to deal with up until that date. To quote from the article,

‘This included one case of a critically ill pneumonia patient who exposed 41 healthcare workers in the course of four days before being diagnosed with covid-19. These were high-risk exposures, including exposures during intubation and hands-on intensive care. Eighty-five per cent of the healthcare workers involved used only surgical masks.’

It is possible that other measures taken in Brigham and Women’s Hospital were partly responsible for the fall in cases among clinical staff there, and it is also possible that Singapore’s incredible success (no known healthcare-related transmission up until 21st March) was due in part to other measures. But it is also quite possible that the surgical masks rule made a big difference. Public Health England updated its guidance on 10th April to recommend that protective equipment be worn by healthcare workers in all cases of direct contact with patients (not just those with patients with a confirmed or suspected case of covid-19). This was welcome, but in the light of how important this might be, the UK government should perhaps be careful to ensure that sufficient supplies of surgical masks are maintained, to ensure this measure can be implemented in all cases, going forward. The opportunity-cost of failure to do so, could be severe.

Update 17 (6th May): On the NHSX contact-tracing app currently undergoing trials on the Isle of Wight, and the desirability of switching to a decentralised system compatible with the joint Apple-Google API, or putting in place contingency plans to do so.

There is an unfortunate situation developing at the moment, regarding the NHSX contact-tracing app currently undergoing testing on the Isle of Wight.

There are essentially two models for covid-19 contact-tracing apps, the ‘decentralised model’ where the proximity computations are done locally, on the user’s phone, and the ‘centralised model’ where the proximity computations are done on a central server (generally controlled by the government or health service, or a private company). The centralised model carries much greater privacy risks. These privacy risks are all but impossible to completely mitigate against, even with a team of top engineers working solidly on doing so for two months (time we don’t have); this kind of data is very difficult to fully anonymise, particularly if other databases can be used for deanonymisation – and these privacy risks may well significantly reduce people’s willingness to download the app. There is concern among many privacy and security experts that a government (or a private company, or a bad actor) could use the data from a centralised system (perhaps in conjunction with other databases) to recover sensitive personal information, e.g. about people’s close contacts. This concern was expressed in an open letter from nearly 300 internationally known privacy and security experts, who advocate instead a decentralised model. (A similar open letter from a group of 173 UK experts is here.) Worldwide, a majority of academic cryptanalysts are firmly in favour of the decentralised model, according to a world-renowned expert in the area. Similarly, the UK’s Information Commissioner stated on 17th April that ‘The starting point for contact tracing should be decentralised systems that look to shift processing on to individuals’ devices where possible.’ And this week, the Information Commissioner’s Office stated to the UK Parliament’s Human Rights Joint Committee that ‘As a general rule, the decentralised approach allows most readily for best-practice compliance with the data minimisation principle.’

Another crucial issue is that Apple and Google are currently developing a joint API (application programming interface) that will enable contact-tracing apps to work very effectively on both iPhones and Android phones, even when the apps are in the background – but, crucially, only if they use the decentralised model. A contact-tracing app that does not have access to the joint Apple-Google API will only be able to work well when it is running in the foreground, or when it is temporarily ‘woken up’ for a short period. This in turn depletes battery power (especially on iPhones), which will almost certainly discourage people from using the app in the way it’s intended – though of course, ‘waking up’ the app for short periods depletes the battery power quite a bit less than keeping the app running in the foreground.

Many Western governments have concluded, for the above reasons, that it is better to sponsor an app using the decentralised model – using the centralised model could reduce uptake due to privacy worries, and uptake needs to be pretty high, at over 60% of the entire population according to an Oxford study (of Fraser et al), for the app to be really effective at reducing the spread of covid-19. Further, the inability of apps using the centralised model to interact with the Apple-Google API will almost certainly lead to poorer performance, which (as well as making the contact-tracing less effective), may further reduce uptake. Germany switched last week from a centralised to a decentralised model. Other countries using decentralised model include Austria, Canada, the Czech Republic, Finland, Iceland, the Republic of Ireland (importantly – see below), Israel, Italy and Switzerland.

However, the contact-tracing app currently being developed by NHSX for use in the UK (and currently being tested on the Isle of Wight) uses the centralised model. This has been justified on the basis that, besides contact-tracing, it allows the NHS and the government to collect useful additional epidemiological information, e.g. regarding potential infection hotspots. But, the decision to go with the centralised model means that the NHSX app cannot access the joint Apple-Google API and will therefore not work so well on iPhones or Android phones (the problem with iPhones being worse – see below). This decision (if it is not reversed) carries with it the grave risk that the app will have reduced uptake – both due to privacy concerns, and due to not working well enough on iPhones and Android phones. It could therefore fail in its primary purpose, which is contact-tracing. This is clearly and impartially outlined in this Verge article (see also this Register article, which has a less balanced tone). The Australian ‘COVIDSafe’ app, which also uses the centralised model, indeed appears to have particular problems working on iPhones, arising from the fact that it cannot access the joint Apple-Google API. A report today in The Guardian suggests that, in view of the severity of these problems, the Australian government is going to switch their app to a decentralised model that can utilise the joint Apple-Google API.

Speaking to The Verge, digital rights expert Prof. Michael Veale, who is part of an international consortium developing decentralized contact-tracing protocols, said yesterday that there really is no way to build an effective contract-tracing system without the help of Apple and Google. A world-renowned expert in the area (and former colleague of mine) said they expected the NHSX app (and similar apps using the centralised model) to be almost impossible to use on iPhones, as a result of not being able to interact with the joint Apple-Google API. (And we should note that iPhones constitute more than 50% of the UK’s smartphone market.) NHSX engineers claim to have found a partial workaround, but it probably relies on the presence of Android phones in the near vicinity of iPhone users, and is unlikely to work well throughout the UK (except perhaps in busy city-centres). Some UK experts have already been analysing preliminary results from the Isle of Wight trial, and Prof. Michael Veale expressed the following view to The Guardian today.

