Until very recently, the US and UK governments were taking a relatively gentle approach to controlling the new coronavirus epidemic – compared with most other governments around the world. A very recent report from UK academics shows that the strategy would probably have led to a huge number of deaths — well over a million in the US. The report is based on a detailed model using information from many sources. This blog explains how the model works, what it finds and why it is likely those numbers changed US and UK government plans for the better. It also explains the Yo-Yo control strategy that the UK government has started to mention.

We know the new coronavirus, which causes the disease COVID-19, is going to kill a lot of people. Within the last week, academics at Imperial College, London University released a report that aims to put a number on the likely number of deaths in the UK and US. They looked at how effective different approaches are likely to be at controlling the virus. The model takes into account the capacity of the US & UK healthcare systems as well as what we know about the virus spreading. The US and UK governments had this report around a week before it was released.

• Do nothing
• “Flatten the curve” (minimal)
• Keep a lid on it
• Yo-yo control to give people a break

Here in the UK, the government was receiving a lot of criticism for its “laissez-faire” laid-back approach to managing the epidemic and many scientists were demanding the government release the model it claimed justified its approach. Curiously, at the same time the model emerged, the government seems to have radically shifted away from a relaxed approach to a more aggressive one. “A handbrake U-turn”, said one commentator. This shift might be because the new model shows just how many people would die if the governments carried on with its relaxed approach.

How the model works: virtual people in a virtual world

The authors took an existing model used to predict outbreaks of flu and tweaked it to model what is likely to happen with the new coronavirus. They used census and other data to create an artificial world that closely maps to Britain (and the US).

They created households with an age and size make-up based on census data. The authors created artificial networks of schools and workplaces based on the number of people in the households and on other information. Individuals were allocated to the schools and workplaces based on where people lived. So that’s the virtual world.

The coronavirus (called SARS-COV-2) is spread by infected people carrying the infection when they come into contact with other people. This can be within the household, at work or school, or randomly in the community. (The model assumes that the closer together people live in the community, the more readily the virus spreads.) The model predicts that roughly one-third of infections spread through each route:

• in households
• at school/work
• within the community

Assumptions used in the model

For any epidemic, the key number is R0 (R nought), the number of new people each person with the virus goes on to infect. This is the “natural” figure, without any control measures. The aim of all the actions we are now, such as washing hands and working from home, is to reduce R0.

Reducing R0 but keeping it above 1 will slow down the infection. Reducing R0 to under 1 will put the epidemic will go into reverse.

Detailed assumptions

• R0 = 2.4, based on early Wuhan data.
• Doubling time = 5 days. This is almost certainly an underestimate; most experts put it around 3, which means the epidemic will move faster, with more cases sooner than this model predicts.
• People with symptoms are more infectious than people carrying the virus but not showing symptoms.

To kick off the infection, the model was “seeded” with enough infected people to give the number of cumulative deaths seen in the GB or US by 14 March 2020.

The effect of infection on health:

• Overall, 0.9% of people with the virus will die.
• 4.4% of infections are hospitalised.
• 30% of hospitalised cases require intensive care.
• 50% of intensive care cases die.

Age plays a big role in this: younger people and children do much better than older people, and the model allows for this:

Do nothing scenario

The authors plugged these assumptions into their model and watched what happened. For simplicity, they first assumed that nobody would do anything to stop the spread of the virus, individuals or government.

Unsurprisingly, the results were awful, with a prediction that 81% of the GB and US populations would be infected over the course of the epidemic. The vast majority of people would get infected within the next 3-4 months.

For the GB, they predicted half a million deaths, and for the US it was over 1.2 million deaths from the virus.

However, these figures are way too optimistic because the model assumed that the health system has enough critical care beds (ICU) to cope. Yet at the peak, the model also predicts that only 1 in 30 people that a critical care bed would get one. So many more people would die than the forecast suggests.

Okay, that is the Do Nothing scenario – no government was doing it but it helps to explain the model and we can compare other approaches to it.

Mitigation scenario (“flatten the curve”)

Until very recently the UK & US governments were taking a much more relaxed approach to controlling the virus than most of the rest of the world. The UK government called this “flattening the curve”, simply slowing down the virus so that the health system could manage the cases. Most people would still catch the virus.

