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Once we reach a social distancing tipping point, more restrictions won’t help at all

Once we reach a social distancing tipping point, more restrictions won’t help at all

How long should the lockdown last? Should it be tightened or relaxed? An abstract concept from both epidemiology and network theory can give a powerful insight into these highly practical problems.

This is the concept known as the “threshold”, sometimes called the critical point or the tipping point.

The basic idea is a very familiar one. Imagine you take a cube of ice out of the freezer. It will be ice regardless of whether the temperature is set at minus 10 or minus 2 degrees. Changing the starting temperature makes no difference.

But as soon as the temperature is above zero, it starts to turn to water. A threshold has been passed. You put the water in a pan and heat it up. It stays as water until it gets to another threshold — boiling point — when it changes into steam.

Close to thresholds, small changes can make massive differences.

The maths of epidemic models tells us that as soon as the degree of social distancing is sufficiently high, the number of true new cases of any virus begins to drop immediately.

In other words, there is a threshold in terms of the amount of social distancing in a society. Below this critical level, more distancing has little impact on the spread of the virus. Above it, being more rigorous and having more restrictions yield diminishing returns.

The essential thing is to get above the threshold.

Last week, a group at Sydney University published a study which modelled the spread of Covid-19 across all 24m inhabitants of Australia, linking epidemiological models with detailed census data. In terms of social distancing, they found a powerful threshold effect.

Suppose zero represents the usual world in which there is no social distancing at all. At the other end of the scale, 100 is absolute and total lockdown — something that not even the Chinese police state could enforce.

The Sydney team argued that the threshold for coronavirus was around 70. Moving, say, from 40 to 60 did very little to check the virus; moving from 80 to 90 controlled the spread a bit better. But the key thing was to get above 70.

In the UK, we seem to be well above the threshold. Before social distancing measures came in, epidemiologists were predicting at least 250,000 deaths in the UK from the virus. The various experts are properly cautious, but there is now every hope that the eventual toll will be 25,000 or fewer.

What does this mean in practice? Anyone who is now working from home and follows government guidelines has probably on average increased his or her social distancing from zero to at least 90. A minority of people still have to work, but even then their social interactions have been curbed substantially. Overall, as a society we seem to be well above the threshold at which social distancing works.

There is therefore no need to hand more powers to police forces, some of whom are already seeking to emulate the Stasi. Mid to late April will be the time for fewer, not more, restrictions.

As published in City AM Wednesday 1st April 2020
Image: Social Distancing by GoToVan via Wikipedia is licensed for use CC BY 2.0
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How mathematical models attempt to predict the spread of disease

How mathematical models attempt to predict the spread of disease

The various pronouncements on coronavirus are a source of puzzlement to many.

On the one hand there are lurid predictions of millions of cases and hundreds of thousands of deaths. On the other, while the actual numbers are growing, they seem tiny so far compared to the scale of the predictions.

Almost 100 years ago, two Scots, Anderson McKendrick and William Kermack, developed an apparently simple mathematical model to explain and predict the spread of viruses. This abstract model remains the basis of our modern understanding. It gives insights not just into the spread of diseases, but how things like fake news disseminate on the internet.

These economists proposed that people at any point in time are in one of three conceptual states.

The first defines those who are susceptible to any particular virus. For example, a certain type of person may be susceptible to rumours that Elvis Presley is alive. It is not clear yet who is susceptible to Covid-19. It seems to be affecting most demographic groups, but the World Health Organisation pondered last week that children might not be susceptible, for example.

The next category is those who are infected, which is straightforward enough. The final one is “recovered”. This could mean genuinely recovered, or actually dead — at any rate, no longer susceptible.

Kermack and McKendrick set up three non-linear differential equations to describe how a virus might spread. Their apparent simplicity disguises a fiendish complexity.

From the names of the categories, it is known as the SIR model — susceptible, infected, recovered.

A major uncertainty is whether to use this model or its SIS variant.  Here, the final “S” also means susceptible. The SIS model means that people can get re-infected. The common cold is a good example.

The key part of the system is determining how many susceptibles any given infected person passes the disease onto before he or she recovers. In turn, this depends on how much the susceptibles and infected intermingle (hence the drastic quarantines in China and Italy), the probability of catching the virus from a single contact, and the length of time someone is infected.