‘The workarounds NHSX on both iOS and Android are using to create a centralised database seem to be fragile, disruptive to users and risk apps not registering contacts when they should. iOS apps are forbidden from using Bluetooth for long after they are minimised. To keep iPhones registering contact events appears to require either the user to constantly remember to reopen and refresh the app or, stranger still, sufficient Android ‘herd immunity’ among app users, where a nearby user of a non-iPhone, if in range, nudges nearby iPhones to not fall asleep, and to keep listening out.’

There is also the issue that the Republic of Ireland has opted for a contact-tracing app using the decentralised model; if this were not interoperable with the NHSX app, contact-tracing on the island of Ireland would be much less effective, as pointed out in this report of the UK Parliament’s Joint Committee on Human Rights, on digital contact-tracing, published today.

In the light of these issues, I strongly believe NHSX should strongly consider switching to the decentralised model; at least, they should put in place a contingency plan to do so, in the event that their centralised-model app has limited uptake and/or does not work sufficiently well on iPhones and Android phones. It is not too late to switch; Germany switched from the centralised model to a decentralised one only last week. If performance and/or uptake problems arise during the Isle of Wight test, there would perhaps be an even stronger case for switching. High-profile contact-tracing protocols using the decentralised model include the MIT-led PACT, the University of Washington’s PACT (which has the same acronym but is not formally linked to MIT’s PACT), the TCN Coalition and the Swiss-led D3-PT; NHSX could perhaps adopt one of these protocols, or make contingency plans for doing so. In his evidence to the UK Parliament’s Joint Committee on Human Rights, NHSX CEO Matthew Gould accepted that the technical difficulties of switching the NHSX app to a decentralised system were manageable (see the Committee’s report here). 

If the UK’s decision-makers decide not to switch, a second-best option would be for those concerned about privacy and/or poor functionality to download a different app (an app using a decentralised model), but as many people would stick with the government sponsored-app and would be unwilling to download a second, this would lead to a very unfortunate situation where two significant proportions of the UK population were using no app in common with each other. Plus, it may be unlikely that Google/Apple would grant access to their API to an app in the UK that would ‘compete’ with the government-sponsored one; they have already said that a maximum of one app per country (or per state, in the US), will be granted access to their API, to reduce the risk of competition between apps. A decentralised app without access to the Google/Apple API would still suffer from functionality issues, though not from privacy issues. The best solution would surely be for NHSX to switch their app to using the decentralised model – or at least, to make contingency plans for doing so.

Update, 8th May: the Financial Times reported on 6th May that NHSX has awarded a £3.8 million contract to Zuhlke Engineering, including a requirement to ‘investigate the complexity, performance and feasibility of implementing native Apple and Google contact-tracing APIs within the existing proximity mobile application and platform’, and with a deadline of mid-May. On 8th May, the Financial Times reported further that Matthew Gould, CEO of NHSX, had given the go-ahead to a project to develop a second contact-tracing app using the Apple-Google API, in parallel to the original NHSX app. This is very welcome news, particularly in view of continued doubt over whether the original NHSX app will work sufficiently well on iPhones.

Update 18 (16th May): On the preliminary results from the UK’s COVID-19 Infection Survey pilot.

Two days ago, preliminary results from the UK’s COVID-19 Infection Survey were released. The main points are listed as follows:

  • At any given time between 27 April and 10 May 2020, it is estimated that an average of 0.27% of the community population had COVID-19 (95% confidence interval: 0.17% to 0.41%).
  • It is estimated that an average of 148,000 people in England had COVID-19 during this time (95% confidence interval: 94,000 to 222,000).
  • For individuals working in patient-facing healthcare or resident-facing social care roles, 1.33% tested positive for COVID-19 (95% confidence interval: 0.39% to 3.28%); of those reporting not working in these roles, 0.22% tested positive for COVID-19 (95% confidence interval: 0.13% to 0.35%)
  • There is no evidence of differences in the proportions testing positive between the age categories 2 to 19, 20 to 49, 50 to 69 and 70 years and over.

However, the report states ‘We do not know the exact false-positive or false-negative rate of the current swab test for the virus. However, based on the very low number of positives in the results so far, we know the false-positive rate is very low (as even if every single positive result was false, this rate could only be 0.30%). We do not have information on the false-negative rate.’ It will be important to estimate properly the false-negative rate (equivalently, the ‘sensitivity’ of the test); if the false-negative rate is rather high, then 148,000 could be a significant underestimate. It will also be important to estimate properly the rate of false positives (equivalently, the ‘specificity’) of the test. Serology results (concerning the proportion of England’s population that have antibodies, and have therefore been infected at some point), are still awaited, but Sir Patrick Vallance said on 11th May that, based on very early results, it appears that very roughly 4% of the UK’s population might have been infected/recovered by early April. This is less than half the figure one would expect from the analysis in Update 13 above (which was just over 10%), suggesting that the Infection Fatality Rate for the UK might be over twice that of Germany (before adjusting for differences in recording protocol, and after adjusting for the different age profiles of the populations). But as the results are still very uncertain and lack sensitivity/specificity estimates, we will need to wait for better estimates before drawing any firm conclusions.

