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In virology they have a key figure which they call "R0" which is the number of people who each infected person infects. A common quoted figure for R0 was 2.6. This compares with what actually happened which is that in most countries the number of cases increased exponentially by about 10x in 6 to 9 days. From this we can work out the average time between someone getting infected and passing it on to those 2.6 people. 2.6^2.4 =10. Which means the average time for a 2.6x increase is the time for a 10x increase over 2.4. So the average time to pass it on is about 2.5 to 4 days. However, there is a problem with this figure. Because the average time for someone to start showing symptoms such as a cough is about 5 days. So for an R0 value of 2.6, people must be spreading the virus BEFORE they start to cough, which is one of the main ways to pass it on.
So, let's approach this the other way. We know it is increasing by 10x in about a week. We also know that symptoms first appear in 5 days and evidence suggest peak virus shedding (coughing) another 4 days on. So, peak infection is about 9 days after infection. Because the virus is spreading by 10x in a week, that means that R0 must be at least 9 and probably nearly 20, or 8x the figure that virologists believed it was.
At the simplest level the exponential growth can be modelled as N = exp(A . (d-d0)) When d0 is the day where N is 1 and d is the time (i.e. days) and A is a constant.
If we use a simple concept that people infect everyone on day d1, then we know that if the number they infect is R0 then, on day d1 the number of newi infections is:
N = R0
R0 = exp (A . d1-d0)
A = ln (R0) / (d1-d0)
If we take do as being "day 0" then this becomes simply:
A = ln (R0) / d1
Thus the rate of growth is set by two factors: R0 (the number each person infects) and d1 (the time for them to infect others).
We have data for the growth rate (about 10x in about a week). If we also know the average time to infect other people then we should be able to calculate R0. Symptoms appear on average on day 5 after infection. The peak infectivity is on day 4 after symptoms appear, so the time from infection to peak infection is 9 days.
For ease of calculation, let's say the rate of growth was 10x in nine days, then we know on day 9 (if day 0 has one case) that the number of total cases is 10. On day nine d1 = 9 and N = 10, so:
R0 = 10
But because we used a 10x increase in nine days rather than the more typical faster increase of 10x in a week, we can say that:
Why the difference - the tip of the iceberg
CV19, whilst caused by one virus, has behaved in extremely different ways in extremely different people. In the vast majority of people, at least 90% but perhaps as high as 98%, the virus has been so mild that most people didn't think it any different from a normal cough. These people did not feel very ill and kept on with their normal lives. But in a small group (2-10%), the virus was severe enough that they sought medical attention. Amongst this group, the tip of the iceberg, the virus behaved in a very different way, causing them to feel very unwell with a high number (of this small group) going into hospital and a substantial number of those going into hospital ending in Intensive care (about 20%) and a large number of those dying. These are the group the medics saw. The differene is that in this group, despite it being just as contagious as the rest, because they felt very ill they stopped their normal lives and to some extent isolated. This, I think, is why the virologists got the R0 value so terribly wrong. The group the medics saw, had a low R0, because they stopped their normal lives so the R0 value was about 2.6. But the vast bulk of those with the virus, so the vast bulk of the spreading was amongst those who continued their normal lives who had an R0 value over 10.
Timing of the epidemic
Early on we were being told that the virus would not sprad quickly. A peak in 3 to 4 months was being suggested and that different parts of the UK would have peaks at up to a month apart. That was totally at odds with the evidence that showed the virus was going to peak in about 1-2months and that there was less than a day difference between Scotland and the rest of the UK. Clearly the models were dependent not only on a very low R0 of 2.6, but there must also have been a presumption that there was over a week delay beween infection on one person and the next. This explains why several times the UK PM gave a figure of "doubling in a week", when the evidence showed about 10x in a week. It also explains the initial slow response.
Severity of the epidemic
Bizarrely as it may seem, the higher the R0 value, the less concerned we should be about the epidemic. Because a very high R0 value is symptomatic of a very mild disease, whereas diseases that tend to have very bad outcome, tend to have a low R0 because both the patient and the society around them, tends to take very strong measures to contain the outbreak. This all adds to the growing evidence that the Infection Fatality Rate (the number of those infected who die) is around 0.15%. Of these around 90% are over 50. So, for the majority of young people the IFR is around 0.015% or 1 death in 7000 infections. This is about the same as an under 50s yearly risk of dying from a road accident.
Ending the epidemic
If on average each person who gets the virus passes it on to less than 1 person (i.e. many do not pass it on to anyone), then the number of people with the virus will decrease, until (it is hoped) that after a long enough time there is only one person with the virus and they happen to be one who doesn't pass it on and then no one has the virus.
That strategy seems realistic if the R0 valuei is 2.6. Because, to put it simply, if instead of meeting 100 people a week, we drop the number of people we get close enough to infect to less than 38 people a week, then as there are <1/2.6 fewer oportunities to infect peple the R0 value should drop below 1. So, modest social distancing could kill off the virus.
But if the R0 value is 10, then instead of cutting our social interactions from 100 to 38, we need to cut them from 100 to 10. But that only reduces the R0 value to 1. We actually need it to be less than 1, so the real cut is from 100 per week to perhaps 5x a week. Given the number of people we come into contact just supermarket shopping, let alone if we are a nurse or a bus driver, this reduction is very extreme social distancing which would be extremely difficult to enforce.But worse, even if R0 falls to 0.5, if we start with 16,000 cases, the time to get to one case is 14 x 9 days (18 weeks). There are very likely more than 16,000 cases, so, we require almost the total shut down of society for much of the year. There is no way on earth that is feasible, for the simple reason that we'da all starve or if we didn't the economy would be so wrecked the miniscule numbers of deaths from the virus would be far far outstripped by the horrendous death toll from the economic collapse (when e.g. we couldn't afford the NHS).