Basically, a virus will spread if a sufferer infects on average more than one susceptible. The current number for Covid-19 seems to be between two and three.

Typically, solutions of the model start with a very small number of cases relative to the size of the population. Then, very quickly, these accelerate dramatically.

Imagine a city of one million. People are only infectious for one day and infect two susceptibles. Someone catches the disease. There are only 128 cases at the end of the first week. But in less than three weeks, everyone will have had it.

Modern versions of the model look more closely at how people intermingle in reality, and use big data to map infection patterns. This is the basis for the search for so-called “super spreaders”.

In practice, predicting the course of any particular virus is a challenge. My sympathies lie with those who have this task. But a 100-year-old mathematical model tells us that the very large numbers we read about could easily become reality.

As published in City AM Wednesday 11th March 2020
Image: Monitoring Passengers by  China News Service via Wikimedia is licensed for use CC BY 3.0
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From A&E waiting times to the Windrush scandal, beware bureaucratic targets

From A&E waiting times to the Windrush scandal, beware bureaucratic targets

Last week, health secretary Matt Hancock signalled an important change of strategy.

Accident and Emergency Departments have a target that 95 per cent of patients should be admitted, transferred or discharged within four hours. Hancock suggested that the target will be scrapped. Instead, wait times will be determined by clinical need.

Cue predictable hyperbolic outrage. The president of the Royal College of Emergency Medicine, for example, claimed that this change would have a “near-catastrophic impact on patient safety”.

The NHS is not meeting the target by a long chalk. In December, the actual figure assessed within four hours slipped to under 70 per cent.

A key reason seems to be increased demand for A&E services. Since the Conservatives came to power in 2010, admissions have increased by almost 25 per cent.

It is inherently implausible to imagine that cases of genuine emergencies have risen by this amount. Road casualties, for example, far from increasing, have actually fallen by 24 per cent since 2010.

There is much anecdotal evidence to suggest that people are bypassing GP surgeries and turning up at A&E with trivial complaints. Perhaps GPs are so oversubscribed that people who cannot get appointments go to hospital instead, or maybe limited out-of-hours care means that patients feel they have little choice if they fall ill at weekends.

But regardless, the lengthening waits indicate excess demand for A&E care.  Some form of rationing is necessary to allocate resources and to decide who gets treated.

There are two ways to ration. One is by price — whoever is willing to pay the most gets dealt with first. The other is by queue.

Even the most hardline free marketeer would surely balk at the idea of making people involved in genuine accidents wave their credit cards. So queue it has to be. And in such circumstances, it is entirely appropriate that decisions on who to treat first should be made on clinical grounds rather than a purely arbitrary target on the length of wait.

This controversy demonstrates the wider problem with setting targets: sooner or later (and usually sooner), people work out how to game them.

In A&E departments, once a patient has waited more than four hours, they have zero priority. The hospital incurs no more downsides if the wait is 14 hours rather than four hours plus a single minute.

We see this in other sectors too. Schools can, for example, meet exam targets by getting rid of weaker students — hardly what the target was designed to achieve.

And the Windrush scandal had its origins in the Home Office targets for the numbers to be deported. Officials could have tried to track down members of eastern European criminal gangs. Instead, they focused on the seemingly easier task of deporting elderly people who had lived in Britain for decades. They worked out how to meet the targets by minimising their effort.

Examples of gaming the system proliferate. Hancock is to be applauded for taking the first step to dismantle the culture of bureaucratic, counter-productive targets.

As published in City AM Wednesday 22th January 2020
Image: Ambulances outside A&E Department by D-G-Seamon via Wikimedia licensed for use CC BY-SA 2.0
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Tragedy awaits if we don’t bridge the gap between beliefs and reality in the NHS

Tragedy awaits if we don’t bridge the gap between beliefs and reality in the NHS

A tragic story over the weekend revealed how a man who died of lung cancer was failed abysmally by the NHS.

Two separate sets of doctors omitted to tell him for over a year that he had the disease.

The added poignancy of the news item was that the victim was a relative of Nye Bevan, the Welsh socialist politician who founded the NHS in the late 1940s.