Update 19 (16th May): On the value of postponing the EU/UK Brexit trade talks (and extending the transition period) until the covid-19 crisis has eased.

Yesterday, both sides of the EU/UK post-Brexit trade talks reported that precious little progress had been made. Even without the covid-19 pandemic, the timeline of completing the hugely complex talks by 31st December 2020 would have been tight. Regardless of one’s view on Brexit, to devote a large amount of government resources to the trade talks (which would be needed to meet the 31st December 2020 deadline, given the complexity), surely risks compromising the government’s ability to deal effectively with the pandemic. I strongly believe a postponement of the talks, and an extension of the transition-period, should seriously be considered, even though I note that the government responded negatively (on 9th April) to an earlier Parliamentary petition to this effect. As well as the issue of prioritising the government’s bandwidth, UK companies will also struggle greatly to simultaneously adapt to covid-19 and prepare properly for a new trading regime for the EU. Alex Veitch, head of international policy at the Freight Trade Association, said planning for an exit from EU rules at the same time as navigating the coronavirus crisis was ‘not possible’. Finally, it is very important that supply chains between the EU and the UK not be imperilled further by an abrupt change (in December 2020), before the worst of the pandemic is over; these supply chains are of crucial importance, and are under great strain already, in view of the pandemic. A very strong case for an extension is made by Prof. Anand Menon (Professor of European Politics and Foreign Affairs at King’s College London, and Director of The UK in a Changing Europe) and Dr Angus Armstrong (also of The UK in a Changing Europe), in this article. Polls in early April estimated that about twice as many UK citizens think the UK government should extend the 31st December deadline, as do not. (And the former category must include a significant number of pro-Brexit voters.)

Update 20 (25th May): On ways to reduce risk in human ‘challenge trials’ for a covid-19 vaccine.

As covid-19 infection-rates in European countries go down, it will become progressively harder and harder to find out from field trials whether prototype vaccines are significantly effective. (The ONS Infection Survey currently estimates that 0.25% of the UK population were infected with covid-19, at any given time between 4th May and 17th May; the 95% confidence-interval for this estimate is 0.16% to 0.38%, so fairly narrow.) The CEO of Astra-Zeneca, Pascal Soirot, referred yesterday on The Andrew Marr Show to a ‘race against time’ to test prototype vaccines in the general community before infection rates become so low as to make this infeasible. The trouble is, if a vaccine is tested by a field trial (that is, simply by distributing it to a large number of members of the population who have not yet been exposed to covid-19, and then monitoring how many of them become ill with covid-19) – then even if the vaccine is tested on 1000 people, if the prevalence is only 0.25% and infections last 10 days on average, then in expectation, only about five of the 1000 subjects will get exposed to the virus over a 20-day period – not enough to test properly the effectiveness of the vaccine. Professor Lawrence Young, of Warwick University Medical School, expressed the following view to The Guardian yesterday:

“Levels of infection in the community are already low, and if this virus behaves like other respiratory diseases and coronaviruses, there may be even lower levels over the summer. There will not be enough people secreting the virus to be in contact with volunteers in vaccine projects. It is just not going to work.”

This has prompted many UK and US scientists and campaigners to advocate that human ‘challenge trials’ for covid-19 vaccines be seriously considered. (In a ‘challenge trial’, healthy volunteers agree to be given a prototype vaccine and then deliberately exposed to the pathogen in question – in this case, to coronavirus.) The campaign-group 1 Day Sooner, which campaigns for human challenge trials for a covid-19 vaccine, has so far signed up over 25,000 volunteers for covid-19 challenge trials. Human challenge trials have been used successfully in the 1970s in the development of the Vaxcholera vaccine for cholera, in the 1980s and 1990s to aid the development of the Tamiflu influenza vaccine, in the early 2000s to aid the development of the FLU-v influenza vaccine, and in 2013 to test the vaccine for typhoid fever now recommended by the World Health Organisation for everyone over six months old who lives in a region where typhoid fever is common.

The Guardian article quoted above gives some idea of the balance of different opinions on challenge trials for covid-19.

‘[Prof. Lawrence] Young argues that human challenge trials should be considered “very seriously” for the UK. These would involve giving volunteers either a placebo or a vaccine, as is normally done in trials. But instead of waiting to find out how the two groups fare without interference, scientists would deliberately infect them with the Covid-19 virus. This would very quickly show if a vaccine works or not.

“Only very healthy young people – around the age of 25 – who have given informed consent would be used,” added Young, who points out that such trials have already been used to test the efficacy of vaccines for flu and the common cold. However, these ailments pose relatively low risks to volunteers. Covid-19 can have serious side-effects, mainly for the elderly but also in a few rare cases of young, apparently healthy people. This point is acknowledged by Young. “Before we went ahead with challenge trials, we would need to have developed some very effective therapy – an anti-viral drug perhaps – that could be used in the few cases where something went seriously wrong. This latter point has been stressed by the W.H.O. in its guidelines for human challenge trials. It suggests the least risky group to infect would be those aged 18–30 years. Only 1% of this group end up hospitalised with Covid-19, while fatality rates are around 0.03%. “Challenge studies should then be conducted in specialised facilities, with especially close monitoring and ready access to early supportive treatment for participants,” add the guidelines.

The idea of carrying out human challenge trials for a Covid-19 vaccine was also backed by Professor Arpana Verma, of Manchester University. “Vaccines give us the ability to protect the most vulnerable people in society. That is one of their key strengths. So I think it would be entirely justifiable to go ahead with such trials.”

