The problem
The World is confronted with a highly infectious disease, Coronavirus, which, thanks to the dreadful animal welfare standards prevailing in China, has jumped the species barrier to human beings. Consequently humanity has no immunity to this disease as the disease has evolved in animals not humans. Moreover, there is no vaccine for this disease and nor is there a serum or any proven curative therapy for it. The disease causes death in a minority of cases, although an accurate mortality is not known. However the mortality is observed to be a strong function of age, with almost no deaths recorded at all for babies, infants or small children but deadly for the elderly, with a mortality which increases progressively from low levels in adolescents and younger adults, higher levels in people over 40 and mortality rates possibly as high as 10% in people over 70. Overall mortalityrates of 1% have been cited.
How the World has responded
With a very few exceptions, governments across the World including the British government, have responded in the same way: lockdowns. The reader can surely appreciate the massive downsides to lockdown: mass house arrest, thousands of businesses put at risk, the finances of families and the state put at risk, damage to the education of millions of schoolchildren, and this list does not include the health downsides like suspended cancer treatments.
The British response
The British government has to its credit more than doubled the Country’s ICU capacity and is on course to double it again. The UK began with only 4,000 ventilators, we now have 10,000 and are producing a thousand per week. I commend the government’s decision to ramp-up British production of ventilators and of vital PPE. I also commend the government’s Nightingale hospital program, which is an outstanding success. The government can perhaps justifiably claim that the British lockdown was necessary to build British ICU and PPE capacity by slowing down the pandemic whilst these resources were built up.
Nevertheless, the reality must be faced that we cannot stay in lockdown indefinitely. We do need an exit plan from the lockdown, and fast. This Blog addresses this vital question. Before tacking the exit plan, it is worth examining the situation of Coronavirus in the UK.
The disease in the UK
Until very recently the UK had performed relatively few tests, around 2,000 per million, compared with five times this number in Germany, and with Switzerland managing nearly 20,000 tests per million. So the picture given by the record of cases in the UK is very misleading because so few tests have been carried-out. Consider that recorded deaths are currently running at around 800 per day, which implies that in a single day some 80,000 people must have become infected if one assumes the 1% mortality. Now the total number of recorded cases in the UK is 65,000 (on 9th April) i.e. less than the probable number of infections in one single day some 2 to 3 weeks ago. And this conclusion is reached using the relatively high 1% mortality number, which is around ten times the 0.1% mortality that is generally accepted for influenza.
Therefore last Friday I carried-out a calculation (click on Coronavirus Calculation below) to determine the spread of the infection in the UK – the calculation text was updated today to correct an error of terminology. The calculation assumes that mortality is constant, which has the useful corollary that the fractional growth rate for deaths and cases are the same. Now the deaths data, unlike the cases data, is complete, allowing direct calculation of this fractional growth rate: k in the calculation below (this is the constant in equation 4 in the calculation: Number Infected = exp(k x time)). The first reported case in the UK was 1st February 2020, but the media has reported people returning from Italy and Northern Italy two weeks earlier with strong Coronavirus symptoms. I therefore assumed the infection began on 14th January with one person. Having already calculated the fractional growth rate k, this allowed direct calculation of the number of cases on any given day, and hence the mortality, as the ratio of deaths to cases. To do the mortality calculation I assumed that victims died two weeks after becoming infected.
The results are:-
Mortality = 0.29%
Number of cases* in UK as of 3rd April 2020 = 24.4 million
*This is all infections, and therefore includes people who have recovered and are no longer infected.
k = 0.213 per day
Yesterday the Daily Telegraph reported on a study by the German government where a single town was studied and tested in depth. The conclusion of the study was a mortality of 0.37%, quite close to the 0.29% number I calculated last week from a completely different data-set.