That means anyone trying to end the epidemic by "social distancing" is wasting theirs and our time and our money. The only way this virus is going to end, given the earliest anyone is talking about a vaccine is September, long after the virus will have peaked, is for the majority of us to get "herd immunity". And, to make it worse, if the R0 value is 10, that requires an infection rate of about >90%. As half the deaths occur in over 70s who are 10% of the population, on the face of it, that suggest we could protect all this group, but only if everyone else has got immunity. Realistically not everyone will get the virus which means that some over 70s will have to have had it to get herd immunity. On the good side, the rate of death even in this group is less than we thought earier on. But it is still quite horrendous as the deaths in care homes amongst the most vulnerable elderly have shown.
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It is a simple fact that from the start, if like Sweden (link) we had protected the old and vulnerable then, then even under the worst case scenario, under 50s households could have continued with their normal life with minimum impact on the NHS which could have coped even without the additional resourcese that were made availabe. But recently more and more evidence has been coming out (link)(link)(link) that we have massively over estimated the impact of CV19 because of the very high number of people who get it without serious symptoms, leading us to believe the total number of deaths would be about 5x the actual number. This now means that the NHS could have just coped if we had only strictly isolated those over 70 and the vulnerable.
Please sign the petitions to support this plan:
UK gov (still to be approved)
For further discussion on the underestimation of R0 see: "The Failure of R0"
The problem in the UK is that we allowed the virus to spread to older people who are far more likely to end up in hospital and as a result we risked crashing the NHS. To understand this, here is a graph showing the number of deaths by age in Italy (yellow) as well as China (red).
It is very clear that in both countries the vast majority of deaths occurred in those over 60 and the level of deaths in under 40s is so small it cannot be destinguished from zero. If then we use this to estimate the effect on the health service it produces a graph as follows:
The dotted blue line shows the fraction of the population up to the specified age. The red line shows the estimated demand from CV19 of everyone up to that age. So for example 70% of the population are under 50 but that 70% create only about 10% of the demand on the NHS. In contrast, over 70s are about 10% of the population but create 50% of the demand.
What that means, is that if we could have totally isolated the over 70s, the demand would halve. Or to put it another way, we could have got through the crisis in half the time. If we could isolate everyone over 50, we could have got through the crisis in a tenth of the time - or without any longdown. Below is a curve estimatng hospital beds and intensive care beds required just for the under 50s.
The red line represents the total beds available before the crisis. As we can see the demand on NHS beds is minimal, and although a lot of Intensive care beds might be needed, the NHS could easily cope if only under 50s were exposed to CV19.
So, can we release under 50s now? The answer I believe is yes (if we stop under 50s households infecting older people) for the following reasons:
- The NHS could cope with under 50s if at the same time we have a very tight lock down of other age groups.
- Many younger people have already had the virus, the impact on the NHS is now even less
- The virus is known to predominantly affect people with underlying conditions. As such if we protect these individuals in the under 50s group, then the problems will be much less
- Even if the government told everyone that they could immediately return to normal, many people are now so scared of CV19 that they will not return to normal life.
Households versus Individuals
An important caveat, is that whilst the analysis is for individuals, we live as households and so that plan for coming out of lockdown most fit the way we live. Fortunately, the nature human fertility and human nature, means that most people with school age children are under 50 except for a few in senior schools and men who married much younger women. Likewise, single adults either tend to be living on their own or with similar aged adults (except in special circumstances like prisons). So, for most reasable purposes "families with school age children" are under 50. But to be sure we could say that "families with young children where no resident is over 50 and under 50s living on their own on where there are no over 50s" can return to normal life ... with the proviso that "normal" cannot include mixing with over 50s or those from households with over 50s.
Whilst there is no problem under 50s returning to normal life, things get more complex the older we get becaue the death rate is about 10x the average for under 50s for 50-60 year olds approaching 100x for the most elderly. Fortunately, the number of very elderly people is relatively small, with 10% over70. The very elderly and those of other age groups who are most vulnerable to CV19 should be protected from the virus. To this end, they should be given all the necessary PPE and for example they must have priority for supermarket home delivery. The aim for them is to maintain a strict isolation until the virus has died out. At first this isolation must be compulsory, in order to permit younger people to pass through the epidemic without the beds being used by older people. But once younger people are through then we can advise older people to remain isolated, but they have a right to freedom.
So under 50s household return to normal life immediately. Over 70s are isoalted until it is safe. This leaves the 50-70s.
Because of their higher risk, and therefore higher risk of inundating the health service there may have to restrictions for this group for a short time. But after that we need people to decide which group they belong to. Whether they join normal society, albeit at the risk of contracting CV19, or whether they isolate until the virus dies out. What we cannot allow, is someone who has not had the virus to suddenly decide to re-enter society at the time the virus is dying out. Because if this happens in large numbers there could be another surge of infections, meaning that the over 70s may be in isolation for perhaps another month longer than need be. Nor can too many rejoin society if that risks over-whelming the health service. As such, we may have to stage the return of this group, but this will depend on what is happening in the NHS at the time.
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On Tuesday 17 March, Prime Minister Boris Johnson announced that anyone aged 70 and over in the UK must self-isolate at home from this weekend (21 March) for up to four months to prevent them from contracting the virus.