But the proposal was firmly opposed by immunologist Professor Eleanor Riley of Edinburgh University. “Challenge studies are done for many diseases but only when strict criteria are followed. Firstly, the virus should be really well studied and its clinical behaviour understood in detail. It should also be incapable of causing severe illness in healthy individuals, or there should be a highly effective drug to clear the infection. None of these criteria are met for Covid-19, and I would be very concerned to hear challenge studies were being planned.”

The crucial point is that we should be thinking now whether we want to go ahead with human challenge trials, said Young. “We shouldn’t wait until we have a vaccine candidate on our hands and not know what to do with it.”’

20 Responses to “Nine proposals for combatting the coronavirus pandemic in the UK”

  1. davidellis2 Says:

    Update, 24th March: Yesterday evening, the UK Prime Minister announced measures that almost amount to a Spain-style lockdown, effective immediately. It is permitted for citizens to leave home only for the following reasons:

    – Shopping for basic necessities, such as food and medicine – which should be as infrequent as possible.

    – One form of exercise a day, for example a run, walk, or cycle – alone or with members of your household.

    – Any medical need, or to provide care or to help a vulnerable person.

    – Travelling to and from work, but only where work absolutely cannot be done from home.

    Government instructions state that ‘These four reasons are exceptions – even when doing these activities, you should be minimising time spent outside of the home and ensuring you are 2 metres apart from anyone outside of your household.’ Gatherings in public of more than two people are prohibited (unless those two people belong to the same household), and all non-essential shops and businesses are required to close.

    The police do not yet have the required powers to enforce these measures (e.g. to fine those who violate the instructions), so legislation allowing enforcement will need to be passed with the utmost speed. Widespread testing is still urgently required, and as mentioned in the post, the police may require the support of the army.

  2. Darij Grinberg Says:

    David, speak for yourself when you claim that “most people will not be seriously at risk from having to exercise indoors for three weeks”. I, for one, have never managed to keep an intramural routine for longer than a few days (even when I did have the machines), but the outdoors reliably gets me active (and keeps me from overeating). I don’t know about you, but I need nature. I’m not a vertex in a graph. I have never seen evidence for hikers, joggers or bikers transmitting the disease — it would require aerosol transmission, which is far from proven for COVID-19 and not likely to do the heavy lifting in the transmissibility ( https://www.statnews.com/2020/03/16/coronavirus-can-become-aerosol-doesnt-mean-doomed/ ).

    I agree that shared exercise equipment as well as swimming are dangerous, so closing playgrounds and beaches makes sense. And public transport is probably a problem, too — something I think should be mitigated rather than attacked with the hammer of law. If anyone has ideas how to de-crowd buses and trains at rush hours (fare hikes like Uber’s? more flexible schedules that guarantee some reasonable worst-case wait times?), that could be very useful. If not for the possibility of injuries, I’d also say this is the best time ever for a cycling renaissance.

    As to the sudden wanderlust recently appearing in some towns and national parks, my best guess it is due to the same dynamics as the toilet paper shortages: People hear they might get locked down, so they hasten do use the last chance they have to see some nature in the coming few months. (“Three weeks” is also a rather optimistic expectation for the length of the lockdowns; I’m seeing much scarier predictions.) As a politician, you could prevent that by setting clear boundaries for the restrictive measures in advance (e.g., no closing grocery stores, or no war on jogging), but so far I have seen little of that happen (and many politicians do not command enough trust to do something like this successfully anyway).

    The press isn’t very helpful either, constantly amplifying the most panicked reactions from both camps. Epidemiologists make predictions, which are then used to justify unrelated policies. Politicians are starting to put the crisis to use, while demonstrations are outlawed; we’ll probably need years to get rid of all the bad laws that will be enacted during this crisis. As a scientist, you can surely do better than asking for “heavyhanded measures now” without cost-benefit analysis or human-factors corrections.

    (This is all concerning Proposal 1. I mostly agree with the rest of your proposals.)

    • davidellis2 Says:

      I would only advocate removing the exception for taking exercise if it were abused on a large scale, and only then for the initial 3-week period of the lockdown announced by the government (after which it would be revisited). I appreciate there would be long-term costs to restricting exercise for longer than 3 weeks, and of course I agree that a (quick) cost-benefit analysis should be performed before extreme measures are introduced. The lack of time makes it harder than usual to perform very accurate cost-benefit analyses, and it is also important to hedge to some extent against the worst-case scenarios, when there is so much uncertainty in the data.

    • davidellis2 Says:

      Yes, perhaps I should have said ‘Spain-style without the cycling ban’, though this would have been more complicated and therefore less easy to digest. I think the German lockdown may be problematic, as the instructions don’t explicitly encourage people to e.g. keep shopping to a minimum and to stay at home as much as possible when not taking exercise; what happens if everyone simply heads outside for much of the time? Finally, they only stipulate a 1.5 metre distance from others when in public. I actually think the new UK requirements are better than Germany’s. The UK restricts exercise to 2 hours per day, which seems proportionate. Your points about supermarkets encouraging contactless payments and the wearing of gloves are very good ideas.

      • Darij Grinberg Says:

        > Yes, perhaps I should have said ‘Spain-style without the cycling ban’, though this would have been more complicated and therefore less easy to digest. I think the German lockdown may be problematic, as the instructions don’t explicitly encourage people to e.g. keep shopping to a minimum and to stay at home as much as possible when not taking exercise; what happens if everyone simply heads outside for much of the time?

        What’s wrong with that? Transmission, from what I understand, mostly comes from touching infected surfaces and standing close to someone shedding the virus.