Almost everyone has an account of how either they or someone well-known to them has been let down by the NHS.

On a mundane level, a few years ago I had an accident which involved knee surgery, so I was on crutches for a few weeks. I had been waiting for months for a minor operation on my hand. By coincidence the date was fixed while I was on crutches.

The mere fact that I could not attend meant I went to the back of the queue. In vain, I pointed out that I had just had a knee operation at the same hospital and needed hands for the crutches. It was many weeks later I discovered that the knee and hand consultants had offices literally next door to each other. But their staff were somehow unable to communicate.

The evidence of poor performance by the NHS is not just based on casual empiricism and anecdote. In terms of survival from lung cancer, for example, a major study by the Swedish Institute for Health Economics shows that only one country in the EU has a worse record than the UK: Bulgaria.

Cancer survival rates are improving everywhere, but the UK lags behind. Five-year survival from colon cancer, for example, averages 58 per cent across the EU. It is 52 per cent in the UK.

Bevan was a great believer in Soviet-style central planning, so it was natural for him to set the NHS up on these lines. Significantly, no other developed country has chosen to design their own health service in a centrally-planned way.

Despite the widespread knowledge of the failings of the NHS, it continues to attract strong emotional support across the electorate and defensiveness whenever anyone tentatively suggests reforming it. Witness the frenzied rage which greeted the US ambassador’s remarks earlier this month that America would want access to the NHS in any post-Brexit trade deal.

This dissonance between beliefs and reality is an example of an important challenge to the rational choice theory of economics.

As published in City AM Wednesday 26th June 2019
Image: NHS by Gordon Joly via  Flickr licensed under CC BY-2.0
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Believe it or not, Britain is getting happier

Believe it or not, Britain is getting happier

The dominant economic narrative in the UK is a pretty gloomy one just now.

True, employment is at a record high. But, counter the whingers and whiners, zero hours contracts and low pay proliferate.

The political discourse is full of the struggles of the JAMs – the Just About Managing The public sector moans about its pay. During the election, Labour played ruthlessly on the fears and anxieties of the elderly about inheritance and the value of pensions.

All in all, the picture seems bleak. But a much more positive vision is given by the Office for National Statistics (ONS) in its measure of well-being.

The Measuring National Well-being (MNW) programme was established in November 2010 under David Cameron. It is not without its critics. But if we take it at face value, compared to a year ago the country is definitely happier.

As the ONS puts it: “the latest update provides a broadly positive picture of life in the UK, with the majority of indicators either improving or staying the same over the one year period”.

There seems to be a bit of a glitch. The ONS boasts of using no fewer than 43 separate indicators to measure well-being. But they go on to state, in the very same sentence, that of these 43 measures, “15 improved, 18 stayed the same and two deteriorated, compared with one year earlier”. Perhaps the relevant statistician here received his or her basic training at the Diane Abbott School of Arithmetic.

No matter, it could be that some of the series have simply not been updated at all. Certainly, many people might not be too concerned to learn that “on environmental sustainability, the proportion of waste from households that was recycled fell over a one-year period, while remaining unchanged over the three-year period”.

But compared to a year previously, on some key indicators, as a nation we were more satisfied with our jobs, felt our health was better, and enjoyed our leisure time more.

This does not fit readily with political discussion recently in the mainstream media.

One possible reason is that many of the ONS measures rely on conventional survey techniques. These can take some time to carry out. So the ONS only release new data every six months, and the latest one was in April. The indicators could just be out of date.

However, a very similar story is told by a real-time analysis of Twitter data, which I have been carrying out with my UCL colleague Rickard Nyman since June 2016 (admittedly just for the London area).

We use advanced machine learning algorithms which essentially measure the sentiment level of a tweet as a whole, rather than relying on the now obsolete approach of looking for specific positive and negative words.

Sentiment in London started to rise quite sharply last autumn, dipped down slightly in April and May, but is now back up again.

Many conventional economic statistics are not really designed for the modern economy. So, despite, all its faults, the ONS well-being measure may be a step in the right direction, and regardless of what the media tells you, Britain may indeed be getting happier.

As published in City AM Wednesday 19th July 2017

Image: Happiness by Geralt is licensed under CC by 2.0
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