In the last week the value of k has, by my calculation, fallen to around 0.12 per day. Using this value, and taking 24.4 million as the number of cases last Friday, I find that the number of cases today in the UK is:
Number of cases as of 10th April 2020 = 24.4 million x exp(0.12 x 7)
Number of cases as of 10th April 2020 = 56.5 million
If the above is correct then the UK, with a population of 66 million, has already acquired herd immunity, and in plain English, the general lockdown is no longer needed. The afore-mentioned German study reaches a similar conclusion.
Conclusions and Recommendations
- To anybody reading this blog I recommend fully complying with the letter and spirit of the Government’s general lockdown, until such time as this lockdown is lifted. This blog and its attendant calculations is arguing that most people in the UK have or already have had Coronavirus. But this is a hypothesis not a fact. In crisis situations it is very important that people are disciplined and act in a co-ordinated way. Obedience to government directives is therefore vital to avoid chaos.
- The government must level with the British People. Most British people are going to get coronavirus, and it is likely that most people already have. Taking the 0.29% mortality this means that around 100,000 people or more may well be taken away by the virus. I cannot see any other possible outcome given that the virus is so infectious and there is no vaccine or curative therapy. Obviously I hope that I am wrong, but even if the 0.1% mortality number for influenza is used then the total death toll is likely to exceed 30,000 people in the UK.
- The general lockdown must be brought to an end before the end of this month (April 2020). The government needs to move the national conversation away from stay at home. It is simply not possible for the Country to hide from the virus in our dwellings indefinitely, especially as the lockdown may well be becoming futile right now.
- The government must publish the disease progression modelling so that it can be scrutinized. It is very disturbing that it has not already done so.
- Whereas the general lockdown must be swiftly ended, there is a strong case for a selective lockdown based on age and health complications, as it is an established fact that the elderly and infirm are especially vulnerable to coronavirus. Now the elderly and infirm are not usually economically active. So the British economy can be fully restarted and rebooted whilst protecting the most vulnerable. A lockdown of the elderly and infirm is manageable over much longer timescales, and could be used to protect this section of the population whilst vaccines and curative therapies are developed.
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I fully believe this. I had mild symptoms at the start of March (2nd of March), which included a burning sensation in my sinus, blocked nose, general feeling of unwellness (malaise), slight weakness and some muscle aches in my lower back.
I have determined that along with this data, my suspicions were true that I was infected with COVID-19 and as with so many millions of cases, I only experienced very very mild symptoms that lasted 5-6 days maximum.
My job involves being in large crowds of people without divulging too much information, and 1 week prior to my infection I was within huge crowds.
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A good article which contains (IMHO) a major flaw – it assumes that the spread of the disease is uniform throughout the country.
Anecdotal evidence (and some reading between the statistical lines) suggests this is far from the truth: Most of the infections are probably confined to hospitals and care homes where the death rate is very much higher than the figure for the general population.
If this is correct, it is quite plausible that most of those in hospitals and care homes have or have had the disease (and hence the death rate will shortly peak and then drop) but most who are secluded at home have not yet had it.
If that is the case, then we should expect another spike of deaths after lockdown ends. How big a spike? I don’t know, but if you have already counted most of those most at risk, then the death rate for the remaining population would be very much lower, so even if 50 million people are not yet infected, we should not expect 1% of these (500,000) to die.
I agree with the conclusion (that lockdown must end soon) but not for the reasoning given above.
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As at 18 April, 357,023 people have been tested in the UK of which 114,217 tested positive. You reckon that 56.5 million out of 66.5 million in the UK had Coronavirus as of 10 April (and presumably your latest figures would show an even higher figure). The people who have been tested are those most likely to have the virus (showing symptoms or working in high risk situations such as hospitals). I cannot see how 32% positive tests from a highly biased sample most likely to have the virus is possibly consistent with your reckoning that 85% have had the virus a week earlier. I would love to think your conclusions are correct but this comparison of your predictions and the facts suggests to me your modelling assumptions are incorrect and therefore your conclusions are incorrect.
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