        > Finally, they only stipulate a 1.5 metre distance from others when in public. I actually think the new UK requirements are better than Germany’s. The UK restricts exercise to 2 hours per day, which seems proportionate.

        Answering as I’m returning from a 5-hour hike 🙂 (Arguably, it would have been shorter if I had planned better and my GPS hadn’t malfunctioned — but that’s part of the charm. And yes, I’m on a binge, as I’ll have to return to a less hiker-friendly country in a few days.) I don’t think I’ve ever stood less than 2 meters away from anyone during the hike, including when taking a train. I have passed a few people closely (back to back, which probably eliminates most of the chances for transmission?), but other than that I’ve had less contact than I would have at home (and because the severity of COVID-19 depends on the viral load, we cannot pretend that people sharing a home will infect each other anyway — they probably will, but it still matters how much!). I can hardly see a better place for social distancing than the middle of a forest.

        Is this necessary? To me, yes. To some, probably no. I don’t know how to explain this; I think we’re in personality difference territory (which is not surprising — we’ve been agreeing on a lot before we got down to this level of detail). How would you react to this blog getting closed down because wordpress.com has taken a look in the mirror and discovered it is a security basket case? 😉 (For better comparison, imagine there being no other web hosters around.)

        Let me mention another badly legible reason why people need to go outside (“legible” in the sense of James Scott, https://www.ribbonfarm.com/2010/07/26/a-big-little-idea-called-legibility/ ): Some families live in a permanently unstable state that, when left alone, gravitates towards infighting and domestic violence; in normal times, most of the family is away most of the time (kids are at school, one of the parents is at work, etc.), which acts as an escape valve. If actually required to stick together in a small apartment for 3 weeks, these little reactors can become supercritical. How frequent is this? We’re going to see soon, but the first bits of Chinese data incoming don’t look very good ( https://www.axios.com/china-domestic-violence-coronavirus-quarantine-7b00c3ba-35bc-4d16-afdd-b76ecfb28882.html ). You can be formalist and say “if you’re afraid of your partner, call the police, etc.”, but the same reasons that prevent this from happening even in better days will still be in place now (plus the police caring less because it’s a crisis).

        > the instructions don’t explicitly encourage people to e.g. keep shopping to a minimum

        This is a double-edged sword. I’ll take you at your word and assume when you say “encourage”, you mean “encourage”. The moment you start *enforcing* something like this (e.g., mandating at most one grocery visit per 3 days), you’ll see the following happen: The first 300 shoppers buy as much as they can carry away; everyone after them will see empty shelves and start foraging for other shops in their wider neighborhood (which, of course, will mostly suffer from the same shortages, thus causing lots of unnecessary movement and cross-infection). Even *encouraging* can lead to panic buying, if it gets interpreted as a hint of possible restrictions later on. Food supply chains are already expecting serious supply-side disruption in Europe ( https://de.reuters.com/article/deutschland-baywa-versorgung-idDEKBN21D1V5?il=0 ); it doesn’t help to add chaos on the demand side.

        If I was managing a grocery store, I’d play around with ways to make distribution less chaotic and more efficient: e.g., webcams directed at all stalls (so people can see what is in store from the safety of their homes); a web service that prints shopping lists with shortest-path directions (of course, this goes against the common wisdom of marketing, which says that buyers should spend as long as possible in the store, so the longer they need to find what they want, the better — but marketing needs to take a backseat now); possibly moving stalls around for better navigability. I might get rid of some luxuries if the space freed would allow me to do something helpful with it. (And as I said, I’d put plastic bags everywhere, nevermind the environmental regs.) Under no circumstances would I artificially constrain buyers from serving their basic needs; this would only lead to adversarial behavior causing inefficiencies and thus only helping the virus spread.

        The same applies to any tricks with first letters of surnames and the likes. That would require placing cops at the entrances of all stores and requiring everyone to show their ID. Does this help enough to justify the extra time required of everyone? the viral load on whoever does the checking because everyone will be talking?

        This is all not part of your graph-theoretical model (vertices in a graph don’t start moving around hectically because they can’t find fresh fruits), nor of the epidemologists’ SIR(E) models (which don’t know what basic needs people have), but it’s no less valid; just ask anyone who has lived in the Soviet Union. Economists have models for demand-driven shortages, but even they don’t usually study martial-law-style regulations. It’s a problem with models in general — and not exactly a new one. Nevertheless, the models that we have sing a siren song that is particularly hard to withstand for us mathematicians and other scientists. The Curve and the Graph are dominating the conversation, but basing our decisions entirely on them is no less arbitrary than doing so on the Dow Jones (which, too, is a measure of a form of social health). What can we do with the knowledge that models have limits? Well, one thing we can do is be less coercive and leave as much room as we can for people to react flexibly to whatever unpredicted problems come up. Bad or particularly dangerous behavior can be restricted narrowly as it appears, rather than pre-emptively in maximum generality. Messaging can be kept friendly, as lots of people will happily help they aren’t getting scolded or talked down to (lessons of the 2016 US elections apply here).

        Sorry for the length. As mentioned above, I agere with so much of your post, this almost looks like pedantry — but I think these little differences reveal important fundamental questions beneath them. Thanks a lot for pooling so much information in a single blog post!

      • Darij Grinberg Says:

        Short update to my previous comment: a 36% increase in domestic violence in Paris reported by the French Minister of the Interior ( https://www.sudouest.fr/2020/03/26/violences-conjugales-32-en-une-semaine-castaner-reagit-7366285-4697.php ). I am not sure how much the measure they are proposing (namely, a way to report at the pharmacy) will help, in particular when it comes to children.