The idea is to get the pain over as quickly as possible so that people can get back to their lives and the economy will suffer as little damage as possible.

However, this new model makes it clear that with this approach many people would still die and the health system would still be overwhelmed. The situation would be the same for the US and UK alike.

The UK was considering five measures to control the epidemic, though not all are included in the “best” mitigation approach.

Control measures

The model then looks at the effect of 5 specific ways to cut down the spread of the virus, together with the assumed compliance rates:

Case isolation Anyone with symptoms isolates themselves at home for 7 days. 70% comply

Home quarantine If anyone in the household has symptoms, the whole household isolates for 14 days. 50% comply

Social distancing for those aged over 70 (and those with existing health conditions). 75% comply

Social distancing of the whole population. 100% comply: 75% reduction in community contacts, 25% increase in home contacts.

Closure of all schools and 75% of universities

Here is how mitigation plays out in the model. It isn’t pretty Note the red line at the bottom of the graph shows critical care bed capacity in the health system.

Let’s consider the strictest combination of controls that the authors modelled. This is household quarantine plus social distancing for the over 70 – but no quarantine for the whole population or closure of schools and universities. The model predicts 250,000 deaths.

However, just as for the “do nothing” scenario, this assumes that there are enough critical care beds – even though the model predicts there won’t be. So again, the actual number of deaths would be much higher.

I can only assume the authors made no attempt to model the real likely number of deaths simply to spare the government’s blushes.

So, mitigation or “flattening the curve” looks like a poor strategy.

Suppression strategy: “keep a lid on things until help arrives”

With suppression, the goal is to go further – controlling the epidemic, not just slowing it down. In the jargon, the aim is to reduce R0 to less than 1, pushing the epidemic into reverse.

Crucially, suppression aims to keep the number of infected cases who need intensive care beds below the available number of beds within the NHS and US healthcare systems. This, many more people will survive. And most people won’t get infected (which also means that they remain vulnerable).

There is an eyeful of graphs below, which I will then take time to explain.

Graph A, black line, shows the “do nothing” scenario, as before. But this time, more control measures are used, including school and university closure and social distancing for the entire population (orange and green lines). Although it doesn’t say so, the green line does seem to include household isolation/quarantine as well as case isolation (so if one person gets sick their whole household isolates). Graph B just zooms in on the lower portion of graph A.

Assuming an R0 = 2.4, deaths could be kept under 40,000, and under 10,000 if there is almost no let-up at all in of any of the measures. That is very different from the far more than 250,000 deaths predicted by the mitigation strategy.

The light blue shading indicates a period of five months when these control measures are in place. The right-hand side of the graph shows that when those control measures are released, there is a new and very large peak of infections.

In fact, the more successful the suppression in the first stage (green line more effective than the orange line), the bigger the subsequent peak when controls are released. This is because most of the population hasn’t been exposed to the virus, so as soon as controls are released a full-blown epidemic kicks off.

And what that means is that control measures need to be kept in place to keep a lid on things. The only time it will be safe to release the measures is when effective vaccines and/or treatments are ready.

Yo-yo control

Because these onerous control measures could be in place for two years, the authors have simulated a situation where population-wide social distancing and school/university closures are relaxed whenever there are enough critical care beds with the NHS. The idea is that giving people a break allows the control measures to stay in place over a much longer period of time.

See figure 4 below.

The study authors do stress that no one has ever tried this level of measures to control the population before – not for such a long time. How willing people will be to do to this is unknown. And for this reason the authors say there is no easy choice.

Though don’t forget that the authors admit they have underestimated the deaths from the mitigation strategy. That’s because there won’t be anything like enough intensive care beds available and so many more people would die than indicated by their estimate.

In the UK, the government insists it is simply doing the right thing at the right time – just as they always planned. All the same, a week ago what they were following looked a lot like a mitigation strategy. And seven days on, it looks a lot like a suppression strategy, including school closures.

Make up your own mind about motives – but what the UK and US are doing now looks a lot more like the approach in the rest of the world. But well behind the leading countries.