        Jonathan Kay, in https://quillette.com/2020/03/27/covid-19-science-update-for-march-27-super-spreaders-and-the-need-for-new-prediction-models/ , has another suggestion for refining the epidemological model — he thinks R_0 should be regarded as a distribution, not a constant, as people differ heavily in how much they spread. I’m wondering what this means mathematically — how much does the spread change if we replace a constant R_0 by (say) a normal distribution peaking at that constant?

        Following quotes from Kay’s article, here is a Japanese medRxiv preprint https://www.medrxiv.org/content/10.1101/2020.02.28.20029272v1.full.pdf that suggests that “closed environments” (as opposed to open-air ones) “contribute to secondary transmission of COVID-19”:

        > As of 26 February 2020,3 34 we examined a total of 110 cases among eleven clusters and investigated who acquired infection from whom. The clusters included four in Tokyo and one each in Aichi, Fukuoka, Hokkaido, Ishikawa, Kanagawa and Wakayama prefectures. All clusters were associated with close contact in indoor environments, including fitness gyms, a restaurant boat on a river, hospitals, and a snow festival where there were eating spaces in tents with minimal ventilation rate.

        > The number of secondary cases generated by each primary case was calculated using contact tracing data. Of the 110 cases examined, 27 (24.6%) were primary cases who generated secondary cases. Figure 1 shows the distribution of these transmissions, of which the mean and variance were 0.6 cases and 2.5 cases, respectively. The odds that a primary case transmitted COVID-19 in a closed environment was 18.7 times greater compared to an open-air environment (95% confidence interval [CI]: 6.0, 57.9).

      • davidellis2 Says:

        The data on closed versus open-air environments is interesting (though I assume there will be some selection-bias here, as one can keep track of contacts more easily if two contacts were together in a ‘closed’ environment, than if they were together in an ‘open’ one, e.g. sitting less than a metre apart in a small public park). In large cities with a high population density and relatively few open spaces, such as London, if everyone heads outside to a small public park I think this could create a ‘hub’ (see update 10) which would be problematic. But I need to look more closely at the data on indoor vs outdoor transmission. Re domestic abuse: this is an important point, in fact the UK Home Secretary updated the lockdown instructions today to make it clear that people at risk could still go out: https://www.bbc.co.uk/news/uk-52081280.

      • Darij Grinberg Says:

        @David: I have to admit I don’t know where the “contact tracing data” in the preprint came from. If it comes from phone networks, it might not be biased. We’ll probably have to wait for the “real” version of that preprint.

        Big cities with a lack of greenery are a problem, not just from the point of view of taking walks. I’m not surprised NYC is dominating the US numbers…

        > Re domestic abuse: this is an important point, in fact the UK Home Secretary updated the lockdown instructions today to make it clear that people at risk could still go out: https://www.bbc.co.uk/news/uk-52081280.

        This is a great start (and good to hear that politics and police both are aware of the problem), but it’s far from a replacement for the opportunities that a regularly functioning society with free movement would provide. A typical situation, I think, is “husband seems to be getting upset lately; I better take the kids to friends before something happens and let it cool down”. This is best done long before things have gotten sufficiently heated that you can reasonably call the police. (Also the police isn’t known to be great at this in Britain.)

  3. Jeff Says:

    We do not know if contact tracing works:

    Asian countries with heavy contact tracing have heavy lockdowns too. Also these Asian countries could reasonably expect their population to obey social distancing, except for more people working in factories or shopping slightly more.

    We’re discussing contract tracing as an excuse to ignore lockdowns, which makes contact tracing extremely dangerous. We should take contract tracing off the table entirely for the foreseeable future.

    • davidellis2 Says:

      Singapore does not have a lockdown, but has made extensive use of contact-tracing. I envisage that contact-tracing would be used in the UK on a large scale only after the lockdown has been lifted, and if it is done via voluntarily downloadable apps, it will be voluntary (i.e., on an opt-in basis). Also, the apps would involve no upload of location-information to government servers. So I don’t think contact-tracing via voluntary apps (after the lockdown) would have any serious down-sides.

  4. Gil Kalai Says:

    My naïve feeling is that if we succeed (for most people excepts those who are essential) that people stay mostly in their home and always in small distance to their home (so no outdoor exercise and more painfully no usage of private cars as well as public transformation) then the connectivity graph will loose its expansion properties and this will suppress the exponential growth. Is this naïve thinking correct?

    • davidellis2 Says:

      I don’t think it will be feasible to completely ban the use of private cars, because of the issues around essential journeys in Update 1 above. But I think there should be stronger penalties for those making non-essential journeys with private cars over long distances. It would be good if the heuristic you describe could be backed up by a proper probabilistic/computational analysis, at which unfortunately I’m not an expert. Do you know of any mathematicians / computer-scientists working on this problem?

  5. Joseph Says:

    In France, outside exercise is limited to 1 hour per day, at most 1 km (0.6 mile) distance from home. It is of course difficult to check that people are not going out several times. A solution would be to fix the time, of course not the same for everybody, but probably it is too complicated to organize this in a few days. It may be not impossible to forbid outdoor exercise for three weeks, but it is very likely that the lockdown will last longer.
    I fell it may be useful to test a random or representative sample of a few thousand people in order to have an idea of the true number of cases. Iceland did this kind of tests of general population, with volunteers (which may biases the result). For that, we need enough available tests in order to make socially acceptable that fact that we “waste” a few thousand of them for such poll. For tests made in order to isolate people with the virus, I would a priori suggest this order of priority for the tests (at least until we are able to test almost everybody): people with serious symptoms related to the virus, close contacts of people with the virus, people in hospital (workers and patients), other workers related to health (e.g. medical doctors, pharmacies), other essential businesses (e.g. food), other people working “physically”, people with mild symptoms related to the virus, people living in areas with a larger proportion of people with the virus. This being adjusted in function of further epidemiological studies.

    • davidellis2 Says:

      Yes, I completely agree with your points about testing – we need both randomized/systematic testing to find out the prevalence in each region, as well as separate testing to isolate those who are most likely to infect the greatest number of others (healthcare workers, delivery drivers, those with mild symptoms, etc, with a sensible order of prioritisation). Re exercising at most 1km from home: in areas with a high density of population like London and Paris, the 1km rule might lead to an unsafe concentration of people in the major parks. Cycling to a less crowded place further away (cycling further than 1km from home) might be better, though there is a tradeoff between this and trying to cut down transmission over large distances (e.g. if people drive a long way to the place where they take exercise – maybe the latter could be banned in the UK?). In areas with a high population density, to prevent too many people exercising at close quarters it would make sense for the government to encourage those working from home to exercise during normal working hours (so they are not exercising when key workers are exercising), and also perhaps to exercise at different times based on e.g. the letter their surname begins with. There will be some personal incentives not to exercise at popular times, among the majority of people (who are careful), but relying on personal judgment / chance to ensure a uniform distribution of exercise-times will be risky in high-population-density areas as it can lead to strange ‘bunching’ effects (this phenomenon is well-known in chaos theory).

      • Joseph Says:

        For places with high density of people, it may make sense to further reduce the distance and to forbid places where there are significant risks of too high concentration. The idea of fixing a time of exercise depending on “random information” on people (first letter of the surname, month of birth, etc.) seems good to me at least theoretically, for people who are not obliged to go out for work. It may be difficult to control this in practice (can a “strong recommendation” be enough to have sufficient effect?)

  6. Joseph Says:

    “As the letter points out, Lombardy has a total population of 10,060,574. Despite stringent control-measures (a lockdown of the worst-hit provinces starting 21st February, and a complete nationwide lockdown starting 9th March), the total number of people in Lombardy hospitalised with coronavirus is 10,905. Hence, the number of hospitalised cases of coronavirus per head of the population in Lombardy is 1.03%!”. There is a missing factor of 10 somewhere.

    • davidellis2 Says:

      Now corrected, very many thanks indeed. I don’t think I would have made this error if the letter hadn’t been behind a paywall, but there’s really no excuse for it. Luckily the main point (which I still firmly believe, and which the Oxford paper states as its main policy recommendation) is that systematic testing is urgently required to determine the true prevalence rates (in different regions). Also that we don’t know how long immunity will persist for.

  7. Joseph Says:

    I give here a summary of how I can see the evolution of the epidemics, already from an oversimplified model, namely the SIR model when the number of infected and recovered people is small with respect to the population, i.e. we neglect herd immunity.
    In all the discussion below, I suppose that we always try to avoid to reach herd immunity (until a vaccine is found) since it would imply a very large number of deaths. This strategy may be modified if either herd immunity is in fact not avoidable (e.g. if R_0 > 1 even with quite strict lockdown) or if the mortality rate is much lower than expected (this may happen if the true number of cases is extremely underestimated, or if we find a very effective treatment in the coming weeks or months). Of course, the model I look here is extremely oversimplified, but I still expect that its qualitative implications will be approximately correct.
    The SIR model with negligible herd immunity gives the following evolution: the number of active infected people is exponential with the time, with rate b – c where b is the average number of persons infected by an individual per unit of time and c is the proportion, per unit of time, of infected people who are recovered, isolated (e.g. just after being tested positive) or who die. The reproduction number is
    R_0 = b/c. If R_0 = 2.5 and b-c = 0.24 per day, which is roughly the observed natural rate of increase of the epidemics, we get b = 0.4 (each infected individual contaminates another one every 2.5 days) and c = 0.16 (each infected individual, including asymptomatic cases, recovers, is isolated or dies in about 6 days in average). According to this very basic model, the goal of the lockdown is to decrease b in order to get R_0 way below 1, which needs to divide b by at least 3, possibly more. In case we manage to divide by 4, we get b = 0.1 and R_0 = 0.625 after the lockdown. Under this assumption, the rate of increase of the number of infected people is b-c = – 6% per day. Notice that this rate is very sensitive to the precise value of the divisor, and then the effectiveness of the lockdown is very important. It can be useful to evaluate it as soon as possible, and to tighten the rules if our evaluation of the true number of infected people is still increasing, or is decreasing too slowly. Such evaluation can be done by testing samples of the population, or via the number of deaths, but this last number gives a reasonable evaluation only with a delay of 2-3 weeks, if we refer to the example of Italy. Under lockdown, people have still quite a lot of contact at work (if they are obliged to work physically) and at the supermarket: it is then very important to protect workers and to make social distancing as much as possible. Delivery seems to me way less risky than supermarket since one contact only is needed, between the costumer and the person who delivers (this person should be of course very well protected) whereas going to supermarket (and more generally hubs) implies very quickly to go quite close to a large number of people. This can still be partially avoided by a rigorous policy of social distancing in supermarkets, but it may be not easy to make it effective and well respected. Cashiers should be very well protected, and it can be useful to strongly encourage automatic payment (in case the line has not too many people).
    After 2 months of lockdown with the quite successful rate of decay of 6% computed above, this would divide the number of cases by about 40, and then make the situation manageable. In order to lower the number of cases to a few cases, we would need about 6 months. A consequence of that would be the following:
    – We can reasonably hope that a long, but still reasonable lockdown will put the epidemics to a manageable level for the health system.
    A lockdown of 6 months or more is probably not realistic (too many economic, social, psychological consequences), and then there will remain a significant number of infected people after the lockdown. We need to do further action in order to avoid to have again a quick increase of the epidemics.
    After the lockdown, we need to keep R_0 below 1, at least in average. The lower the better, but it is not as critical as now to be much below 1, because the number of cases is supposed to be low at the end of the lockdown. The following things can continue to be done in order to decrease b without being too restrictive for the individual freedom:
    – Improve hygiene (easy to do in principle, more difficult to effectively control).
    – Wear masks in public (it would be interesting to evaluate the impact of masks on the parameter b, example of countries in Asia suggest that it may be very significant).
    Social distancing is a more significant restriction, it may be useful to keep closed highly concentrated public places (restaurant, bars, pubs, main parks in dense cities, big sport events, etc.) for some time after the lockdown (more or less, slowly reversing the recent successive restrictions).
    Contact between different communities has not necessarily a huge effect on the total number of infected people under the following conditions: the communities are already significantly infected, the total number of contact of people is not significantly increased, and none of the communities has significant local herd immunity. It should still be useful to isolate local communities with significant herd immunity, i.e. a quite large number of cases with respect to the population. Moreover, contact between different communities can have an important influence on the geographical distribution of the infected people, even with a small change of the total number of cases.
    Another way to decrease R_0 is to increase c, i.e. to isolate a larger part of infected people. A significant increase of c means that we should find a significant proportion of all cases (including asymptomatic ones) every day, which means that a very large part of the population should be tested at least once, since most of the cases are now unknown. Moreover, tests should be continued in a regular basis in order to keep the higher value of c in the long run: in order to avoid to test everybody in a regular basis, we need to prioritize those for which the a priori probability to be positive is the highest. It may be useful to find some way to roughly evaluate this probability. Contact tracing can be very helpful for this task. Anyway, this means that very massive testing is needed, I.e. a number of tests of the same order of magnitude as the population, ready at the end of the lockdown. I hope such thing is possible. Developing medical treatments will not necessarily have a huge effect on the evolution of the epidemics, since positively tested people are supposed to be isolated anyway. However, it is of course the most important for the health of infected people, in particular for their mortality rate. A very large decrease of mortality rate may make a strategy involving herd immunity acceptable (i.e. the number of deaths is not too much larger that seasonal flu).
    A slightly more complex model than the oversimplified SIR above can be given by considering several categories of people, with different rates of mutual infection. In this case, the parameter b is replaced by a square matrix whose size is given by the number of categories, and the rate of exponentially growth of the leading term corresponds to the largest eigenvalue of the matrix, which plays the role of b in the discussion above. An example can be given by taking N categories of people with the same size, the category j infecting, in average, (b_j b_k/N) individuals of the category k per unit of time, the number b_j measuring the “tendency of the category j to be in infectious contact with other people”. In this case, the average number of people infected by one individual is the square of the average of the b_j’s, whereas the largest (and only non-zero in this precise example) eigenvalue of the matrix is the average of the squares of the b_j’s, which is larger. Hence, the “effective b”, and then the “effective R_0” can be higher than its naive interpretation in terms of the average of the number of infections per individual. It can be interesting to study the influence on the “effective R_0” of different social situations: a small proportion of people with a lot of contacts, a small proportion of people who do not respect well the lockdown, etc. I suppose there is literature on this kind of topics, but I don’t know it.
    Another thing which can be looked is the indirect effect of the epidemics: how does one takes care of the other diseases when the health system is overwhelmed, how can one manage the economic shock (around 3% of loss of annual GDP for each month of lockdown) in order to avoid a too dangerous destabilization of the system, how can one help people to physically and psychologically deal with the lockdown (e.g. domestic violence), etc.

  8. Joseph Says:

    In relation with the last update: I feel that it may be possible to anticipate for a adaptable mixture of strategies (1), and (3)/(4) roughly with the following plan:
    – Keep rigorous hygiene, make face covering mandatory (with masks when they are available for general population), develop as much testing capacity and contact tracing as possible. These points should be kept during and after the full lockdown period. In other words, one anyway does as much as one can in direction of strategy (1), even if this strategy alone cannot work.
    – Estimate the value of R during lockdown. After 5-6 weeks, all the deaths should come from contaminations during lockdown, so the evolution of the number of deaths should reflect this new R. Since the number of deaths in Italy is not increasing anymore in average, there is good hope that the new R is not larger than 1, however, we still cannot be more precise.
    – If the R under lockdown is smaller than 1, progressively release some of the lockdown restrictions, in an order depending on their ratio (economic and social cost)/(effect of R), to be estimated.
    – Progressively adding “normal working days”: it may be interesting to make different people working during different day in order to have less contact between people, at least when it does not perturb too much the organization of the work.
    – Interrupt releasing (or even put again more restriction) if the estimated value of R becomes larger than 1. There is an issue about how R can be sufficiently frequently and accurately estimated.
    – If one can manage to keep R lower than 1 after releasing most of restrictions, the plan before will correspond to strategy (1) after some time, if it is not possible, we get a mixture of (1) and (3)/(4) (with a proportion of “normal days” depending on by how far (1) alone is impossible).
    – Release most of the restrictions when one finds either a vaccine, or a treatment lowering the mortality rate to the order of magniture of seasonal flu.
    The very bad situation would be the case where R is still larger than 1 under lockdown: in this case, I have no clear idea about what should be the best strategy, probably we would need to make very hard choices.

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